# 157

This number is a prime.

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(2*n* + 1) is less than phi(2*n*). [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 2^{p} + *p*^{3}, where *p* is prime. [Brown]

Two to the power 157 is the smallest "apocalyptic number," i.e., a number of the form 2^{n} 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 whose binary representation
(10011101_{2}) also forms an emirp in base ten. [Beedassy]

The smallest emirp among sums of distinct emirps. [Capelle]

157^{2} 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 smallest emirp number p such that reversal(p^3) is prime. [Firoozbakht]

The product 13 * 17 * 31 * 37 * ... * 149 * 157 = 2847632021876895870149 of consecutive emirps is pandigital. [Poo Sung]

5^{} is close to 157. [Wesolowski]

157 is the smaller prime of non-palindromic dual emirp pairs differing by 10: (157,167);(751,761). Note that reversal(157) =751 and reversal(167)=761. [Hardisky]

The smallest bisexual emirp, i.e., sharing two pairs of sexy primes: (151, 157) and (157, 163). [Loungrides]

The smallest concave emirp. [Loungrides]

Smallest emirp whose binary conversion (10011101 and its reversal 10111001) remain emirps when read in decimal. [Post]

157 is found in the inverse fine-structure constant formula: 157 - 337p/7 = 137.035 999 168, having three prime numbers with the prime constant p; within the uncertainty of the latest determination 137.035 999 173 (35) by Aoyama, T. et al Physical Review Letters, 109, 111807 (2012) arXiv:1205.5368v2. Reference: Sherbon, M.A. "Wolfgang Pauli and the Fine-Structure Constant," Journal of Science, Vol. 2, No. 3, pp.148-154 (2012). [Sherbon]

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]

If we use the English alphabet code a = 1, b = 2, c = 3, … , z = 26, then número primo = 157.