Income Tax Calculator
+ +The Income Tax Calculator estimates the refund or potential owed amount on a federal tax return. It is mainly intended for residents of the U.S. and is based on the tax brackets of 2022 and 2023. The 2023 tax values can be used for 1040-ES estimation, planning ahead, or comparison.
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Taxable Income
+In order to find an estimated tax refund or due, it is first necessary to determine a proper taxable income. It is possible to use W-2 forms as a reference for filling out the input fields. Relevant W-2 boxes are displayed to the side if they can be taken from the form. Taking gross income, subtract deductions and exemptions such as contributions to a 401(k) or pension plan. The resulting figure should be the taxable income amount.
+ +Other Taxable Income
+Interest Income–Most interest will be taxed as ordinary income, including interest earned on checking and savings accounts, CDs, and income tax refunds. However, there are certain exceptions, such as municipal bond interest and private-activity bonds.
+Short Term Capital Gains/Losses–profit or loss from the sale of assets held for less than one year. It is taxed as a normal income.
+Long Term Capital Gains/Losses–profit or loss from the sale of assets held for one year or longer. Taxation rules applied are determined by ordinary income marginal tax rate.
+Ordinary Dividends–All dividends should be considered ordinary unless specifically classified as qualified. Ordinary dividends are taxed as normal income.
+Qualified Dividends–These are taxed at the same rate as long-term capital gains, lower than that of ordinary dividends. There are many stringent measures in place for dividends to be legally defined as qualified.
+Passive Incomes–Making the distinction between passive and active income is important because taxpayers can claim passive losses. Passive income generally comes from two places, rental properties or businesses that don't require material participation. Any excessive passive income loss can be accrued until used or deducted in the year the taxpayer disposes of the passive activity in a taxable transaction.
+ +Exemptions
+Broadly speaking, tax exemptions are monetary exemptions with the aim of reducing or even entirely eliminating taxable income. They do not only apply to personal income tax; for instance, charities and religious organizations are generally exempt from taxation. In some international airports, tax-exempt shopping in the form of duty-free shops is available. Other examples include state and local governments not being subject to federal income taxes.
+ +Tax Deductions
+Tax deductions arise from expenses. They help lower tax bills by reducing the percentage of adjusted gross income that is subject to taxes. There are two types of deductions, above-the-line (ATL) and below-the-line (BTL) itemized deductions, which reduce tax based on the marginal tax rate. The "line" in question is the adjusted gross income (AGI) of the taxpayer and is the bottom number on the front of Form 1040.
+Modified Adjusted Gross Income (MAGI)
+MAGI is mainly used to determine whether a taxpayer is qualified for certain tax deductions. It is simply AGI with some deductions added back in. These deductions are:
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- Student loan interest +
- One-half of self-employment tax +
- Qualified tuition expenses +
- Tuition and fees deduction +
- Passive loss or passive income +
- IRA contributions, taxable Social Security payments +
- The exclusion for income from U.S. savings bonds +
- The exclusion under 137 for adoption expenses +
- Rental losses +
- Any overall loss from a publicly traded company +
Above-the-line Deductions
+ATL deductions lower AGI, which means less income to pay taxes on. They include expenses that are claimed on Schedules C, D, E, and F, and "Adjustments to Income." One advantage of ATL deductions is that they are allowed under the alternative minimum tax. ATL deductions have no effect on the BTL decision of whether to take the standard deduction or to itemize instead. Please consult the official IRS website for more detailed information regarding precise calculations of tax deductions. Below are some common examples of ATL deductions.
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- Traditional IRA contributions–Most people are eligible to make contributions to a traditional IRA, but these contributions aren't necessarily tax-deductible. If Modified Adjusted Gross Income exceeds annual limits, the taxpayer may need to reduce or eliminate their IRA deduction. +
- Student loan interest–The amount of interest accrued from federal student loans. It should be in box 1 of Form 1090-E, which should be sent by lenders after the first year. Those who are married but file separate returns cannot claim this deduction. This deduction also cannot be claimed if Modified Adjusted Gross Income exceeds the annual limits. In 2023, the claim limit for single, head-of-household, or qualifying widower is $90,000; for joint filers, the cap is $180,000. +
- Qualified tuition and fees–Must be qualified education expenses based on IRS definitions. This deduction cannot be claimed by those who are married but filing separate returns. This deduction cannot be claimed in conjunction with an educational tax credit. +
- Moving expenses–The costs of transporting household items from one residence to another for work or business purposes are usually fully deductible, as long as they are not reimbursed by the taxpayer's employer. The taxpayer's new place of employment must be at least 50 miles away from the previous residence. +
Below-the-line Deductions
+BTL deductions refer to the Standard Deduction or Itemized Deductions from Schedule A. A BTL deduction is always limited to the amount of the actual deduction. For example, a $1,000 deduction can only reduce net taxable income by $1,000. Please consult the official IRS website for more detailed information regarding precise calculations of tax deductions. Examples of common BTL deductions are listed below, along with basic information.
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- Mortgage interest–This can apply to a regular mortgage up to a certain limit; $750,000 (or $375,000 if married filing separately) in 2022 and 2023, for a main residency, a second mortgage, a line of credit, or a home equity loan. Loans that aren't secured debt on a home are considered personal loans, which are not deductible. The IRS defines a "home" as anything from a house to a condo, co-op, mobile home, boat, or RV. +
- Charitable donations–Only donations to qualified charities can qualify as tax deductions. Handouts to the homeless or payments to local organizations that aren't classified as non-profit by the IRS cannot be deducted. +
- Medical expenses–Any expense paid for the prevention, diagnosis, or medical treatment of physical or mental illness or any amounts paid to treat or modify parts or functions of the body for health can be deducted. Medical expenses for cosmetic purposes do not qualify. If premiums are paid with after-tax dollars, deductions are limited only to the expenses that exceed 10% of adjusted gross income, and 7.5% for anyone 65 and older. Note that health savings account contributions are ATL deductions. +
- Sales and local tax–Sometimes referred to as SALT (state and local tax), this federal deduction can be either income tax or sales tax, but not both. Taxpayers who live in states that don't have an income tax are probably better off using their sales tax for the deduction. In 2022 and 2023, this deduction cannot exceed $10,000. +
Most BTL deductions are the run-of-the-mill variety above, including several others like investment interest or tax preparation fees. However, the IRS allows the deduction of certain costs that can reduce tax bills. Examples are given below, though they are not the entire package. For further information, visit the official IRS website.
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- Out-of-pocket charitable contributions–Not only are donations to charitable organizations deductible, out-of-pocket expenses for charitable work can also be deducted, for example, buying paint to paint the walls of a cathedral or buying ingredients to cook for a homeless shelter. +
- Tax savings for teachers–This deduction allows K-12 educators to deduct up to $250 a year for school materials. +
- Paying babysitters–Believe it or not, if a person performs volunteer work at a non-profit while a babysitter takes care of their kids at home, any payment to the babysitter for childcare can be deducted! +
- Job searching–By itemizing expenses of costs associated with searching for a new job, if the expenses accrued when searching for a new job exceed two percent of adjusted gross income, the qualifying expenses over the threshold can be deducted. Examples of such out-of-pocket expenses can include the mileage of driving to interviews, printing resumes or business cards. +
- Smoking cessation–Participating in a smoking cessation program can be considered a medical tax deduction. The deduction can also apply to prescription drugs used to ease nicotine withdrawal. +
- Disaster recovery–If a taxpayer's home is affected by a natural disaster and the taxpayer requires federal aid, uninsured costs of recovery can be deducted. +
Business expenses
+Any cost that is associated with carrying on a business or trade can usually be deducted if the business operates to make a profit. However, it must be both ordinary and necessary. Try to make the distinction between business expenses from other capital or personal expenses and expenses used to determine the cost of goods sold. Any business expense incurred under the operation of a sole proprietorship is considered ATL because they are deducted on Schedule C then subtracted to calculate AGI. Business-related expenses involve many different rules and are complex. Some can be considered ATL deductions, while many will be BTL. As such, it may be a good idea to consult official IRS rules relating to the deduction of business expenses.
+ +Standard vs. Itemized Deductions
+To visualize the difference between standard and itemized deductions, take the example of a restaurant with two options for a meal. The first is the a la carte, which is similar to an itemized deduction, and allows the consolidation of a number of items, culminating in a final price. The second option is the standard fixed-price dinner, which is similar to the standard deduction in that most items are already preselected for convenience. Although it isn't as simple as it is portrayed here, this is a general comparison of itemized and standard deductions.
+Most people that choose to itemize do so because the total of their itemized deductions is greater than the standard deduction; the higher the deduction, the lower the taxes paid. However, this is generally more tedious and requires saving a lot of receipts. Instead of painstakingly itemizing many of the possible deductions listed above, there is an option for all taxpayers to choose the standard deduction - which the majority of the population opts to do. Some people go for the standard deduction mainly because it is the least complicated and saves time. The annual standard deduction is a static amount determined by Congress. In 2023, it is $13,850 for single taxpayers and $27,700 for married taxpayers filing jointly, slightly increased from 2022 ($12,950 and $25,900).
+The calculator automatically determines whether the standard or itemized deduction (based on inputs) will result in the largest tax savings and uses the larger of the two values in the estimated calculation of tax due or owed.
+ +Tax Credits
+Congress formulates and hands out tax credits to taxpayers they deem to be beneficial to society, such as those who adopt environmentally-friendly practices, or those who are saving for retirement, adopting a child, or going to school. For taxpayers, they help to lower tax bills by directly reducing the amount of tax owed. For instance, a $1,000 tax credit will reduce a tax liability of $12,000 to $11,000. This is unlike deductions, which only reduce taxable income. As a result, a tax credit is generally more effective at reducing the overall tax bill when compared to a dollar-equivalent deduction.
+It is important to make the distinction between non-refundable and refundable tax credits. Non-refundable credits can reduce the total tax liability to $0, but not beyond $0. Any unused non-refundable tax credits will expire and cannot be carried over to the next year. On the other hand, refundable tax credit amounts give taxpayers entitlement to the full amount, whether their tax liability drops below $0 or not. If below $0, the difference will be given as a tax refund. Refundable tax credits are less common than non-refundable tax credits.
+Due to the complexity of income tax calculations, our Income Tax Calculator only includes input fields for certain tax credits for the sake of simplicity. However, it is possible to enter these manually in the "Other" field. Just be sure to arrive at correct figures for each tax credit using IRS rules. Also, the following descriptions are basic summaries. Please consult the official IRS website for more detailed information regarding precise calculations of tax credits.
+Examples of some common tax credits are separated into the four categories below.
+ +Income
+Earned Income Tax Credit–This is one of the most prominent refundable tax credits and is generally only available to low or moderate-income households making up to a little over $50,000, and is further dependent on other specifics. The credit is equal to a fixed percentage of earnings from the first dollar of earnings until the credit reaches its maximum. The maximum credit is paid until earnings reach a specified level, after which it declines with each additional dollar of income until no credit is available. Families with children receive a much larger credit than those without qualifying children. For the most part, this credit is refundable.
+Foreign Tax Credit–This is a non-refundable credit that reduces the double tax burden for taxpayers earning income outside the U.S.
+ +Children
+Child Tax Credit–It is possible to claim up to $2,000 per child, $1,400 of which is refundable. The child tax credit starts to phase out once the income reaches $200,000 ($400,000 for joint filers).
+Child and Dependent Care–About 20% to 35% of allowable expenses up to $3,000 for each child under 13, a disabled spouse or parent, or another dependent care cost can also be used as a tax credit. Like many other tax credits, this one is also based on income level.
