# 491

$t_title is "491"

$t_adjust_path is "/~caldwell/curios/"

$t_class is "prime"

$short is "491"

$nunber_id is "4088"

$t_meta['description'] is "One of many pages of prime number
curiosities and trivia. This page discusses 491
Come explore a new prime today!"

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]

(There are 5 curios for this number that have not yet been approved by an editor.)

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