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]
257 is the first 8-dimensional Centered Cube prime. Note that 257 = 1^8 + (1+1)^8. [Post]
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 only one of the known Fermat primes not to be of
the form
222...
+ 1. [Beedassy]
The largest prime consisting only of prime digits and the
absolute difference between any two of its digits is also
prime. Can you find the smallest? [Green]
257 = prime(|2 - 57|). It is the only Fermat prime with this property. [Firoozbakht]
As many as 257 Texian may have died at the Battle of the
Alamo, according to eyewitness accounts.
|