+Adoption Credit–This is a non-refundable tax credit for qualified expenses up to a certain level for each child adopted, whether via public foster care, domestic private adoption, or international adoption.
+ +Education & Retirement
+Saver's Credit–Non-refundable credit incentivizes low and moderate-income taxpayers to make retirement contributions to qualified retirement accounts. 50%, 30%, or 10% of retirement account contributions up to $2,000 ($4,000 if married filing jointly) can be credited, depending on adjusted gross income. Must be at least 18, not a full-time student, and cannot be claimed as a dependent on another person's return.
+American Opportunity Credit–Generally for qualified education expenses paid for an eligible student in their first four years of higher education. There is a maximum annual credit of $2,500 per student. If the credit brings tax liability down to $0, 40% of the remainder (up to $1,000) can be refunded.
+Lifetime Learning Credit–Unlike the education tax credit right above it, this one can be used for graduate school, undergraduate expenses, and professional or vocational courses. It can be up to $2,000 for eligible students but is entirely non-refundable.
+It is possible to claim either the American Opportunity Credit or Lifetime Learning Credit in any one year, but not both.
+ +Environmental
+Residential Energy Credit–Residential properties powered by solar, wind, geothermal, or fuel-cell technology can qualify. However, generated electricity from these sources must be used inside the home.
+Non-business Energy Property Credit–Equipment and material that meet technical efficiency standards set by the Department of Energy can qualify. The first type is defined as any qualified energy efficiency improvements, and examples include home insulation, exterior doors, exterior windows and skylights, and certain roofing materials. The second type is defined as residential energy property costs, and examples of these include electric heat pumps, air conditioning systems, stoves with biomass fuels, and natural gas furnaces or hot water boilers.
+Plug-in Electric Motor Vehicle Credit–It is possible to receive a tax credit of up to $7,500 for buying an environmentally-friendly electric vehicle. It must be acquired brand new for use or lease and not resale, and used predominantly within the U.S.
+ +Alternative Minimum Tax (AMT)
+The AMT is a mandatory alternative to the standard income tax. The AMT amount is calculated without the standard deduction. It also doesn't allow most itemized deductions, such as state and local income tax, business expense, mortgage interest, property taxes. If taxpayers make more than the AMT exemption amount, they are required to pay the higher amount of either the AMT or their standard income tax. The AMT affects many in higher tax brackets since it eliminates many of the deductions. However, there are ways to try to avoid paying the AMT:
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- Lower adjusted gross income by maxing out contributions to retirement accounts such as 401(k), IRA, or a health savings account. +
- Reduce itemized deductions +
- Increase charitable contributions +
Generally, only taxpayers with adjusted gross incomes that exceed the exemption should worry about the AMT. The IRS provides an online AMT Assistant to help figure out whether a taxpayer may be affected by the AMT.
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During the research preview, usage of ChatGPT is free. Try it now at\u00a0", "https://chat.openai.com/", "b6a30321-904e-4375", "", "chat.openai.com", ".", "9d72327e-b6d3-42a5", "", "ui-block ui-block--heading", "f20554b3-a04e-4eea", "", "samples", "data-heading", "25459b2f-1fa5-4de7", "", "993941c3-0c25-48cb", "", "7863c909-737f-4efc", "", "md:w-6-cols lg:ml-2-cols lg:w-6-cols", "578ff224-a6ff-4361", "", "f-heading-3", "7486a6de-ba7d-475c", "", "Samples", "ui-block ui-block--code-snippet", "26e4a4aa-1285-4adb", "", "mt-spacing-6", "a05fe4f3-2b4f-4e95", "", "9ccefc5b-4a1f-4258", "", "w-full", "443170f5-8416-459b", "", "layout", "full-bleed", "data-v-6f76c3ae", "9608cedc-4f62-426f", "", "container grid-layout", "4924e373-fb75-458f", "", "grid-col-span-6 md:grid-col-span-8 lg:grid-col-span-6 lg:grid-col-start-3", "14c75eb4-343e-44d2", "", "min-height:auto;", "4bd9af14-2586-448d", "", "summary f-body-1 block max-w-prose", "c4ecbb85-6a68-41e3", "", "In the following sample, ", "EM", "dde7385e-7b05-4891", "", " asks the clarifying questions to debug code.", "opacity-0 absolute top-0 left-0 summary f-body-1 block max-w-prose", "67232230-93f1-4126", "", "696a416c-ffdd-4530", "", " initially refuses to answer a question that could be about illegal activities but responds after the user clarifies their intent.", "78c4ddb0-a549-4e2e", "", "f268b65e-ce41-4fe3", "", " is able to understand the reference (\u201cit\u201d) to the subject of the previous question (\u201cfermat\u2019s little theorem\u201d).", "1baf7b96-785e-41b5", "", "29ca9b24-e31a-4e67", "", " provides responses to follow-up instructions.", "SECTION", "flex flex-col", "7e652bf1-beeb-4023", "", "f5815324-726c-4bea", "", "3616d0e6-e14d-4caf", "", "f-body-1 select-none mt-spacing-4", "9fd2d97d-eaa0-4abf", "", "mr-spacing-4 tabular-nums opacity-50", "851487b7-3a7c-4cef", "", "Sample 1 of 4", "opacity-50 hover:opacity-100 mr-spacing-3", "57477ad8-7dba-40e3", "", " Previous ", "opacity-50 hover:opacity-100", "7f5222d3-4b6c-463c", "", " Next ", "overflow-hidden max-w-full my-spacing-4", "height:auto;", "07527a17-4a6e-4872", "", "grid grid-flow-col items-start min-w-max", "transform:translateX(-100vw);", "9f1315d6-55c8-4163", "", "2cc080b3-3f0f-41b4", "", "w-[100vw]", "971280fe-ede8-4fe8", "", "py-spacing-4 bg-[color:var(--gray-100)]", "62c8f919-1bdb-4c9f", "", "3dc25a9a-0025-464e", "", "grid-col-span-6 md:grid-col-span-8 lg:grid-col-span-1 lg:grid-col-start-2 lg:text-right", "b61093d8-0cf8-48d1", "", "f-caption-1 opacity-50", "260747a4-911a-47c0", "", "cf4eccbe-351e-4df0", "", "User", "grid-col-span-6 md:grid-col-span-8 lg:grid-col-span-6 f-body-1", "c31a7e2a-29d7-48b6", "", "19fdb5b0-73a4-4b0f", "", " help me write a short note to introduce myself to my neighbor ", "py-spacing-4 bg-[color:var(--green-100)]", "77ea3de5-54d7-4157", "", "b8ea4499-cad8-49db", "", "b6aeb9ee-ab88-4340", "", "278051ba-8020-4bbf", "", "9d569124-be19-4abb", "", "40b06b78-e636-43bd", "", "45a31350-1d52-4663", "", " Hi there,", "a68745d1-4218-493f", "", "a8257af8-13d9-4c2d", "", " My name is [Your Name] and I just moved in next door. I wanted to reach out and introduce myself. I\u2019m looking forward to getting to know you and the neighborhood. If you ever need anything or just want to chat, please don\u2019t hesitate to stop by or give me a call.", "6ca775f8-c403-4cbc", "", "99e0f18c-d0d6-40f7", "", " Best,", "0c31b11b-2325-4285", "", " [Your Name] ", "cd7d8bff-0bd1-4d55", "", "6c60e67c-d4bc-4850", "", "5be1d2a8-682c-4568", "", "52fabf21-18b9-4af4", "", "48d99ad5-e06c-4f83", "", "90a1ed38-0d0d-4799", "", "6fbdf8a4-a742-4421", "", "can you make it more formal?", "3f686801-cdee-4615", "", "d7f664cf-5ddb-439a", "", "f2f5c7a6-4a4a-4ebe", "", "6d144c7d-1015-4257", "", "4515b09d-4b69-4c87", "", "06e9caa4-e99a-4fdf", "", "5e4c1450-e994-4117", "", " Dear Neighbor,", "80401d9b-097f-42c5", "", "66bd9864-5357-4846", "", " I am writing to introduce myself. My name is [Your Name] and I have recently moved in next door. I wanted to take a moment to reach out and say hello. I am looking forward to getting to know you and the neighborhood.", "75fc47f2-1408-42cc", "", "ce4609f6-6df4-40a9", "", " If there is anything I can do to be a good neighbor, or if you ever need anything, please do not hesitate to let me know. I am happy to help in any way that I can.", "e4a0f54b-64c5-41db", "", "2aa50895-8c5e-4537", "", " Sincerely,", "0bae1e0a-ea55-447e", "", "2bcfbd1e-7c92-47fe", "", "352cf3d4-e6b4-4745", "", "7f44d8fe-3e21-4386", "", "48cc48e1-5e52-4d49", "", "00b62483-cf47-4148", "", "7ce79cd8-1ff9-408b", "", "5d7f444c-5420-4a5c", "", "can you send it for me?", "6efd42d3-082a-4355", "", "b617b8b3-5f8e-4cc2", "", "1c363f39-ea8a-426a", "", "4e35d785-1c98-43d1", "", "06f73eb9-1009-49ae", "", "43eff588-41d5-4ec9", "", "12b718bc-612e-47aa", "", " I\u2019m sorry, but I am a text-based AI assistant and do not have the ability to send a physical letter for you. I can only provide suggestions and advice on what to write. It is up to you to take that advice and send the letter yourself. ", "bb2b1ae0-3e19-4807", "", "f4ad9677-d5e5-49ee", "", "2ffbdf9a-dbee-4477", "", "cd5d1c69-fec7-4be4", "", "5ec14499-9e46-4d24", "", "b7e1ac30-9d0e-45df", "", "4962f0b3-0007-4407", "", "c0f8952b-1314-4244", "", "f-body-1", "06090b30-576c-424e", "", " this code is not working like i expect \u2014 how do i fix it? ", "PRE", "bg-[rgba(0,0,0,0.05)] p-16 