# 2917

This number is a prime. The smallest of three primes formed by concatenating two consecutive double-digit Pythagorean primes, i.e., primes of form 4n+1. The other two are 4153 and 6173. [Loungrides] The smallest odd prime that is equal to number of polykites with n components (case n=9). [Gudipati] The largest known prime p equal to the digital length of a Mersenne prime, i.e., of the 21st Mersenne prime. Note that the order of this Mersenne prime, i.e., 21, followed by p and p followed by 21 are also primes, i.e., 212917 and 291721. [Loungrides] The smallest of only two primes of form n^2 + 1 that is concatenated from two double-digit primes, i.e., 54^2+1 = 2917. (The other is 3137 = 56^2+1). [Loungrides] Ten thousand is the 2917th positive integer with exactly one 1. Note that the sum of the first 2917 such numbers (12698731) is also prime. [Gaydos] Largest known prime of the form reversal(2^p)-1 such that 2^p-1 is a Mersenne prime, (case p=13). [Sariyar]

(There are 2 curios for this number that have not yet been approved by an editor.)