37

37
Basic Information
Cardinal Number	thirty-seven
Ordinal Number	thirty seventh
Roman Numeral	XXXVII
Greek Numeral	ΛΖ´
Factorization	37
Standard Form	3.7 × 101
Different Representations
Binary Form	1001012
Ternary Form	11013
Quaternary Form	2114
Quinary Form	1225
Senary Form	1016
Septenary Form	527
Octal Form	458
Nonary Form	419
Undecimal Form	3411
Duodecimal Form	3112
Tridecimal Form	2B13
Quattuordecimal Form	2914
Quindecimal Form	2715
Hexadecimal Form	2516
Septendecimal Form	2317
Octodecimal Form	2118
Novemdecimal Form	1I19
Vigesimal Form	1H20
Unvigesimal Form	1G21
Duovigesimal Form	1F22
Trevigesimal Form	1E23
Quattuorvigesimal Form	1D24
Quinvigesimal Form	1C25
Hexavigesimal Form	1B26
Septenvigesimal Form	1A27
Octovigesimal Form	1928
Novemvigesimal Form	1829
Trigesimal Form	1730
Untrigesimal Form	1631
Duotrigesimal Form	1532
Tretrigesimal Form	1433
Quattuortrigesimal Form	1334
Quintrigesimal Form	1235
Hexatrigesimal Form	1136
Previous	31
Current	37
Next	41

37 is a prime number from 1-100. 37 has 2 factors, 1 and 37. It is the twelfth prime number, and the twelfth prime number from 1-100. The primorial of 37 is 7,420,738,134,810

Proofs

• — 37 is divisible by 1.

• — 37 is not divisible by 2-36.

• — 37 is divisible by 37.

• Therefore, 37 has 2 factors and is prime.

As an Exponent of Mersenne Number

2³⁷ - 1, which is the number 137,438,953,471, is divisible by 223, and is therefore a composite number.

Rela​tionship with other odd numbers

The numbers before

• 31 is the previous prime number.
  • The difference between 37 and 31 is 6. Therefore, they are sexy primes.
• 33 is a composite number. It can be factored into 3 x 11.
• 35 is a composite number. It can be factored into 5 x 7.

The numbers after

• The next odd number, 39, is not a prime number. It can be factored into 3 x 13.
• 41 is the next prime number.
  • The difference between 41 and 37 is 4. Therefore, they are cousin primes.
• 43 is the second next prime number.
  • The difference between 43 and 37 is 6. Therefore, they are sexy primes.
• 47 is the third next prime number.

Usage

Science

• 37 is the atomic number of rubidium.
• 37°C = ~99°F is the normal temperature of the human body.

Trivia

2 and 3 is medianes of smallest prime factors of all prime numbers, however 37 is mediane of second smallest prime factor of all prime numbers

• 37 is a mediane value for the second smallest prime factor of all prime numbers of an integer. (2,3,5,7,11,13,17,19,23,29,31,37,41,43,47......∞). So when we exclude 2, then 37 will be the median of the second smallest prime factor of all odd numbers, from 3, 5..... to thousands, millions, billions, googols, all the way to infinity.
• The secretary problem is known as the 37% rule by ${\frac {1}{e}}\approx 37\%.$
• 37 is an emirp and permutable prime, since its reverse, 73, is also prime.
  • Additionally, 37 is the 12th prime number, and 73 is the 21st prime number.
• 37 is left-truncatable (37, 7) and right-truncatable (37, 3).
  • 37 is also left-and-right-truncatable and two-sided.
• Since 37 is not part of a twin prime pair, it is an isolated prime.
• 37 is the value of the central cell of the smallest magic square that uses only prime numbers and 1.

Prime Numbers 1-1,000