| ||||
---|---|---|---|---|
Cardinal | thirty-seven | |||
Ordinal | 37th (thirty-seventh) | |||
Factorization | prime | |||
Prime | 12th | |||
Divisors | 1, 37 | |||
Greek numeral | ΛΖ´ | |||
Roman numeral | XXXVII | |||
Binary | 1001012 | |||
Ternary | 11013 | |||
Senary | 1016 | |||
Octal | 458 | |||
Duodecimal | 3112 | |||
Hexadecimal | 2516 |
37 (thirty-seven) is the natural number following 36 and preceding 38.
37 is the 12th prime number and the third unique prime in decimal.[1] 37 is the first irregular prime,[2] and the third isolated prime without a twin prime.[3] It is also the third cuban prime,[4] the fourth emirp, and the fifth lucky prime.[5]
In base-ten, 37 is a permutable prime with 73, which is the 21st prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime.
In moonshine theory, whereas all p ⩾ 73 are non-supersingular primes, the smallest such prime is 37.
There are exactly 37 complex reflection groups.
For a three-digit number that is divisible by 37, a rule of divisibility is that another divisible by 37 can be generated by transferring first digit onto the end of a number. For example: 37|148 ➜ 37|481 ➜ 37|814.[12]
Any multiple of 37 can be mirrored and spaced with a zero each for another multiple of 37. For example, 37 and 703, 74 and 407, and 518 and 80105 are all multiples of 37.
Any multiple of 37 with a three-digit repunit inserted generates another multiple of 37. For example, 30007, 31117, 74, 70004 and 78884 are all multiples of 37.
José María López used this number during his successful years in the World Touring Car Championship from 2014 until 2016. He still uses this number in Formula E since joining in 2016-17 season with DS Virgin Racing.
Thirty-seven is: