101 (number)

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101 (one hundred [and] one) is the natural number following 100 and preceding 102. When written without the "and," 101 is the smallest number requiring thirteen letters in English.

<< 100 101 102 103 104 105 106 107 108 109 >> List of numbers -- Integers << 100 110 120 130 140 150 160 170 180 190 >>
Cardinal	101 one hundred [and] one
Ordinal	101st one hundred [and] first
Factorization	prime
Roman numeral	CI
Binary	1100101
Hexadecimal	65

1 In mathematics
2 In science
- 2.1 In astronomy
3 In other fields

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In mathematics

101 is the 26th prime number and a palindromic number (therefore also a palindromic prime). The next prime is 103, with which it comprises a twin prime (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 <math>3n - 1</math>.

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.

For a 3-digit number in base 10, this number has a relatively simple divisibility test. The 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. This might not be as simple as the divisibility tests for numbers like 3 and 5, and it might not be terribly practical, but it is simpler than the divisibility tests for other 3-digit numbers.

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

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In science

The atomic number of mendelevium, an actinide.
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).

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In astronomy

The Messier object M101, a magnitude 8.5 spiral galaxy in the constellation Ursa Major, also known as the Pinwheel Galaxy
The New General Catalogue object NGC101, a magnitude 12.9 spiral galaxy in the constellation Sculptor
The Asteroid 101 Helena.

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In other fields

101 is also:

At universities in the United States, sometimes the course number of basic or entry-level courses. By extension, it is informally used elsewhere to indicate things that are meant for beginners. At universities with four-digit course numbers, the equivalent course number is 1001 or 1010. Americans should be aware that this usage is limited elsewhere, and usage of the "101" label is likely to be met with baffled bemusement in many places such as in the United Kingdom.
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'.
Room 101 in George Orwell's novel Nineteen Eighty-Four.
The Hundred and One Dalmatians by Dodie Smith (and the various movie versions thereof).
The (arguably) tallest building in the world, Taipei 101.
The emergency telephone number for the police in Argentina.
The new telephone number for non-emergency calls in the United Kingdom, intended to relieve pressure on 999. (The Register)
101, a live album and movie by Depeche Mode.
101st kilometre, a condition of release from the Gulag in the Soviet Union
The (minimum) number of keys on a standard computer keyboard.
U.S. Route 101, which runs from California to Washington.
Unit 101 of the Israeli Defense Forces.
101st Airborne Division of the United States Army
In DisneySpeak, a ride breakdown in a Disney theme park.
For new checking accounts, the default number for the first check.