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The largest Fermat prime F_{n} = 2^{2n} + 1 with n digits. [Beedassy] The largest known prime of the form n^{n} + 1. It is very likely that 2 and 5 are the only others. The smallest threedigit prime with distinct prime digits. [Moore] 257 = 2^{8} + 1, (2^{8} + 1)^{2}  2 and (((2^{8} + 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 F_{n} (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 onedigit nonprime 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] 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 Départements. Paris: Courcier, vol. 1, p. 139. [Olry] The only known Fermat prime that is not a member of a twin prime pair. [Honaker]
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