# 157 (number)

 ← 156 157 158 →
Cardinalone hundred fifty-seven
Ordinal157th
(one hundred fifty-seventh)
Factorizationprime
Prime37th
Divisors1, 157
Greek numeralΡΝΖ´
Roman numeralCLVII
Binary100111012
Ternary122113
Octal2358
Duodecimal11112

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, with which 157 forms a prime triplet.
• a balanced prime, because the arithmetic mean of those primes yields 157.
• an emirp.
• a Chen prime.
• the largest known prime p which ${\frac {p^{p}+1}{p+1}}$ is also prime. (see ).
• 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.

In base 10, 1572 is 24649, and 1582 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.

157 is also: