157 (number)

← 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

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 ${\frac {p^{p}+1}{p+1}}$ 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.

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.

References

External links