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101 (one hundred one) is the natural number following 100 and preceding 102.

It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one". As an ordinal number, 101st (one hundred first), rather than 101th, is the correct form.

In mathematics

101 is:

• the 26th prime number and the smallest integer above 100.
• a palindromic number in decimal, and so a palindromic prime.
• a Chen prime since 103 is also prime, with which it makes a twin prime pair.
• a sexy prime since 107 and 113 are also prime, with which it makes a sexy prime triplet.
• a unique prime because the period length of its reciprocal is unique among primes.
• an Eisenstein prime with no imaginary part and real part of the form ${\displaystyle 3n-1}$.
• the fifth alternating factorial.
• a centered decagonal number.
• the only existing prime with alternating 1s and 0s in decimal and the largest known prime of the form ${\displaystyle 10^{n}+1}$.
• the number of compositions of 12 into distinct parts.
• the smallest number that can be expressed as the sum of three distinct nonzero squares in more than two ways: ${\displaystyle 9^{2}+4^{2}+2^{2}}$, ${\displaystyle 8^{2}+6^{2}+1^{2}}$ or ${\displaystyle 7^{2}+6^{2}+4^{2}}$ (see image).

Given 101, the Mertens function returns 0. It is the second prime to have this property after 2.

For a 3-digit number in decimal, this number has a relatively simple divisibility test. The candidate number is split into groups of four, starting with the rightmost four, and added up to produce a 4-digit number. If this 4-digit number is of the form ${\displaystyle 1000a+100b+10a+b}$ (where a and b are integers from 0 to 9), such as 3232 or 9797, or of the form ${\displaystyle 100b+b}$, such as 707 and 808, then the number is divisible by 101.

On the seven-segment display of a calculator, 101 is both a strobogrammatic prime and a dihedral prime.

In books

According to Books in Print, more books are now published with a title that begins with '101' than '100'. They usually describe or discuss a list of items, such as 101 Ways to... or 101 Questions and Answers About... . This marketing tool is used to imply that the customer is given a little extra information beyond books that include only 100 items. Some books have taken this marketing scheme even further with titles that begin with '102', '103', or '1001'. The number is used in this context as a slang term when referring to "a 101 document" what is usually referred to as a statistical survey or overview of some topic.

In education

In American university course numbering systems, the number 101 is often used for an introductory course at a beginner's level in a department's subject area. This common numbering system was designed to make transfer between colleges easier. It can also indicate a course for students not intending to major in the subject; e.g. a student intending to major in English would take English 111 not English 101.

In theory, any numbered course in one academic institution should bring a student to the same standard as a similarly numbered course at other institutions. One of earliest such usages, perhaps the first, was by the University of Buffalo in 1929.

Based on this usage, the term "101" (pronounced /ˌwʌnoʊˈwʌn/ WUN-oh-WUN) has gained a slang sense referring to basic knowledge of a topic or a collection of introductory materials to a topic, as in the sentence, "Boiling potatoes is Cooking 101". The Oxford English Dictionary records the usage of "101" in this slang sense from 1986.

In other fields

In public life:

• In Hinduism, 101 is a lucky number.
• 101st kilometre, a condition of release from the Gulag in the Soviet Union.
• 101 is the main Police Emergency Number in Belgium.
• 101 is the Single Non-Emergency Number (SNEN) in some parts of the UK, a telephone number used to call emergency services that are urgent but not emergencies. 101 is now available across all areas of England and Wales.

In technology:

• An HTTP status code indicating that the server is switching protocols as requested by the client to do so.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): page 133. ISBN 978-0-14-008029-2

1. "Sloane's A005165 : Alternating factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 27 May 2016.
2. "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 27 May 2016.
3. Prime Curios! 101
4. Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 24 May 2022.
5. Sloane, N. J. A. (ed.). "Sequence A025349 (Numbers that are the sum of 3 distinct nonzero squares in 3 or more ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Sloane, N. J. A. (ed.). "Sequence A025341 (Numbers that are the sum of 3 distinct nonzero squares in exactly 3 ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 27 May 2016.
8. "Sloane's A100669 : Zeros of the Mertens function that are also prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 29 May 2016.
9. Renault, Marc (November 2006), "Stupid Divisibility Tricks 101 Ways to Stupefy Your Friends", Math Horizons, 14 (2): 18–21, 42, doi:10.1080/10724117.2006.11974676, JSTOR 25678653, S2CID 125269086
10. "Sloane's A134996 : Dihedral calculator primes: p, p upside down, p in a mirror, p upside-down-and-in-a-mirror are all primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 17 December 2020.
11. Kovalchik, Kara (20 November 2013). "Why Are Introductory Classes Called '101'?". mentalfloss.com. Retrieved 30 September 2023.
12. ^ Forest, J.J.F. (2002) Higher education in the United States: an encyclopedia p.73. ABC-CLIO. ISBN 1-57607-248-7. Retrieved October 2011
13. ^ Engber, Daniel (6 September 2006). "101 101". Slate Magazine. Retrieved 9 May 2017.
14. "Report a crime or antisocial behaviour – GOV.UK". direct.gov.uk. Retrieved 4 April 2018.
15. Welcome to 101, Home Office, retrieved 5 April 2009

• Integers
• Academic slang