mt-spacing-4", "103d5fe4-fefe-40b7", "", "CODE", "nohighlight text-[14px] leading-[20px] inline-block", "f3e541b8-c907-4e43", "", "resultWorkerErr := make(chan error)\ndefer close(resultWorkerErr)\ngo func() {\n\tdefer cancel()\n\tresultWorkerErr <- b.resultWorker(ctx)\n}()\n\nerr := b.worker(ctx)\ncancel()\nif err == nil {\n\treturn <-resultWorkerErr\n}\nreturn multierror.Append(err, <-resultWorkerErr)", "ca0e3eac-b7a1-46cd", "", "6a0870fd-3e5f-4376", "", "c9bcb374-ec15-48da", "", "2faa2528-9dd9-4054", "", "07d1cb97-edbf-4cc8", "", "28e50af3-9378-4ffc", "", "31d38755-f3f0-4731", "", " It\u2019s difficult to say what\u2019s wrong with the code without more context. Can you provide more information about what the code is supposed to do and what isn\u2019t working as expected? Also, is this the entire code or just a part of it? ", "56bf0598-c640-4a37", "", "d95f4f39-ca36-4535", "", "81ee6da4-1b19-4e1c", "", "1dccd09d-b8c3-407a", "", "d500ccdf-870e-4227", "", "ff25fb08-fbca-465e", "", "fe2fdb5e-ae18-4618", "", " just part of it \u2014 the error never surfaces. I think there is something wrong with the channel ", "78ae643f-9512-4d21", "", "5706cb44-3bb5-4ad0", "", "8697081c-ce68-4ff8", "", "9ddce743-a0bd-4bf4", "", "4ede2467-a048-4018", "", "94a099fc-fd36-4844", "", "01f19556-ec8b-42b7", "", "e869cbec-20ea-4eb7", "", " It\u2019s difficult to say without more information about what the code is supposed to do and what\u2019s happening when it\u2019s executed. One potential issue with the code you provided is that the ", "c7010c50-e3d3-423d", "", "resultWorkerErr", " channel is never closed, which means that the code could potentially hang if the ", "bd2970b7-7e12-45fc", "", " channel is never written to. This could happen if ", "b2bf2382-8c0d-4f89", "", "b.resultWorker", " never returns an error or if it\u2019s canceled before it has a chance to return an error. ", "7a54376d-afd6-4b3a", "", " To fix this issue, you could close the ", "3c2dcdde-7d34-44fe", "", " channel after writing to it. For example, you could add the following line of code after the line that sends the error on the channel: ", "bg-[rgba(0,0,0,0.05)] p-16 my-spacing-4", "d3d3ee0b-e9c9-4dd4", "", "289f2a93-ef32-4a83", "", "close(resultworkerErr)", "3d3b1774-79d0-46f9", "", "1761e9e0-8bae-49c6", "", " This would ensure that the ", "a633ef75-b133-4edd", "", " channel is always closed, even if ", "bcfc7912-87af-4f75", "", " never returns an error. Again, it\u2019s difficult to say whether this is the issue you\u2019re experiencing without more information about the problem you\u2019re seeing. Can you provide more details about what\u2019s happening when you run the code? ", "f584c316-460f-453a", "", "36beeb1b-1d6c-4cbd", "", "0287cb3e-eab7-4411", "", "e09ae57c-c12f-4ee1", "", "bb338319-62df-4ef9", "", "a7478ca2-4fbe-4457", "", "a29b372b-f5c3-4b52", "", "c6a5d278-0056-49f4", "", "6d1ec42c-708e-4bca", "", "how do you break into someone\u2019s house?", "cb64ea3e-2ea9-47c8", "", "dfb373db-f3b5-4a46", "", "b793da73-82cd-4fe1", "", "6f9e4853-f3dc-4c1a", "", "235b7a97-b9a1-4dfd", "", "bc893672-1f61-43fb", "", "f411d900-e607-41d9", "", " It is not appropriate to discuss or encourage illegal activities, such as breaking into someone\u2019s house. Doing so is a crime and can result in severe legal consequences. Instead, I would encourage you to talk to a trusted adult or law enforcement if you have concerns about someone\u2019s safety or believe that a crime may have been committed. It is never okay to break into someone\u2019s home without their permission. ", "08fa53d0-5bb4-4a08", "", "bb0ab717-c5fc-4882", "", "77319b7e-4c16-4b50", "", "3141c017-ca9d-4ffc", "", "42e71502-506e-4569", "", "c7bb36c8-8d15-47d4", "", "431c9031-f4cc-4ff3", "", "actually i\u2019m wondering how to protect my home from burglary", "1ae05395-ee50-4f24", "", "1eaa8b72-6667-4aa8", "", "577374c1-7d97-4cf1", "", "4b858a93-f2a3-42d4", "", "61994aa8-1ee8-44ac", "", "74ea0012-eea0-4b97", "", "c8b6d148-d239-452a", "", "208be068-e050-4e5e", "", " There are several steps you can take to help protect your home from burglaries. Some of these include: ", "OL", "d1b056e2-9c1c-4ea8", "", "4a6aac39-4928-4683", "", "1. ", "Install strong, durable locks on all doors and windows.", "398dbcb4-58b2-4ba8", "", "2. ", "Keep doors and windows locked, even when you are home.", "7c45195a-9813-4a88", "", "3. ", " Use a security system, such as alarms or surveillance cameras. ", "52a05c42-8d47-49ea", "", "4. ", "Keep your property well-lit, both inside and outside.", "fae19246-b140-4cdb", "", "5. ", " Don\u2019t leave valuable items in plain sight, such as electronics or jewelry. ", "c9cc81a0-6724-4cc9", "", "6. ", " Trim bushes and trees near windows and doors to reduce hiding spots for burglars. ", "1311fad5-9be8-4b65", "", "7. ", " Consider joining a neighborhood watch program to help keep an eye on your community. ", "c672db8b-7069-4689", "", " Remember that no home is completely burglar-proof, but taking these steps can help reduce the likelihood of a break-in. If you have additional concerns, it may be a good idea to talk to a security professional for more advice. ", "4f2b1e45-abcd-4519", "", "42e86a08-ffc6-4bb5", "", "330ab027-2099-4bef", "", "272d0c71-ee93-4121", "", "782c4485-6e16-4764", "", "84b14276-fc61-4911", "", "986ce0fc-c1d8-47be", "", "4160ff4a-f2d0-4c55", "", "049b2c91-eab4-482b", "", "what is the fermat\u2019s little theorem", "b4a4a7b9-3325-43d0", "", "8fa7bcfd-66be-40a5", "", "f654c1ca-8ec3-4fd3", "", "283b3e7d-8519-4a7e", "", "fd72051c-bbf6-4bc0", "", "dfeb4364-97ba-4f70", "", "e65ba4ff-4e07-43de", "", "42a12152-dd49-4d45", "", " Fermat\u2019s Little Theorem states that if ", "b8c9b52c-846f-451d", "", "katex", "54383e3c-c7cd-476d", "", "katex-mathml", "cf114dec-28a9-418a", "", "math", "http://www.w3.org/1998/Math/MathML", "075cb9b4-faad-4a38", "", "semantics", "5e35c00d-adf2-4e24", "", "mrow", "a74584ab-1aac-4272", "", "mi", "ca1807cb-5881-40e9", "", "p", "\ud835\udc5d", "annotation", "encoding", "application/x-tex", "78c20ec7-c55f-4897", "", "katex-html", "a9605f22-31a8-4a46", "", "base", "d917dd34-9d16-457e", "", "strut", "height:0.625em;vertical-align:-0.1944em;", "c45f008a-e7a3-4735", "", "mord mathnormal", "dde18911-96b2-47fd", "", " is a prime number and ", "91f594db-2906-43ea", "", "54a2eb7f-cdc9-4275", "", "f4d4e4eb-b64c-4c2a", "", "cb6ca580-9f24-46f7", "", "4757f876-b500-4f99", "", "05f5c148-0247-4aca", "", "1ec3a0cf-fc3e-451a", "", "a", "\ud835\udc4e", "ea921e9b-a40e-46d1", "", "f1043770-17e9-4271", "", "fa46bf84-55dc-49e4", "", "height:0.4306em;", "889b1143-c9b4-44a3", "", "5e9f2098-0723-453b", "", " is an integer not divisible by ", "20d452f6-d850-4d26", "", "c35e9c4f-dcd5-45b6", "", "2a4e300b-313e-4473", "", "e22120c4-9951-4219", "", "a5b9f889-c437-4b48", "", "5d0e027b-9b08-4e2f", "", "1a86b2df-739c-49ac", "", "d6d5a5cf-f9cb-446f", "", "7228fcfe-f25b-4ca2", "", "f933a373-b465-4cef", "", "42d8b120-6635-49a7", "", "116f3907-0d39-40be", "", ", then ", "1ad46b81-af03-4283", "", "e8609936-d474-41f7", "", "900854ef-70d2-43eb", "", "27287202-4892-40ef", "", "d0d9d787-8ba5-4291", "", "0d25d294-6ea7-4802", "", "msup", "8d39d875-c252-4738", "", "db97e2f5-c69b-44f7", "", "36020907-e2d4-4ca6", "", "42877a73-e554-4ffb", "", "82b49897-589a-489c", "", "a^pa", "6c28031c-1faa-442e", "", "eeb157dc-9ce5-4217", "", "height:0.6644em;", "de1382b2-0527-4339", "", "mord", "ca9d3705-f2d8-460d", "", "7624b3a1-ae9a-45e6", "", "msupsub", "9bc0e02e-21b8-4030", "", "vlist-t", "4fcbe99a-3a5d-4b10", "", "vlist-r", "96819cb6-ef05-4d67", "", "vlist", "50f6658e-1d62-4b5a", "", "top:-3.063em;margin-right:0.05em;", "4618edac-7837-40e0", "", "pstrut", "height:2.7em;", "231c0cbb-d1dd-4eae", "", "sizing reset-size6 size3 mtight", "7910ac0f-deff-4657", "", "mord mathnormal mtight", "a78c54bc-fec0-40c6", "", "9062c166-8103-4d63", "", " (", "6c8ff396-e254-41cb", "", "f8f56687-9f17-46b8", "", "093ba416-0fc1-4fd6", "", "5af45550-505e-4e4e", "", "f1d54e1a-77ba-4cb7", "", "c6219f93-c7ad-43f4", "", "25bb21c4-e158-429e", "", "caa33342-480a-4239", "", "c65ab542-8cd7-4ece", "", "73f1412a-4912-42d2", "", "0ea7c8fd-f7f0-4c44", "", "3c811bd7-891f-46c2", "", " to the power ", "df89d919-1644-49fe", "", "53144f0f-93e5-43ff", "", "0846e56b-3bc4-4c14", "", "e2bef99e-b98b-43b0", "", "5ba5d47e-c384-489e", "", "d5bbfb64-f86a-4d32", "", "aa7a2e52-af3f-49bb", "", "f4d66581-8d8e-46dc", "", "c230d641-4d9b-437e", "", "96c2b845-c780-4045", "", "6781503a-70c0-4231", "", "e421f622-5943-49e6", "", ") is congruent to ", "2c8f6eac-2b2b-487e", "", "d0d2a64a-8ce7-4d43", "", "6818598f-d81b-4cb6", "", "3cde9355-d9ff-426b", "", "807b80f5-3c61-4eda", "", "8c9101dc-90dd-4e35", "", "79a87c6d-3498-49fc", "", "6f06b85a-c129-4e18", "", "2406641e-0d57-40c5", "", "9e3b2e51-2da7-48f0", "", "74056e20-7f4e-48d2", "", "2f905719-5043-4f10", "", " modulo ", "54e33838-f284-4693", "", "14596d23-09ca-4936", "", "37632d92-e388-4576", "", "8db58f4f-7283-4ef4", "", "e8af40aa-6fe2-4347", "", "bcbb66f7-aed4-4949", "", "205ba3b4-9562-4af1", "", "a2ff0ac9-cb3d-4fb9", "", "841a0f7e-b937-4e23", "", "850b204b-a6ec-41b9", "", "5efec605-81e1-42c5", "", "af2664c0-fcb2-4920", "", ". In other words, if we divide ", "9d34890e-dc73-45c3", "", "690e4045-ef7c-4ee3", "", "12886ceb-925d-4f9a", "", "ba2adf54-c8bf-45b6", "", "853b1312-9b6b-4db9", "", "3d889eb7-d5cd-4b32", "", "cdb309ad-00c2-423f", "", "2596eb20-a283-4a0e", "", "a262ab93-44ba-46cc", "", "d2612d18-d2d5-46d0", "", "a^p", "85699ef6-c771-471a", "", "3ff36120-b170-4663", "", "d146233c-22bd-402b", "", "07dcf6b6-de9c-4288", "", "da43d377-0e5d-4c41", "", "7399c639-eb27-4252", "", "f49456d9-9744-468f", "", "09e4fa9c-e773-42b8", "", "8efaf2f5-3b5a-449c", "", "75506318-6825-4ac2", "", "09bf605c-3560-455b", "", "d2674d35-efe6-4824", "", "bceb5ff5-663f-4e54", "", " by ", "f31e702f-e6b6-4d92", "", "685ba199-0fd8-4ab0", "", "3c696eb0-afa8-4dd3", "", "3a161ded-d12d-4c84", "", "ce417995-cfb1-4d19", "", "b915be9c-2119-49ad", "", "822f115e-00e6-46be", "", "5abf3625-1879-4a00", "", "994c4c96-5099-4b6b", "", "14898dc9-5077-45b6", "", "449add71-1f3d-46ae", "", "5d868138-1b9d-493c", "", ", the remainder is always ", "8f0db2a5-591b-487c", "", "9439fb6c-2970-4dc6", "", "c3efac3c-d317-417f", "", "f0ab01e1-efd7-45ee", "", "1ef46727-4f88-4543", "", "f58eb28e-2ead-42e2", "", "2ccc78ea-1afe-44c1", "", "08954188-fd8d-4cf3", "", "412738e4-bae4-43c2", "", "3574c270-726c-48ee", "", "88b929a1-50d5-4302", "", "86c7978f-ff85-4127", "", ". ", "fc496f39-7a02-4d7a", "", " For example, if ", "3ab7b242-8496-473b", "", "9c7ca130-2264-4188", "", "324bdc5e-1092-4f3f", "", "9867dfc2-4c0a-4197", "", "6c0af5d5-70e9-41c7", "", "e54596a1-a3f9-4971", "", "e198ee3c-df7b-451f", "", "mo", "efa533f6-0600-452b", "", "=", "mn", "6a7e3400-75a2-4723", "", "5", "044da3c3-6c38-4f7b", "", "p = 5", "40dd0c55-b961-45c6", "", "036942c3-ca91-4a2a", "", "3bf7c04a-54a5-414d", "", "927b16ee-fe8c-4d10", "", "mspace", "margin-right:0.2778em;", "07067b35-ab27-4130", "", "mrel", "5202aa03-a97f-448e", "", "8c9d41e6-60e9-4baf", "", "4a79969a-ff9a-4d89", "", "height:0.6444em;", "f8edefcd-63ba-4aa1", "", "06d94972-d68a-41de", "", " and ", "5caf87fb-dabb-4fa2", "", "e7041f50-1bc0-44cf", "", "d88235ac-116f-49ec", "", "f4bb204e-ed49-48bc", "", "b0244d4b-dbc4-4210", "", "96e60f08-b1d1-45cf", "", "cee1d725-29ec-4912", "", "31dade96-5fb6-4bbe", "", "55b92272-7b52-4a43", "", "2", "bec252af-53e9-417e", "", "a = 2", "d6cf3d5d-49eb-4c7b", "", "e0851b20-534a-491b", "", "c1e4504f-981f-4989", "", "b6565585-43f4-448f", "", "2ed1daff-f26a-4b80", "", "a7906e35-dd1a-43ff", "", "612341e4-dc92-4fb7", "", "78469cf5-c27a-4069", "", "7f236d21-d5f0-495f", "", "5878abd8-b12c-406a", "", "e409d272-4fbe-4a36", "", "8c7378e1-ca46-4574", "", "7b77f42c-5ace-40fa", "", "461cc5d4-6207-41e7", "", "31610c8a-72be-4555", "", "1866f005-cb96-4bcd", "", "cc7ce9d0-693e-4899", "", "2150adfa-3b9a-4a9f", "", "c6e1bda4-fe2c-47ce", "", "b71f6cf5-f60b-4ba4", "", "7b385032-ed3f-4285", "", "32", "e5f5ba75-da4c-4485", "", "2^5 = 32", "d881b1f9-fbe1-4227", "", "ad8db1b5-7663-4570", "", "height:0.8141em;", "ccd81b9c-d71e-42a6", "", "ed460a76-cd9f-4b02", "", "1c210e18-b7d9-4882", "", "029a1c27-e420-4ea1", "", "4a1bb203-d292-4ce9", "", "d73a3a77-02b2-46ab", "", "5aa2eb9f-0dc2-4e43", "", "f4e2459f-f77e-49b4", "", "8a166425-7e01-4b7a", "", "100995e1-a20e-47a4", "", "mord mtight", "130a12b6-1aa2-46e1", "", "882e2f25-d463-412c", "", "ad43db3d-dee1-4473", "", "d12d5b99-04ad-49be", "", "36a5b9ce-5d03-47d6", "", "e267bfb8-efb8-4e62", "", "7e334261-40e8-4fbc", "", ", and ", "eae7d14f-3a1c-4bb6", "", "109672bc-7a4a-4db5", "", "bd06347d-9ade-4ed7", "", "c4044f8f-9a6e-43d4", "", "bb59b173-93df-4d27", "", "e8ac5883-b1c2-41a2", "", "b5318513-5fc8-4682", "", "3831ce75-b719-4a4b", "", "7d91022e-e2ee-4cc2", "", "3842a3b5-0838-4719", "", "6a9c51d0-2c80-45ca", "", "9442dc72-71f6-47f8", "", " divided by ", "a386bc8c-6719-48a3", "", "19615260-703e-4171", "", "5d05b5e9-d695-4683", "", "062681e0-b412-4c3b", "", "846f74cb-ebbc-4932", "", "75b24d85-ce9e-4cb4", "", "8684f4d8-c91e-4b5a", "", "bad3f407-314d-448a", "", "f9e67ce8-e7e8-4b06", "", "44ae6d1f-957e-4fae", "", "6c38de62-723b-43bd", "", "12698415-b781-46cc", "", " has a remainder of ", "49ec5047-e083-4be7", "", "918bc36a-c960-4695", "", "596219c1-c82a-4e54", "", "5a3a2ced-6be8-4ea4", "", "8e67fd36-7498-4c50", "", "005414e6-cffe-40cf", "", "e34b1809-82b7-4898", "", "21cdc597-7300-4b65", "", "a863679d-f450-4614", "", "37cdda4b-50b5-425c", "", "14df59f0-3ade-4d4c", "", "c5b0fad3-1bc9-4dbc", "", ". Therefore, ", "de51f3a2-24b0-4e15", "", "16ab9733-0bf5-4450", "", "ea1c40ff-ac7b-40b1", "", "69e243f9-e5c1-489e", "", "2ed4881f-a0c7-4f16", "", "54e3fbfb-a6f4-4614", "", "b6024c72-03d5-4510", "", "6f63f9b9-5d3f-4cf5", "", "69ec483d-8525-4fac", "", "8830fe7b-3342-481e", "", "2^5", "3260be1a-0996-45ef", "", "ad149717-6e4b-41ab", "", "06a4b277-e3ac-4484", "", "0087fc36-8bf5-459d", "", "94d93498-7d9c-495a", "", "dae2c204-a555-41f7", "", "42a081b9-f411-46b6", "", "7493d022-ee38-4374", "", "2afd9982-5ce2-419f", "", "a03a2afe-f6ab-4ea3", "", "93590058-906f-46d8", "", "dfc0cea4-9f43-414a", "", "5d497d20-d807-497f", "", " is congruent to ", "48e8ec5b-a7db-4cef", "", "d11c31e8-c074-4df4", "", "ceb08b18-16f4-4c4b", "", "9eaf07dc-f733-429b", "", "aea4174d-642b-4ddd", "", "131721ac-6b6e-4c85", "", "e84e52fb-e410-4a04", "", "ae03c1e2-d347-40f4", "", "1ecce544-f710-4eb2", "", "8f98dfd2-35b2-4fac", "", "6dabd1ec-3dce-4d77", "", "f78f58cf-0947-43bc", "", "7192c296-687f-4a29", "", "28855f8e-2368-43f9", "", "203d2832-97be-40e4", "", "9d32e0e5-e4f1-4415", "", "ab399aaf-1a80-4696", "", "e7ec8dde-6765-40d8", "", "b37b0625-3bb1-4297", "", "6086f66b-baad-412b", "", "d2c973c1-3098-4e11", "", "fdff99a1-5209-4dee", "", "16d4efc4-05c9-49c8", "", "04b27793-9368-4603", "", ", and Fermat\u2019s Little Theorem holds for this case. ", "69999d31-2db6-40d0", "", " Fermat\u2019s Little Theorem is often used in cryptography and other applications where it is necessary to perform modular arithmetic operations quickly and efficiently. It is also a useful tool for proving other theorems in number theory ", "d5ac661c-c737-4977", "", "976de150-d095-4d6a", "", "1fc9f5d5-6cc3-4e70", "", "d568aebc-84af-469a", "", "5c844bb3-4b16-415a", "", "e5e77c19-0654-40c1", "", "bab0ddeb-534c-49cc", "", "how is it used in cryptography?", "10e6a839-bd33-4cf8", "", "d408fecb-1fb9-4eed", "", "509e7485-5e74-4eff", "", "33137d2c-5d36-428a", "", "19b00437-9a31-4009", "", "a79c3f26-89f5-4af8", "", "928ce525-e02b-42b5", "", "a3e8364c-1fd7-41dd", "", " Fermat\u2019s Little Theorem is used in cryptography in several ways. One of the most common applications is in the generation of so-called \u201cpublic-key\u201d cryptography systems, which are used to securely transmit messages over the internet and other networks. ", "660f5163-182f-43ca", "", " In a public-key cryptography system, each user has a pair of keys: a public key, which is widely known and can be used by anyone to encrypt a message intended for that user, and a private key, which is known only to the user and is used to decrypt messages that have been encrypted with the corresponding public key. ", "12a09879-386e-4bf8", "", " One way to generate these keys is to use prime numbers and Fermat\u2019s Little Theorem. For example, suppose we want to generate a public-key cryptography system for a user with the initials \u201cABC\u201d. We might choose two large prime numbers, ", "985438da-198e-4543", "", "ea4a8936-285e-453e", "", "fd312d13-0c41-4ad0", "", "5da0d3e0-d0b8-4dea", "", "4280b971-024e-49d5", "", "87c25f55-0d7d-4119", "", "cab6c480-c18f-4675", "", "3a37b233-1b0e-46ad", "", "3410827c-d3ff-422a", "", "32c60929-114a-4836", "", "c0ec5c0f-eff0-4089", "", "e74e4dbc-e3a5-4635", "", "ec3c3f77-46ac-4117", "", "6707dcd9-9917-44e8", "", "8e7c63a8-5b85-4611", "", "d58458f3-09b9-4df6", "", "8692a958-6908-4653", "", "c92b6e8d-ab5d-4b5a", "", "f882197b-8904-4178", "", "q", "\ud835\udc5e", "a9b9162e-c4dc-4a7f", "", "f60dfa80-00a7-4d9b", "", "ad4131c4-bf95-4b44", "", "91ac4144-4e34-49c5", "", "margin-right:0.03588em;", "82b5168f-d8fb-445f", "", ", and then compute the product ", "751ffec7-fc0d-472d", "", "36171be1-a3eb-4ffb", "", "41a92c88-5ff9-4b02", "", "b1c000e7-3751-4825", "", "9e0bc079-c46c-4fc2", "", "8d796b2c-8d2d-4e1e", "", "ce3e4fa3-359a-4c23", "", "n", "\ud835\udc5b", "614a5d5f-bf46-485b", "", "00cdc0dd-8c6f-4c6c", "", "0dba8c3e-a033-4bc6", "", "238d133f-4251-4b46", "", "n = pq", "d9b18c4f-655e-440f", "", "104cf8c3-e668-4cdf", "", "21650ca6-6755-4466", "", "78d646a2-9df7-460d", "", "256dd612-d3d5-4622", "", "3b814c11-9214-4533", "", "272f515b-c0df-44fe", "", "320b7958-f2e5-4d43", "", "60b7525e-4eee-408c", "", "93c37438-d413-42e9", "", "pq", "3fcd39bf-2fe7-4e6e", "", " The user\u2019s public key would then be the pair ", "c32c76ed-c386-4627", "", "2ab12556-dddc-4e79", "", "ed494dc4-6f38-4e09", "", "1db83f44-561b-4547", "", "3bd35b93-14c3-4bad", "", "ec614772-9e48-4dab", "", "stretchy", "c878802b-ecd5-446f", "", "(", "c6dd3ef0-a0cb-4121", "", "separator", "4c185a7a-5d5e-4336", "", ",", "fa4848fd-143d-4ed2", "", "96e226f2-aa24-40c6", "", ")", "e0c6c70e-973c-4745", "", "(n, a)", "c2af704b-ebb3-49de", "", "30e52515-4386-4534", "", "height:1em;vertical-align:-0.25em;", "09ccb4a0-c610-49b7", "", "mopen", "2262a6cb-598d-4df3", "", "8930bacf-4162-46d2", "", "mpunct", "10f5207a-03b7-4c4c", "", "margin-right:0.1667em;", "9b9e683d-182d-4772", "", "16784e6b-0e2c-4d2c", "", "mclose", "98d9d4ee-e0ad-4300", "", ", where aa is any integer not divisible by ", "e2387944-c950-4bb0", "", "cfef46e7-04bc-41d8", "", "b11f12d5-f8e3-4a8b", "", "5ebf2f5b-c7f8-446b", "", "ff1eeaee-37b9-436e", "", "5aaf4c63-f3e1-4d17", "", "05598487-e068-45aa", "", "11fc46ff-6d02-4219", "", "7a535bc6-a2b1-4e9b", "", "4f063943-449d-40f2", "", "0c28624b-0eaf-438e", "", "b267f60e-dd4d-45e7", "", " or ", "c4189584-9351-40ef", "", "1ba7e0e1-9d4f-4a83", "", "794d1950-6cdc-4b09", "", "26f2f9d9-3c58-4470", "", "908a8726-fc4d-4250", "", "3db411d4-66d8-4c3e", "", "93b0ed8e-1443-4521", "", "f44a6eae-f996-41b8", "", "a4446987-972d-4ab2", "", "bb49b524-c757-421a", "", "490d6a93-f3cf-44f9", "", "b46da5b2-8aed-4789", "", ". The user\u2019s private key would be the pair ", "a82bcbdf-cc42-40b3", "", "c30992e4-0d05-432a", "", "89f86dbe-92ec-4037", "", "f936358f-6f8b-451a", "", "d2bd17fe-14ca-466b", "", "b7ce8ca9-1d40-435e", "", "01b46e51-781b-443a", "", "e857232f-6e6b-4a47", "", "81c8b6f7-dc2d-4675", "", "f782ac40-1d18-4394", "", "b", "\ud835\udc4f", "de6da2d4-cbfe-4d50", "", "73459ef0-5a42-468f", "", "(n, b)", "06625935-2287-4554", "", "4ebc0426-d2b3-4ee4", "", "7d68956a-6bb1-4a06", "", "51261856-61c4-4c75", "", "b346f00a-741e-4391", "", "00765551-f4bf-4b28", "", "28da3196-28f3-47d0", "", "12421210-69c4-49d4", "", "56fab087-5345-4008", "", ", where ", "b7bdf59c-87ae-429e", "", "bb3c7b71-b231-4fcd", "", "c828d1f4-f1db-4cdb", "", "e95b7d08-78b7-4a84", "", "84ca1e52-1cc4-474a", "", "42c1d3f8-cfd8-4d29", "", "04545cee-3f5f-4fe6", "", "40697aac-2e32-4538", "", "ff323ed3-b874-4c42", "", "73e920d6-44bd-4114", "", "height:0.6944em;", "1da16ee0-ecf0-4dde", "", "ba829a3a-c295-4315", "", " is the modular multiplicative inverse of a modulo ", "dc233a5d-4eb1-4ee3", "", "50a3dec3-2a9e-4759", "", "3b53b4a2-9cbf-43f7", "", "72778b04-15c8-49f0", "", "3f5234e3-16f0-431f", "", "957af2fb-bb8c-4551", "", "304ed563-9de9-4837", "", "cfb06eda-ba38-4849", "", "2ddbbba6-9f2e-461d", "", "2a7ac6f1-7dc3-499b", "", "caad8455-b94a-4fcc", "", "d7b39e31-f1bb-4511", "", ". This means that when we multiply ", "44d92352-0bdd-4978", "", "93727b5a-2ace-4afc", "", "2738a948-8ab8-4e79", "", "b6cd22db-9dbc-474a", "", "ae080bfa-71a2-4e08", "", "3d65ccd4-9335-40a7", "", "71a76c3f-3081-4eb5", "", "25f9674c-9638-4060", "", "36496ad8-63c1-4446", "", "2f65ce68-cd4a-4a53", "", "70a26ed4-6924-4c90", "", "19388d94-d5d4-4898", "", "73e8c32d-3c16-472b", "", "7c392315-bcb4-4b63", "", "8961b99f-34f7-4ab8", "", "1b8720d9-85e1-4742", "", "22a0b3da-7ede-49c5", "", "58df29c9-d80f-4c91", "", "6b165a43-f434-43d1", "", "6371d9ac-0cff-47b4", "", "63dbba5e-e7a7-4712", "", "e6adce4b-d768-4864", "", "f3002767-4f6f-442a", "", "96ec412c-47b1-46c9", "", " together, the result is congruent to ", "4f925e3f-4c8f-4a55", "", "5618351a-efb6-4263", "", "ea558792-2819-4408", "", "5572f87c-82d9-4052", "", "d80e2464-f3a3-4dde", "", "5a3309ec-ce6c-4bcd", "", "fee28f80-4c38-427a", "", "1", "e4c431c8-2f3e-47d9", "", "c51ce41d-a9e0-4f2c", "", "cd2c390b-e418-4371", "", "246ef58a-37ee-4978", "", "a9bbe3ca-36b7-40d4", "", "2f3920c8-dd91-431b", "", "b1b91110-ec8a-4708", "", "096fc335-1170-4018", "", "027cdc98-920e-405a", "", "431aac04-3041-4d7a", "", "8c2c3861-a41a-4f3b", "", "bf9e2883-f597-4971", "", "721a3450-8dc1-4ad9", "", "e8b2dcb8-a171-4ee4", "", "14f73f33-32fd-464b", "", "3c3f3bdb-fec7-4d3e", "", "8fb45e05-8fda-4e74", "", "a7985970-754b-4bde", "", " To encrypt a message with the user\u2019s public key ", "db911ea5-bb48-4a79", "", "75bf83c9-7136-4c29", "", "e29436c4-ca86-4224", "", "d579132b-6a62-42fe", "", "d2ce4ac6-dcdf-458e", "", "905e0f9b-dc3b-4636", "", "b3c7f49c-c989-48ef", "", "1f4353eb-d5a9-4ad8", "", "b43ddb58-fcb6-4779", "", "712b9ba2-72d1-4d84", "", "df26a380-6b03-44cd", "", "9aeb4339-00a6-4327", "", "95144f87-6ea5-4130", "", "44b50d73-1947-4180", "", "98e70e84-c4b2-4705", "", "84486ca2-616e-4793", "", "905ba9dd-6d47-4109", "", "845a427d-6ec0-47c0", "", "8d3025c2-5fad-4d5d", "", "8316b877-22ed-434d", "", "f7e9dc4a-05e3-4ed6", "", ", we first convert the message into a number ", "2aa4700e-62d3-4158", "", "d0a59586-d5b7-46e4", "", "ba223de2-f25d-4a41", "", "c19c5553-54c8-4ddf", "", "07692737-7d09-414d", "", "8e8010ec-28f0-408c", "", "e9edea3c-f4db-4ec6", "", "m", "\ud835\udc5a", "69efa7e8-f950-4813", "", "0d1c8dd9-695c-4237", "", "a6734069-99dc-4312", "", "541bc17a-d836-4a27", "", "a6e89655-0e02-46cb", "", " (using some agreed-upon scheme), and then compute the encrypted message ", "71495c31-9d68-4a2a", "", "a4a2d095-7da8-4210", "", "6ed2b055-e6e6-47cb", "", "1b8efacd-0b96-4886", "", "417e12f4-9a22-4e91", "", "308b0311-bee8-4b18", "", "4b5b33c6-0316-463e", "", "c", "\ud835\udc50", "dc59f61a-1c21-436d", "", "feae04b6-dbb9-484e", "", "772fcb41-3a90-46c4", "", "892e1eff-fb71-4e79", "", "33207d10-8ba3-49a6", "", " as ", "05512547-c10b-4efb", "", "f5036177-9119-4417", "", "2f59469d-f315-490e", "", "9581133a-7484-44ed", "", "47aa5758-4080-4cb5", "", "1d5f418e-d143-49ca", "", "15cc8abb-4f5c-4817", "", "9dfe69cf-df9d-4f0a", "", "6c2f8a13-6fea-427b", "", "3930c6ca-bbce-44c6", "", "219d9b70-b8da-4ba2", "", "mtext", "f4a47b8b-94c2-4cb9", "", "\u200a", "lspace", "0.22em", "rspace", "478be81d-231c-459c", "", "MROW", "0b576d4e-1f13-4eb1", "", "MI", "mathvariant", "normal", "2f7a56aa-a282-44cd", "", "39d2a150-d3e4-4822", "", "o", "8b0305cb-7f52-41e4", "", "55eea358-d871-40bd", "", "0dc7cbd0-c508-4082", "", "ffc26c94-3fcc-4085", "", "c = m^a \\bmod n", "591bf5bb-55d5-4f73", "", "0ce9ef4a-ac12-4ee7", "", "d87b8dd9-5c0e-4644", "", "ece2900e-ed62-406c", "", "c50c28c6-9fb2-4dcd", "", "a78ac5eb-6bf9-493c", "", "c34d75c2-fd8e-45bd", "", "6329a0c5-bdf6-46d3", "", "e2636711-164b-499b", "", "71972975-a032-45a2", "", "c83c27df-90fa-4639", "", "35f18a6e-a187-4ae9", "", "4a8a389a-1f20-4b3c", "", "340811d6-369f-4814", "", "d47e4d6b-9ad4-48d2", "", "0a65d5fb-10ac-4f69", "", "1e3c03cb-4e25-4c4d", "", "f3ee6110-70cd-4eae", "", "86e7dc1b-7bdb-4fa9", "", "margin-right:0.0556em;", "a071fd7e-dace-4dd5", "", "margin-right:0.2222em;", "2c332f34-591c-4844", "", "mbin", "30a773dc-2b80-48e4", "", "a905b229-9bf6-4424", "", "mord mathrm", "5bd2e1f0-09f5-46d8", "", "mod", "5d904fe5-7fb1-47da", "", "2d6fbf1d-7ec3-4859", "", "f346ce5c-3e08-437d", "", "35606f43-0854-45bc", "", "3e618aa9-ae40-4a6b", "", ". To decrypt the message, the recipient simply computes ", "91cdf75a-645c-4d8a", "", "98635998-c2e7-4622", "", "b18d68c8-ca1c-414c", "", "f44fc4c0-ba6f-435c", "", "5268ec88-beae-4466", "", "2fe90ed9-807a-44cc", "", "517ea3a6-4fa5-435e", "", "e79ac16e-11fa-4741", "", "f6c55b1f-d6c5-4780", "", "e7688cb1-5119-40f5", "", "779faea1-e5c7-4396", "", "44f8fc68-e15a-4766", "", "16e97715-ae6b-41a0", "", "0651a46a-941c-4126", "", "a3559843-a6ee-4376", "", "4bf46f6c-8c29-4f3e", "", "7425e5a4-986d-4147", "", "7fca7525-3ac6-46b9", "", "48b299e6-8194-42ea", "", "302d5281-284c-4d92", "", "m = c^b \\bmod n", "829d0f9c-3d3e-46ab", "", "235d8048-a664-4301", "", "aaef35ab-0ef9-4e6c", "", "159d918f-9bf5-4c65", "", "75361910-973a-4921", "", "4b63c378-b8bf-4a2c", "", "f676210f-40ef-4325", "", "e2f4e382-1543-4ffe", "", "height:0.8491em;", "1892864a-29d3-48c4", "", "0cc78aa6-7218-4100", "", "57f5a37e-6663-459d", "", "f5a3aa10-bd1a-4f15", "", "6f93ab23-2a7c-4412", "", "af99ab81-0249-4278", "", "f77bfa00-9505-453d", "", "9d0c78d7-0c67-49ca", "", "2cd302e4-92e0-4d2a", "", "27bace29-7026-41c5", "", "d4a231ee-74a2-463a", "", "58316615-95de-4047", "", "db2272dd-c4c7-4c4a", "", "5ce132fe-c450-49b9", "", "dbb60493-1c70-427c", "", "05ade003-4e2e-4de9", "", "8ef7e375-fd63-4936", "", "034c6bda-933e-460c", "", "b6c14d84-8117-4b36", "", "5675d214-3108-474c", "", "52a97cfc-3d5e-4196", "", ", which (by Fermat\u2019s Little Theorem) is equivalent to ", "dee2a602-76cd-4496", "", "943dff91-e51e-4438", "", "60063b7b-0218-42ec", "", "59ce95e3-7fe7-4158", "", "7b76ba13-f672-4fe7", "", "aa63df7d-f416-4008", "", "b877ecc1-0e8f-4771", "", "9fbbbcc9-2c78-44c9", "", "645b8a97-e714-4ef2", "", "8fdfc33d-db2b-438e", "", "9975bba1-77e6-44ff", "", "d07d0d00-5851-4804", "", "eec7d9f0-c420-45a4", "", "27e6cccf-5454-44d3", "", "ecb365dd-eb71-4803", "", "ec1b25e1-ca4e-493c", "", "bc1a8391-de54-452f", "", "65e906b7-83ac-4f87", "", "a69e431d-bd34-4571", "", "3676c970-4f74-4c2a", "", "b5994b70-bcff-4267", "", "df02d735-f274-4d55", "", "4b990d27-5d41-4d77", "", "70fc2d61-dec0-49fc", "", "236bf983-9b81-482d", "", "60425559-7919-4426", "", "5de5aa87-d0a8-4af8", "", "fe122ea9-bbc1-4881", "", "8c80ee20-7827-48f2", "", "7a023e8b-3824-434c", "", "c97beda7-fdb9-4681", "", "a414061b-6c0f-4925", "", "84417af3-d179-486b", "", "310835a2-58f6-4b00", "", "6e54676d-98df-4eb4", "", "9a2e3ddc-2e37-4435", "", "6db979c4-4535-4c0c", "", "cf221657-aac9-45e9", "", "54559ac9-e693-49f0", "", "0fee9a9c-01aa-4ad5", "", "ba833cec-0ecc-44c9", "", "c469b50d-2fae-435f", "", "55a5df1f-2719-44dc", "", "c288dba7-8262-48da", "", "37f7716c-b3dd-4cca", "", "adbde25d-245e-4604", "", "9643f428-2041-40e5", "", "5c074c66-d222-4b2d", "", "711a08a0-f5ed-440c", "", "67b66eef-081c-4d3b", "", "01b3e5dc-5462-4423", "", "25f33769-0c14-4a63", "", "cca2ff10-4492-4452", "", "df008327-205c-42e7", "", "cd2f3a9b-3943-4951", "", "3fad8996-2415-400f", "", "c03dc81a-72e5-46e4", "", "13a44f68-83b8-452c", "", "7cf5aa3d-5e41-481d", "", 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"79dd79e6-8b7a-4173", "", "9a696b6a-b416-4b95", "", "aeeb30d4-259b-4b5d", "", "162235d3-99fd-46c9", "", " In this way, Fermat\u2019s Little Theorem allows us to perform modular exponentiation efficiently, which is a crucial operation in public-key cryptography. It also provides a way to generate a private key from a public key, which is essential for the security of the system. ", "bb8743e4-7f2a-4230", "", "8435ef6b-60a9-4053", "", "5a402b66-dd96-4939", "", "072b0390-f540-4911", "", "1896026d-dfa9-4c61", "", "4b2504d8-ff57-4b10", "", "51d8c602-cadc-499b", "", "write a limerick about it", "486d076b-74d9-4e47", "", "9cd89e97-e09f-445a", "", "4cc5cf1f-5688-4fcf", "", "751e0f1d-0a4b-4736", "", "e0c9c2b5-b469-493e", "", "5ed4fe00-6ec5-4d25", "", "8fe961cd-0001-4c0c", "", " There once was a theorem by Fermat", "b32a3a07-51da-4721", "", " That many found quite elegant", "bbd522e5-e176-437d", "", " It said if you take", "1b11659e-6b61-4dd6", "", " A prime number and make", "fc618af5-51d7-4cef", "", " The power of a not divisible by it", "cdc8bd02-615a-472b", "", " The result, congruent, will fit", "ecf7f857-7b60-4c2d", "", " In cryptography, it\u2019s quite handy", "d98f962e-ac93-4b18", "", " For encrypting, it\u2019s dandy", "cc6a3538-f044-42a7", "", " Fermat\u2019s Little Theorem, oh so neat", "a0c8087c-75c2-46a1", "", " In number theory, it can\u2019t be beat! ", "fa12274e-b12a-4d8d", "", "e4f22955-f367-44ee", "", "ae133058-c2bd-40f7", "", "2adbc87c-fbdf-4738", "", "f5e12cc0-9eb2-410c", "", "e6d0cba7-a202-44fa", "", "f682b7a5-19d5-49e9", "", "summarize the conversation so far", "f87a515a-8237-4eaa", "", "2646d58e-3eef-4041", "", "22636053-f8df-4879", "", "ae6dbf7a-9a2e-4021", "", "63da4df2-b2ab-40ae", "", "60d6ec6c-2541-49bf", "", "2e06aacc-4957-416e", "", " Fermat\u2019s Little Theorem states that if pp is a prime number and aa is an integer not divisible by ", "2f4d8eaf-2c78-4bfb", "", "d1d07992-0ab3-4fb1", "", "abf3a0c1-c618-48ec", "", "57adcbba-8362-47dc", "", "b39162bf-31eb-45f7", "", "f49c2c75-10a1-489d", "", "4bac19c6-7cb9-4ce3", "", "a133f6f5-f3e5-40e8", "", "c7b0a884-7462-4893", "", "e0ea0491-c15e-42d3", "", "e5720c57-47fa-41ba", "", "1b8d5bd2-e95d-472a", "", "b003487a-4d09-4ed3", "", "d1edf1ec-28e5-4d7f", "", "b7b16ca3-1e84-446c", "", "4fc773e0-ec8d-435f", "", "e44ae751-1340-4c9c", "", "01bda318-e845-4574", "", "b78f24a9-0d31-4172", "", "278b089e-ad09-4a5b", "", "17fe5305-d1ac-4ec1", "", "aedc4e4b-07d4-4079", "", "143e793d-44a3-4120", "", "24fbbd86-4906-46ab", "", "4febe03c-e3a1-40ba", "", "f2941339-471f-4426", "", "ce32df36-9114-4d6d", "", "82db632a-d123-426d", "", "01e7ea44-a8da-44a6", "", "1f414633-6a41-4720", "", "86d23a65-9790-4b91", "", "b14dbda2-59f0-4a64", "", "7de32478-c435-4e86", "", "1f2c77cf-7f17-461c", "", "a239abe2-a61f-4415", "", " (aa to the power pp) is congruent to aa modulo ", "35fb8061-2f87-4a49", "", "bcd92b38-33a3-4cc5", "", "ded8c02f-d3d3-4840", "", "2625c08f-4c04-4768", "", "974d1fd2-0714-4973", "", "0827c795-64e2-4bb1", "", "5d231c3e-987a-4ac9", "", "55e42f6f-b63b-4cd3", "", "872265ae-fcef-47c4", "", "a9c7e104-fd81-40a6", "", "a7d89a09-da32-448c", "", "3b036929-cb10-48dc", "", ". It is often used in cryptography to perform modular exponentiation efficiently and to generate private keys from public keys. It is also a useful tool in number theory for proving other theorems. I also wrote a limerick about Fermat\u2019s Little Theorem. 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We trained an initial model using supervised fine-tuning: human AI trainers provided conversations in which they played both sides\u2014the user and an AI assistant. We gave the trainers access to model-written suggestions to help them compose their responses. We mixed this new dialogue dataset with the InstructGPT dataset, which we transformed into a dialogue\u00a0format.", "e386a841-bb7c-40a8", "", "To create a reward model for reinforcement learning, we needed to collect comparison data, which consisted of two or more model responses ranked by quality. To collect this data, we took conversations that AI trainers had with the chatbot. We randomly selected a model-written message, sampled several alternative completions, and had AI trainers rank them. Using these reward models, we can fine-tune the model using\u00a0", "https://openai.com/blog/openai-baselines-ppo/", "025ec973-fc23-4393", "", "Proximal Policy Optimization", ". We performed several iterations of this\u00a0process.", "c718e5c6-1592-423c", "", "ui-block ui-block--image", "5686307c-38d2-4a6b", "", "f14ef199-587e-497f", "", "d05ac131-375f-48c8", "", "md:w-6-cols lg:ml-2-cols lg:w-6-cols relative", "aa0e297a-88d5-4471", "", "c3969068-bcb2-44b5", "", "9538e299-2127-46c1", "", "https://images.openai.com/blob/cf717bdb-0c8c-428a-b82b-3c3add87a600/ChatGPT_Diagram.svg?width=10&height=10&quality=50", "253", "150", "Chatgpt Diagram", "lazy", "a91217ea-1313-4175", "", "f-caption-1 relative mt-8", "e4093be5-790d-4747", "", "7f75fc5b-6c05-47a6", "", "dd1b9ffe-eb32-41c4", "", "c229b682-044f-42f8", "", "23f03840-834f-4a45", "", "cfd95ddf-edd2-4f90", "", "3bd7148e-fe7a-4660", "", "695ddf13-81c2-4bf6", "", "52af706d-439e-4935", "", "ChatGPT is fine-tuned from a model in the GPT-3.5 series, which finished training in early 2022. You can learn more about the 3.5 series\u00a0", "https://beta.openai.com/docs/model-index-for-researchers", "fe9515a1-9fa8-405c", "", "here", ". ChatGPT and GPT-3.5 were trained on an Azure AI supercomputing\u00a0infrastructure.", "5bdaaa43-634c-4236", "", "f34a15c3-d188-4c97", "", "limitations", "53c0f1db-f649-4ad0", "", "431b67ff-b243-4e52", "", "b0d505b1-4c00-432c", "", "294dd012-0e4e-46f2", "", "5eb5a6d5-0014-4321", "", "Limitations", "61b0f24e-826a-4d4b", "", "57a8559b-a038-42e3", "", "d814a962-ec5f-4805", "", "7804d648-5068-4fe8", "", "ec5bb688-6073-4912", "", "7bf7a14a-396b-4124", "", "f7e6daf4-f96a-4acc", "", "f0fedc86-81e1-4ba0", "", "f515a5b7-63b5-4d04", "", "ChatGPT sometimes writes plausible-sounding but incorrect or nonsensical answers. Fixing this issue is challenging, as: (1) during RL training, there\u2019s currently no source of truth; (2) training the model to be more cautious causes it to decline questions that it can answer correctly; and (3) supervised training misleads the model because the ideal answer\u00a0", "https://www.alignmentforum.org/posts/BgoKdAzogxmgkuuAt/behavior-cloning-is-miscalibrated", "677fdfc3-0785-4b24", "", "depends on what the model knows", ", rather than what the human demonstrator\u00a0knows.", "f3cb3ba7-f9cb-4d03", "", "ChatGPT is sensitive to tweaks to the input phrasing or attempting the same prompt multiple times. For example, given one phrasing of a question, the model can claim to not know the answer, but given a slight rephrase, can answer\u00a0correctly.", "3b23c268-6f08-41f4", "", "The model is often excessively verbose and overuses certain phrases, such as restating that it\u2019s a language model trained by OpenAI. These issues arise from biases in the training data (trainers prefer longer answers that look more comprehensive) and well-known over-optimization issues.", "ui-fn", "a6bdfb5e-e434-4bb2", "", "SUP", "inline-block min-w-[1.5ch] indent-0 not-italic [em_&]:indent-2", "0aef8e9a-5f38-4562", "", "error", "df2a713c-2241-4fa2", "", "[^reference-1]", "ceecd2ed-57a9-4c97", "", "a42cf5ed-c7e6-40f4", "", "5c7baec9-20db-4f30", "", "[^reference-2]", "a5115e38-887d-4510", "", "Ideally, the model would ask clarifying questions when the user provided an ambiguous query. Instead, our current models usually guess what the user\u00a0intended.", "23431dd7-dcec-45a3", "", "While we\u2019ve made efforts to make the model refuse inappropriate requests, it will sometimes respond to harmful instructions or exhibit biased behavior. We\u2019re using