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]
The smallest odd octavan prime, i.e., of the form p = x^8 + y^8. [Russo]
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]
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.
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]
Wildflower (a 2017 Philippine revenge drama television series) completed with a total of 257 episodes. [Cuenta]
(There are 6 curios for this number that have not yet been approved by an editor.)