# 491

This number is a prime.

The smallest irregular prime having an irregularity index of 3. [Noe]

491 is a Sophie Germain prime. 491 is also a divisor of a Generalized Fermat Number, as 491 * (2^123281+1) divides GF(123280,10) = 10^(2^123280) + 1. [Carmichael]

10000^491-491 is the smallest titanic prime of form 10000^n-n, where n is prime. [Loungrides]

The sum of first two Lychrel numbers is prime, i.e., 196+295. [Loungrides]

It is conjectured that 491 is the smallest prime
not of the form *x*^{3} + *y*^{3}
+ 2*z*^{3}. [Wesolowski]

10000^491-491 is prime. 491 is the smallest number with this property. [Bajpai]

The smallest prime p such that 10*p + 3 is a perfect cube. [Ewing]

The smallest prime p such that the sum of digits of m^p is never equal to m except for m=1. [Gupta]