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157 (another Prime Pages' Curiosity) |
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The most common type of Escherichia coli infection that causes illness in people is E. coli 0157. (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 a string of consecutive economical numbers of length seven. [Santos and Pinch] The largest odd integer that cannot be expressed as the sum of four distinct non-zero squares with greatest common divisor 1. The smallest prime of the form 2p + p3, where p is prime. [Brown] 2157 is the smallest "apocalyptic number," i.e., a number of the form 2n that contains the digits 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]
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