# 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 sustained winds of 157 mph or higher. The 157-foot tower at Cape May has guided ships along the coast and into Delaware Bay since the year Darwin wrote "Origin of Species." [Roxanne] The Australian rocket frog can cover 157 inches in one leap. [DK] 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 13 curios for this number that have not yet been approved by an editor.)