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# 157 (number)

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 Title: 157 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 157 (number)

 ← 156 157 158 →
Cardinal one hundred fifty-seven
Ordinal 157th
(one hundred and fifty-seventh)
Factorization prime
Prime 37th
Divisors 1, 157
Roman numeral CLVII
Binary 100111012
Ternary 122113
Quaternary 21314
Quinary 11125
Senary 4216
Octal 2358
Duodecimal 11112
Vigesimal 7H20
Base 36 4D36

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

## Contents

• In mathematics 1
• In the military 2
• In music 3
• In sports 4
• In transportation 5
• In other fields 6
• References 8

## In mathematics

157 is a prime number. The next prime is 163 and the previous prime is 151, with which 157 forms a prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.

In base 10, 1572 is 24649, and 1582 is 24964, which uses the same digits. Numbers having this property are listed in  A072841. The previous entry is 13, and the next entry after 157 is 913.

157 is a repunit in base 12 (111), so it is a unique prime in the same base.

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 an emirp, a Chen prime, and the least irregular prime with index 2.

157 is the largest known prime p which \frac{p^p+1}{p+1} is also prime. (see  A056826)

157 is also: