101 (number)

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100 101 102
Cardinal one hundred [and] one
Ordinal 101st
(one hundred [and] first)
Factorization prime
Prime 26th
Divisors 1, 101
Roman numeral CI
Binary 11001012
Ternary 102023
Quaternary 12114
Quinary 4015
Senary 2456
Octal 1458
Duodecimal 8512
Hexadecimal 6516
Vigesimal 5120
Base 36 2T36

101 (one hundred [and] 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 [and] first) rather than 101th is the correct form.

In mathematics[edit]

101 is the 26th prime number and a palindromic number (and so a palindromic prime). The next prime is 103, with which it makes a twin prime pair, making 101 a Chen prime. Because the period length of its reciprocal is unique among primes, 101 is a unique prime. 101 is an Eisenstein prime with no imaginary part and real part of the form 3n - 1.

101 is the sum of five consecutive primes (13 + 17 + 19 + 23 + 29). Given 101, the Mertens function returns 0. 101 is the fifth alternating factorial.

101 is a centered decagonal number.

The decimal representation of 2101 − 1 is 2 535301 200456 458802 993406 410751. The prime decomposition of that is 7 432339 208719 x 341117 531003 194129[1]

For a 3-digit number in base 10, 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 1000a + 100b + 10a + b (where a and b are integers from 0 to 9), such as 3232 or 9797, or of the form 100b + b, such as 707 and 808, then the number is divisible by 101.[2]

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

101 is the only existing prime with alternating 1s and 0s in base 10 and the largest known prime of the form 10n + 1.[3]

In science[edit]

  • In mineralogy, a Miller index of 101 is a crystal face that crosses the horizontal axis (a) and 3d vertical axis (c) but does not cross the 2d vertical axis (b).
  • In physics and chemistry, it is the atomic number of mendelevium, an actinide.
  • In astronomy it is the Messier designation given to the Pinwheel Galaxy in Ursa Major.

In books[edit]

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.

Room 101 is a torture chamber in the novel Nineteen Eighty-Four by George Orwell.

Creative Writing 101 by Raymond Carver, "A writer's values and craft. This was what the man (John Gardner) taught and what he stood for, and this is what I've kept by me in the years since that brief but all important time."

In education[edit]

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. 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.[4]

Based on this usage, the term "101" has been extended to mean an introductory level of learning or a collection of introductory materials to a topic.

In other fields[edit]

Main article: 101 (disambiguation)


  1. ^ "Factorization using the Elliptic Curve Method". Alpertron.com.ar. Retrieved 2014-04-29. 
  2. ^ Renault, Marc (November 2006), "Stupid Divisibility Tricks 101 Ways to Stupefy Your Friends", Math Horizons 14 (2): 18–21, 42, JSTOR 25678653 
  3. ^ Prime Curios! 101
  4. ^ 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
  5. ^ Engber, Daniel (6 September 2006), "101 101: How did intro classes get their trademark number?", Slate 
  6. ^ 101, Dictionary.com 
  7. ^ 101-Key "Enhanced" Keyboard Layout, Pcguide.com, retrieved 4 May 2009 
  8. ^ http://www.direct.gov.uk/en/CrimeJusticeAndTheLaw/Reportingcrimeandantisocialbehaviour/DG_185338
  9. ^ Welcome to 101, Home Office, retrieved 5 April 2009 
  10. ^ iCar 101 - The ultimate roadable aircraft, retrieved 6 August 2010