157 (number)

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

← 156 157 158 →
← 150 151 152 153 154 155 156 157 158 159 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred fifty-seven
Ordinal	157th (one hundred fifty-seventh)
Factorization	prime
Prime	37th
Divisors	1, 157
Greek numeral	ΡΝΖ´
Roman numeral	CLVII, clvii
Binary	100111012
Ternary	122113
Senary	4216
Octal	2358
Duodecimal	11112
Hexadecimal	9D16

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 ${\displaystyle {\frac {p^{p}+1}{p+1}}}$ is also prime. (See OEIS: A056826).
• 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 OEIS: A046704)
• a prime index prime
• a super-prime (37 is prime)

In base 10, 157² is 24649, and 158² is 24964, which uses the same digits. Numbers having this property are listed in OEIS: A072841. 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.