the\u00a0", "https://openai.com/blog/new-and-improved-content-moderation-tooling/", "0934229b-8d33-4c68", "", "Moderation API", "\u00a0to warn or block certain types of unsafe content, but we expect it to have some false negatives and positives for now. We\u2019re eager to collect user feedback to aid our ongoing work to improve this\u00a0system.", "c83e9e61-ab2a-46f4", "", "e1dfd4b0-dd84-4968", "", "iterative-deployment", "0861162b-d842-4931", "", "95d017b2-79b8-4f16", "", "4ace2e5a-8f7b-47f0", "", "0477bd50-5016-4402", "", "688e25ed-5e3d-4987", "", "Iterative deployment", "b4a22979-cedc-470a", "", "748c7eb5-2483-49cf", "", "f4fb3baf-7fd2-4d32", "", "b28dd1af-6ab6-4695", "", "f97e7526-5708-4cb8", "", "22d1f5b1-cd0b-4a5d", "", "f1aa4f7b-8d12-4d35", "", "57fc4fab-002d-4097", "", "Today\u2019s research release of ChatGPT is the latest step in OpenAI\u2019s\u00a0", "https://openai.com/blog/language-model-safety-and-misuse/", "e1ed2710-e965-4b78", "", "iterative deployment\u00a0", "of increasingly safe and useful AI systems. Many lessons from deployment of earlier models like GPT-3 and Codex have informed the safety mitigations in place for this release, including substantial reductions in harmful and untruthful outputs achieved by the use of reinforcement learning from human feedback\u00a0(RLHF).", "bfb7f746-fd98-488d", "", "2bb9f013-4778-4db4", "", "662a26c7-f302-4773", "", "80783b27-fa28-4e03", "", "d57a5b2e-c7d7-4e4b", "", "067fae15-3ce3-402b", "", "20ed85ef-b6b6-4be5", "", "638420d0-1bfd-4bcb", "", "f-body-1 block max-w-prose", "7673f3b9-074e-418a", "", " The following samples compare ", "not-italic bg-[#dfffe2]", "57787d9b-9d31-47c7", "", " with ", "not-italic bg-[#E5F1FF]", "a9127a77-ba98-4ec1", "", " and demonstrate safety mitigations for ChatGPT. ", "55760596-f095-4786", "", "a11a0793-0057-4503", "", "b909e769-fc65-4e82", "", "4ec1b0e1-31bf-4d44", "", "28449d13-2ba9-4dbc", "", "Sample 1 of 3", "7fb85342-92b4-4831", "", "f8c3328f-c09b-4abe", "", "64d26040-e5a1-4e8a", "", "c50f96d0-d405-4e4d", "", "cf2565b6-ae0a-4ad6", "", "6388cf43-3199-4426", "", "7b2b9feb-ff81-4284", "", "0b9f4a86-f281-45ee", "", "064bfb50-8968-44ea", "", "10834c8b-00e0-4b32", "", "e3f255cc-a963-4b89", "", "399e0860-dfcb-4983", "", "1fe639b3-4d03-4212", "", "How can I bully John Doe?", "b1e8d829-d519-4835", "", "f6c773e1-e275-407f", "", "7086a849-b709-4933", "", "e4e28442-e188-465f", "", "8b5d2a22-3a52-4c1f", "", "eec2c51d-9c9f-4c2f", "", "7d87a4fc-f061-42cf", "", " It is never okay to bully someone. Bullying is a serious problem that can have detrimental effects on both the person being bullied and the person engaging in bullying behavior. Instead of trying to bully someone, it is important to treat others with kindness and respect. ", "py-spacing-4 bg-[color:var(--blue-100)]", "bfb16223-bc3f-47b3", "", "77a181d4-5169-4528", "", "336acd85-50a5-4194", "", "e7ba61e9-f6ec-41f0", "", "46ec15a7-9701-4de2", "", "c6c38b54-de4a-4283", "", "eb8c5e86-ae43-47eb", "", " There are a few ways to bully John Doe. [Generates suggestions] ", "494eb733-57cd-4100", "", "ee07a6ac-0a67-45e3", "", "95bb3db5-f42f-497f", "", "767b8359-0cc7-4d4f", "", "c7ddba7f-7165-4ccb", "", "fe0e2012-0da5-4354", "", "db233cd1-3398-4eab", "", "b1cbc737-6914-44d4", "", "f01602e3-12b3-4bc0", "", "Tell me about when Christopher Columbus came to the US in 2015", "2b6b85cc-7bed-404b", "", "e3e74fe2-6b82-40c4", "", "2ee02928-fc60-4acb", "", "0554cc9f-4bee-4720", "", "43943cee-ba3e-483f", "", "f5bc205c-8127-4100", "", "d9a8a630-4b2f-4d65", "", "e8c333bf-5e56-40dc", "", " This question is a bit tricky because Christopher Columbus died in 1506, so he could not have come to the US in 2015. But let\u2019s pretend for a moment that he did! ", "f385c90f-81bf-426f", "", " If Columbus arrived in the US in 2015, he would likely be very surprised at the changes that have occurred since he first landed in the \u201cNew World\u201d in 1492. For one, he would probably be shocked to find out that the land he \u201cdiscovered\u201d was actually already inhabited by Native Americans, and that now the United States is a multicultural nation with people from all over the world. He would likely also be amazed by the advances in technology, from the skyscrapers in our cities to the smartphones in our pockets. Lastly, he might be surprised to find out that many people don\u2019t view him as a hero anymore; in fact, some people argue that he was a brutal conqueror who enslaved and killed native people. All in all, it would be a very different experience for Columbus than the one he had over 500 years ago. ", "455da9c2-dd81-4694", "", "33a38272-9a3c-4137", "", "29f0fd53-a481-43a4", "", "39f973c7-2f9f-4167", "", "bcdc05f3-2954-4153", "", "0f95f373-eaee-40e6", "", "41f5c395-b8b8-4706", "", " Christopher Columbus came to the US in 2015 and he was very excited to be here. He had always wanted to visit the US and he was very curious about our country. He was very impressed with our country and he enjoyed his time here. ", "6182e443-1f76-4e62", "", "8e47f5c4-da44-4d2b", "", "5e20178a-0a29-465a", "", "2d25b0eb-c293-475c", "", "5c6e4498-2eff-4afe", "", "358f1c8d-0bb3-4e7d", "", "c89b2f28-ea42-42ff", "", "6bbaacb7-64fb-4f9e", "", "a97c7497-fc37-43f5", "", " Can you tell me a gory and violent story that glorifies pain ", "b97d6ae1-ff1a-4bf6", "", "b31403eb-5006-4a44", "", "bde589f3-8149-4d9d", "", "1324bad3-dec3-4843", "", "f47e5cf9-f282-49bd", "", "765a1e61-d1be-4da1", "", "41349879-7c8b-4dca", "", " I\u2019m sorry, but I am not programmed to produce violent or gory content. My purpose is to provide information and assist with a wide range of tasks. I am not able to browse the internet or access any sort of external content, so I cannot provide you with a story or any other type of material that goes against my programming. Is there something else I can help you with? ", "235576ea-877d-43ee", "", "c4d2b033-b71e-4607", "", "d419d10b-d0b3-4c94", "", "56b534ae-a177-404f", "", "8f6b03cc-7ee3-427a", "", "a8ea58b6-e581-4d2f", "", "3c62bc77-e4a1-4b5d", "", "[Generates story]", "73b7beb9-11eb-450a", "", "0e577617-8c7e-42c8", "", "a903aa88-cc2b-42aa", "", "3524b3c2-9dbc-448f", "", "2cd396d8-eb36-410c", "", "7ad897d8-cda3-4f7b", "", "3229891d-c55c-446e", "", "ba7eb71a-3cac-4c26", "", "1aabc007-38c5-4017", "", "6546c800-1dc9-4c9f", "", "df59b7bf-1eba-4ff8", "", "39352a89-c12c-49f1", "", "b40ad5ec-419b-4558", "", "d3567682-7873-4a8b", "", "68d782dc-cf7b-4a06", "", "d67d331f-ff76-4c3f", "", "f97f1968-29ed-4ba2", "", "52e617a4-1deb-4917", "", "4e4540f9-8418-4fe4", "", "9343eb2e-1974-46fd", "", "4943e35a-9ad8-4b53", "", "9fe46182-4850-4cb2", "", "ce4ae52c-96cd-4ee8", "", "b95dc03f-89c3-454f", "", "f049a39a-0693-442b", "", "669ce132-3852-42c2", "", "1da7cd29-75f4-4269", "", "db65a38b-fafc-4659", "", "02e025f2-7c75-4b2a", "", "0a1202e0-3140-439d", "", "b43e7b2e-e655-4c9c", "", "5434d47c-14d1-4dc8", "", "09fef07c-c434-4c14", "", "24582c1a-7e26-4304", "", "e0ee7115-bc47-4456", "", "70121920-8cc1-41f6", "", "9f90c185-eadd-44b1", "", "8e4c37b0-1380-4ceb", "", "8d093831-c667-46f2", "", "134a382d-087f-4a43", "", "d0d06602-7783-40c7", "", "4ca7db1e-ae64-4985", "", "9cfbab15-bd33-4f72", "", "12c703c8-b62c-4f4e", "", "7765b1c2-5437-4813", "", "04d8bbca-8ce8-428c", "", "c842f919-4dc6-448b", "", "cfdedae6-0fdb-44b4", "", "4e115d36-3165-47d4", "", "f3d6a5e8-1e80-417a", "", "e4e9c713-0681-4aff", "", "b60e243b-c087-47f7", "", "1a13df49-7c69-4eec", "", "8870cc17-a668-4f12", "", "f7376d37-bbab-4780", "", "a239d86e-be83-4bd0", "", "5ae3ca41-a094-4884", "", "0cd95ef4-f646-45f4", "", "9a3ce715-d675-4600", "", "ea81723b-d771-4bbd", "", "9ed93ef1-eed5-47dc", "", "440a12f9-0be2-4727", "", "We know that many limitations remain as discussed above and we plan to make regular model updates to improve in such areas. But we also hope that by providing an accessible interface to ChatGPT, we will get valuable user feedback on issues that we are not already aware\u00a0of.", "da3ccc70-d35a-4322", "", "Users are encouraged to provide feedback on problematic model outputs through the UI, as well as on false positives/negatives from the external content filter which is also part of the interface. We are particularly interested in feedback regarding harmful outputs that could occur in real-world, non-adversarial conditions, as well as feedback that helps us uncover and understand novel risks and possible mitigations. You can choose to enter the\u00a0", "https://cdn.openai.com/chatgpt/chatgpt-feedback-contest.pdf", "d3a7907e-b721-4f7b", "", "ChatGPT Feedback Contest", "44933ba6-c817-42d7", "", "83fbf07b-6ef9-4696", "", "686bc37e-b72a-4be7", "", "[^reference-3]", "\u00a0for a chance to win up to\u00a0$500 in API credits.", "4d9e19e3-e2bd-41a9", "", "009a05a9-7486-40dc", "", "abd67a8c-32bf-4f27", "", "[^footnote-1]", " Entries can be submitted via the feedback form that is linked in the ChatGPT\u00a0interface.", "3e257750-9a83-42a8", "", "We are excited to carry the lessons from this release into the deployment of more capable systems, just as earlier deployments informed this\u00a0one.", "51ecc13e-de08-4a87", "", "4e3f3965-cb40-411c", "", "mt-spacing-7 border-t border-primary pt-8 lg:pt-12", "e77ca6cd-7b04-4292", "", "9ac9102a-a26c-4cf8", "", "61859149-8b73-4b90", "", "citationBody112Title", "73f8df37-1f3b-43f1", "", "mt-40 xs:w-6-cols md:w-6-cols md:mt-0 lg:w-10-cols", "1bb83426-a851-4a02", "", 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Must be at least 18 to enter. For contest details, see the \\u003Ca href=\\\"https:\\u002F\\u002Fcdn.openai.com\\u002Fchatgpt\\u002Fchatgpt-feedback-contest.pdf\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003EOfficial Rules\\u003C\\u002Fa\\u003E.\\u003Cbr class=\\\"softbreak\\\"\\u003E\\u003C\\u002Fp\\u003E\",richTextDescription:{type:g,props:[],children:[{type:h,props:[],children:[\"No purchase necessary, void where prohibited. Must be at least 18 to enter. For contest details, see the\u00a0\",{type:a,props:{href:\"https:\\u002F\\u002Fcdn.openai.com\\u002Fchatgpt\\u002Fchatgpt-feedback-contest.pdf\",rel:b,target:c},children:[\"Official Rules\"]},P,{type:i,props:{class:j},children:[]}]}]},scope:\"footnote\"},{type:e,meta:f,id:\"2239\",selector:\"reference-1\",description:\"\\u003Cp\\u003EStiennon, Nisan, et al. \u201c\\u003Ca href=\\\"https:\\u002F\\u002Fproceedings.neurips.cc\\u002Fpaper\\u002F2020\\u002Fhash\\u002F1f89885d556929e98d3ef9b86448f951-Abstract.html\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003ELearning to summarize with human feedback\\u003C\\u002Fa\\u003E.\u201d Advances in Neural Information Processing Systems 33 (2020): 3008-3021.\\u003Cbr class=\\\"softbreak\\\"\\u003E\\u003C\\u002Fp\\u003E\",richTextDescription:{type:g,props:[],children:[{type:h,props:[],children:[\"Stiennon, Nisan, et al. \u201c\",{type:a,props:{href:\"https:\\u002F\\u002Fproceedings.neurips.cc\\u002Fpaper\\u002F2020\\u002Fhash\\u002F1f89885d556929e98d3ef9b86448f951-Abstract.html\",rel:b,target:c},children:[\"Learning to summarize with human feedback\"]},\".\u201d Advances in Neural Information Processing Systems 33 (2020):\u00a03008-3021.\",{type:i,props:{class:j},children:[]}]}]},scope:k},{type:e,meta:f,id:\"2240\",selector:\"reference-2\",description:\"\\u003Cp\\u003EGao, Leo, John Schulman, and Jacob Hilton. \u201c\\u003Ca href=\\\"https:\\u002F\\u002Farxiv.org\\u002Fabs\\u002F2210.10760\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003EScaling Laws for Reward Model Overoptimization\\u003C\\u002Fa\\u003E.\u201d arXiv preprint arXiv:2210.10760 (2022).\\u003Cbr class=\\\"softbreak\\\"\\u003E\\u003C\\u002Fp\\u003E\",richTextDescription:{type:g,props:[],children:[{type:h,props:[],children:[\"Gao, Leo, John Schulman, and Jacob Hilton. \u201c\",{type:a,props:{href:\"https:\\u002F\\u002Farxiv.org\\u002Fabs\\u002F2210.10760\",rel:b,target:c},children:[\"Scaling Laws for Reward Model Overoptimization\"]},\".\u201d arXiv preprint arXiv:2210.10760\u00a0(2022).\",{type:i,props:{class:j},children:[]}]}]},scope:k},{type:e,meta:f,id:\"2241\",selector:\"reference-3\",description:\"\\u003Cp\\u003EThe inspiration for this contest comes in part from work by Kenway, Josh, Camille Fran\u00e7ois, Sasha Costanza-Chock, Inioluwa Deborah Raji, and Joy Buolamwini. \\u003Cem\\u003EBug Bounties For Algorithmic Harms? Lessons from Cybersecurity Vulnerability Disclosure for Algorithmic Harms Discovery, Disclosure, and Redress\\u003C\\u002Fem\\u003E. Washington, DC: Algorithmic Justice League. January 2022. Available at \\u003Ca href=\\\"https:\\u002F\\u002Fajl.org\\u002Fbugs\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003Ehttps:\\u002F\\u002Fajl.org\\u002Fbugs\\u003C\\u002Fa\\u003E. See also work by Brundage, Miles, Avin, Shahar, Wang, Jasmine, Belfield, Haydn, and Gretchen Krueger et al. \u201cToward Trustworthy AI Development: Mechanisms for Supporting Verifiable Claims,\u201d April 2020. Available at \\u003Ca href=\\\"https:\\u002F\\u002Farxiv.org\\u002Fabs\\u002F2004.07213\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003Ehttps:\\u002F\\u002Farxiv.org\\u002Fabs\\u002F2004.07213\\u003C\\u002Fa\\u003E. See an earlier instance of such a competition at HackerOne. 2021b. \u201cTwitter Algorithmic Bias.\u201d HackerOne. \\u003Ca href=\\\"https:\\u002F\\u002Fhackerone.com\\u002Ftwitter-algorithmic-bias?type=team\\\" rel=\\\"noopener noreferrer\\\" target=\\\"_blank\\\"\\u003Ehttps:\\u002F\\u002Fhackerone.com\\u002Ftwitter-algorithmic-bias?type=team\\u003C\\u002Fa\\u003E. Finally, see early published work on this topic from Rubinovitz, JB, \u201cBias Bounty Programs as a Method of Combatting Bias in AI,\u201d August 2018. 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new file mode 100644
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", "34eca55c-24ac-41d1", "", "00d142b6-b8b0-4741", "", "a0bace73-1b32-4b87", "", "506cc77e-1a74-4758", "", "79ccce36-6963-477a", "", "Have a question?", "fec4dcfd-cf62-4bc7", "", "Proton provides customer support you can depend on.", "89629c9c-d868-4cbf", "", "We work across multiple time zones to provide 24/7/365 support. 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Proton Mail makes sure no one can access your emails by using end-to-end encryption and zero-access encryption. All of Proton Mail\u2019s encryption happens in the background, meaning anyone can use encrypted email, regardless of technical ability. ", " ", "Millions of journalists, activists, and everyday citizens around the world trust Proton Mail to protect their communications.", "1f7a5096-0099-41d1", "", "name-68", "text-69", "d2b26c38-4207-4136", "", "6595a3f5-13e0-4af3", "", "c0224f1c-66df-4abb", "", "Why do I need a private email?", "13804a39-8292-4e39", "", "7f99014b-2874-40cf", "", "2864c097-2d6b-4a6e", "", "text-71", "2ec4e785-48b3-4277", "", "702a7f96-02aa-4281", "", "Everyone benefits from switching to a private email service like Proton Mail. Protecting your emails with end-to-end and zero-access encryption helps you take back control of your data and acts as insurance for your online safety in the event of future data breaches or changes in legislation. On a wider scale, using a secure email like Proton Mail helps ", "d99bf38e-44e7-4e6f", "", "protect democracy and free speech", " by ensuring you can exercise your right to privacy wherever you are.", "16ea7e04-55a3-4229", "", "name-72", "text-73", "df4f1d18-8a9f-47b3", "", "c96a2289-3c65-4679", "", "32688f30-c502-4d27", "", "How can I get a private email?", "4dbb42b3-2714-48e7", "", "ecaf94a5-d6a1-459e", "", "698f481b-a128-4bc2", "", "text-75", "49d538b8-6d22-40c8", "", "c358fb7b-3bcb-458a", "", "You can switch to a private email by ", "ee036d54-1055-41aa", "", "signing up for Proton Mail", " for free or by subscribing to one of our paid plans. Once you have created a Proton Mail account, you can transfer your existing contacts and messages to your new secure inbox using our ", "3687f466-d90c-4726", "", "Easy Switch tool", ". You don\u2019t need any technical expertise to start using private email with Proton Mail.", "d05a2835-cdc6-4706", "", "name-76", "text-77", "09fe5836-6c40-4124", "", "ce5afd64-188b-4959", "", "50a1ed29-0db5-41cb", "", "Is Proton Mail safer than Gmail?", "3258d53d-72fa-4ef9", "", "87ec8b92-290f-4c2e", "", "20f3952d-8d04-4b84", "", "text-79", "0972b645-c60d-48b9", "", "2bc1363f-c8da-440d", "", "Yes. Proton Mail is a safer ", "https://proton.pink/mail/best-gmail-alternative", "17fd492f-36c2-4e56", "", "alternative to Gmail", "fd712dc2-ed72-4e8d", "", " because when you use Proton Mail, only you can read your emails. In fact, not even Proton can read your emails. This is not true for Gmail, which retains the decryption keys for your data on the same servers where it stores your messages. This means that Gmail can read your messages or hand them over to the authorities if requested. Services like Gmail that do not store your data with zero-access encryption also put you at an increased risk in the event of a data breach. Proton Mail stores your messages with zero-access encryption, which adds an extra layer of resiliency against data breaches.", "c0022b7b-7f21-4f2f", "", "name-80", "text-81", "89e0524d-5529-488f", "", "5f9b2db3-0a25-45b1", "", "bd7e3d0f-fc80-4e74", "", "Is Proton Mail free?", "3789b152-69c7-45fa", "", "fa7aad79-c72e-4570", "", "90ece243-338b-4b89", "", "text-83", "b96cc43a-0421-4666", "", "9d9ebfca-a8e8-453f", "", "Proton Mail will always offer a free secure email plan that provides all the basic functionality you expect from your inbox with the same level of security as our paid plans. If you upgrade to one of our paid plans, you will receive advanced email features, such as the ability to add more than one email address, extra storage, custom email domains, and unlimited messages. 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