The book is now available! 257
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ The largest Fermat prime Fn = 22n + 1 with n digits. [Beedassy]

+ The largest known prime of the form nn + 1. It is very likely that 2 and 5 are the only others.

+ The smallest three-digit prime with distinct prime digits. [Moore]

+ 257 = 28 + 1, (28 + 1)2 - 2 and (((28 + 1)2 - 2)2 - 2) are prime. [Luhn]

+ 257 is the fourth of the five known Fermat primes; the other four are 3, 5, 17, and 65537. Many mathematicians believe that no more Fermat primes exist. [Dobb]

+ The smallest odd octavan prime, i.e., of the form p = x^8 + y^8. [Russo]

+ Using the primes up to 257 in a sieve of Eratosthenes on the set of integers leaves only 10% of numbers unfactored. [Rupinski]

+ More than 90% of all positive integers are composite numbers that have a lowest prime factor of 257 or less. [Schuler]

+ The smallest prime with the following property: It is the decimal value of either "FIFTY PLUS EIGHTYEIGHT" or "FIFTYEIGHT PLUS EIGHTY" (with A=1, B=2, ..., Z=26), both giving "ONEHUNDREDTHIRTYEIGHT". Summing up the character representations of that string again results in 257! [Vago]

+ Lab 257, a book by Michael C. Carroll, is (the subtitle asserts) "the disturbing story of the government's secret Plum Island germ laboratory."

+ The smallest prime of the form 128k + 1. Note that any prime factor of Fn (where n is greater than 2) is of this form.

+ The largest prime in a sequence of fifteen primes of the form 2t + 17, where t runs through the first fifteen triangular numbers, i.e., positive integers of the form n(n + 1)/2. [Silva]

+ The only prime of the form a^a + b^b where a and b are one-digit non-prime integers. [Loungrides]

+ The largest prime consisting only of prime digits and the absolute difference between any two of its digits is also prime. [Green]

+ 257 = prime(|2 - 57|). It is the only Fermat prime with this property. [Firoozbakht]

+ According to eyewitness accounts, as many as 257 Texian may have died at the Battle of the Alamo.

+ The only known Fermat prime that is not a deletable prime. [Wesolowski]

+ The only prime-digit prime whose absolute value of the differences between any two of its digits are also prime. [Loungrides]

+ The smallest prime-digit prime with distinct digits that is the sum of three prime-digit primes, i.e., (7+23+227). Note that the concatenation in order of these primes, i.e., 723227 is also prime. [Loungrides]

+ During his imprisonment in the Temple before being guillotined, King of France Louis XVI read 257 books. Reference: Nougaret PJB (1797) Histoire des Prisons de Paris et des D├ępartements. Paris: Courcier, vol. 1, p. 139. [Olry]

+ The only known Fermat prime that is not a member of a twin prime pair. [Honaker]

+ 257^100 is the smallest 100th power whose reversal is prime. [Gaydos]

+ Wildflower (a 2017 Philippine revenge drama television series) completed with a total of 257 episodes. [Cuenta]

+ 257 is the largest known prime of the form N^N+1. Note that if N^N+1 (for N>1) is a prime then it must be of the form 2^2^(2^m+m)+1 (m>=0). So according to the Fermat number factoring status, the next prime of the form N^N+1 (if it exists) is may be 2^2^70+1 and will have more than 8*10^20 digits (!). [Antonious]

+ The 257th, 258th, and 259th centuries are the smallest three consecutive centuries to have no years that are powers of other numbers, i.e., no squares, cubes, 4th powers, etc. [Gaydos]

+ In the Swiss card game Jass, the total number of points is 257 if one team takes all tricks in a game. [Perrenoud]

+ 1068349 is the smallest positive integer that together with its smallest prime factor (257) is pandigital. [Gaydos]

(There is one curio for this number that has not yet been approved by an editor.)




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