37 (number)

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363738
Cardinalthirty-seven
Ordinal37th
(thirty-seventh)
Factorizationprime
Divisors1, 37
Roman numeralXXXVII
Binary1001012
Ternary11013
Quaternary2114
Quinary1225
Senary1016
Octal458
Duodecimal3112
Hexadecimal2516
Vigesimal1H20
Base 361136
 
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363738
Cardinalthirty-seven
Ordinal37th
(thirty-seventh)
Factorizationprime
Divisors1, 37
Roman numeralXXXVII
Binary1001012
Ternary11013
Quaternary2114
Quinary1225
Senary1016
Octal458
Duodecimal3112
Hexadecimal2516
Vigesimal1H20
Base 361136

37 (thirty-seven) is the natural number following 36 and preceding 38.

In mathematics[edit]

Thirty-seven is the 12th prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form

 p = \frac{x^3 - y^3}{x - y} \qquad \left(x = y + 1\right).

37 is the smallest prime that is not also a supersingular prime. It is a centered hexagonal number and a star number.

37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.

Every positive integer is the sum of at most 37 fifth powers (see Waring's problem).

37 appears in the Padovan sequence, preceded by the terms 16, 21, and 28 (it is the sum of the first two of these).

Since the greatest prime factor of 372 + 1 = 1370 is 137, which is obviously more than 37 twice, 37 is a Størmer number.

37 is the only two digit number in base 10 whose product, when multiplied by two, subtracted by one, and then read backwards, equals the original two digit number: 37×2=74, 74-1=73, 73 backwards is 37.

37 is the only two digit number in base 10 with the following property: The difference between the two digits equals the square root of the difference between the number itself and the least common multiple of the two digits.

In science[edit]

Astronomy[edit]

In sports[edit]

The jersey number 37 has been retired by several North American sports teams in honor of past greats:

In other fields[edit]

House number in Baarle (Belgian part)

Thirty-seven is:

See also[edit]

References[edit]

  1. ^ Adam Spencer, Adam Spencer's Book of Numbers. New York: Four Walls Eight Windows (2004): 61
  2. ^ http://catb.org/jargon/html/R/random-numbers.html

External links[edit]