157 (number)
157 (one hundred [and] fifty-seven) is the number following 156 and preceding 158.
In mathematicsEdit
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 Template:Oeis).
- the least irregular prime with index 2.
- a palindromic number in bases 7 (3137) and 12 (11112).
- a repunit in base 12, so it is a unique prime in the same base.
- a prime whose digits sum to a prime. (see Template:Oeis).
- a prime index prime.
In base 10, 1572 is 24649, and 1582 is 24964, which uses the same digits. Numbers having this property are listed in Template:Oeis. 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 musicEdit
- "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.