157 (one hundred [and] fifty-seven) is the number following 156 and preceding 158.

In mathematics

157 is:

  • the 37th prime number. The next prime is 163 and the previous prime is 151.
  • a balanced prime, because the arithmetic mean of those primes yields 157
  • an emirp
  • a Chen prime
  • the largest known prime p which <math>\frac{p^p+1}{p+1}</math> is also prime. (See ).
  • the least irregular prime with index 2.
  • a palindromic number in bases 7 (313<sub>7</sub>) and 12 (111<sub>12</sub>).
  • a repunit in base 12, so it is a unique prime in the same base
  • a prime whose digits sum to a prime. (see )
  • a super-prime (37 is prime)

In base 10, 157<sup>2</sup> is 24649, and 158<sup>2</sup> is 24964, which uses the same digits. Numbers having this property are listed in . The previous entry is 13, and the next entry after 157 is 913.

The simplest right angle triangle with rational sides that has area 157 has the longest side with a denominator of 45 digits.

In music

  • "157" is a song by Tom Rosenthal where the lyrics merely consist of the numbers from 1 to 157. The song was released on April Fools' Day, 2020.

References

  • The Number 157
  • Prime Curios: 157