# 157

This number is a prime. The most commonly identified Shiga toxin-producing Escherichia coli in North America is E. coli O157. (157157 + 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] The product 13 * 17 * 31 * 37 * ... * 149 * 157 = 2847632021876895870149 of consecutive emirps is pandigital. [Poo Sung] 5 is close to 157. [Wesolowski] The smallest bisexual emirp, i.e., sharing two pairs of sexy primes: (151, 157) and (157, 163). [Loungrides] Smallest emirp whose binary conversion (10011101 and its reversal 10111001) remain emirps when read in decimal. [Post] The smallest emirp with an emirp as its prime index, i.e., π(157)=37. [Gaydos] The largest rating on the Saffir-Simpson Hurricane Wind Scale occurs at sustanined winds of 157 mph or higher. The 157 foot tower at Cape May has guided ships along the coast and into Delaware Bay since Darwin wrote "Origin of Species." [Roxanne] 157 = 4396/28 is a zeroless pandigital expression. [Gaydos] 157 is normally the total number of points for "tricks" in the Swiss card game known as Jass. [Perrenoud]

(There are 14 curios for this number that have not yet been approved by an editor.)