The most commonly identified Shiga toxin-producing Escherichia coli in North America is E. coli O157.
(157^157 + 1)/(157 + 1) is prime. [Wagstaff]
The smallest prime number for which phi(2n + 1) is less than phi(2n). [Klee]
The start of the smallest string of consecutive equidigital numbers of length seven. [Santos and
Pinch]
The largest odd integer that cannot be expressed as the sum of four distinct nonzero squares with greatest common divisor 1.
The smallest prime of the form 2p + p3, where p is prime. [Brown]
Two to the power 157 is the smallest "apocalyptic number," i.e., a number of the form 2n that contains '666'. [Pickover]
Samuel Yates, who did an extensive work on the topic of prime period lengths, lived at 157 Capri-D Kings Point in Delray Beach, Florida.
157 is the smallest three-digit prime that produces five other primes by changing only its first digit: 257, 457, 557, 757, and 857. [Opao]
The smallest prime of form n*((n+1)^(n+2))-(n+3). [Vago]
157 is the smallest irregular prime having an irregularity index of two. [Noe]
Bus number 157 is hijacked in the cop thriller Dirty Harry. [May]
The smallest emirp among sums of distinct emirps. [Capelle]
1572 and (157 + 1)2 use the same digits.
The smallest balanced emirp. [Punches]
The fourth (and smallest prime) Koechel number of Mozart's
string quartets. The fourth largest (i.e., preantepenultimate) such number (KV 499) is again (the largest such) prime. [Hasler]
The smallest prime Köchel number of Mozart's string quartets (String Quartet No. 4 in C). [Hasler]
The smallest emirp whose sum of the digits is another
emirp. [Silva]
m = 157 is biggest (known) prime with property that p = m!/4-1 (278 digits) is prime too. Note that k = p and n = p+2 is biggest solution out of 157!/4 solutions of Diophantine equations (generalized Brown triples): 157! + k^2 = n^2. [Krug]
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