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.
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 Départements. Paris: Courcier, vol. 1, p. 139. [Olry]
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]