The first prime Lychrel number (a number that does not form a palindrome by repeatedly applying the reverse-then-add process). The first Lychrel number is the reversal of 691.
G. N. Watson proved that the Ramanujan tau function is divisible by 691 for almost all positive integers. [Terr]
The first irregular prime to appear in the numerator of a Bernoulli number.
The only known prime number which is a square when turned upside down (169) and another square when reversed (196). Note that 169 and 196 are the smallest consecutive squares using the same digits. [Capelle]
The smallest prime that can be written as the sum of thirteen consecutive primes. Recall that 691 is thirteen squared, turned upside down. [Post]
The number of prime unlabeled topologies (i.e., prime homeomorphism classes) on 6 points, and the largest known prime of that form. [Post]
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