# 523

This number is a prime. Together with 541 form the smallest two consecutive primes, such that the sums of the digits are equal. [Smart] A prime (called a RL prime) obtained by concatenating the odd primes alternately on the right and left of the first prime. [Russo] The only three-digit prime containing all three of the first three prime digits. [Patterson] 523! plus the 523rd prime is a titanic prime. [Gupta] The smallest prime formed by concatenating Honaker triplets. [Loungrides] The smallest prime that is followed immediately by 17 composite numbers. [Post] The largest prime with a prime number of distinct prime digits. Note that the remaining prime digit 7 when prefixed (7523) or appended (5237) to it forms two other primes, the reversal of whose product is also a prime (15979393) with all of the odd digits. [Beedassy] The only prime formed from three consecutive primes, one being the sum of the other two. [Silva] Smallest nontrivial prime partial sum of near-repdigit primes: 113 + 199 + 211 = 523 is prime. [Post] Israeli grandmaster Alik Gershon played 523 chess games to break the Guinness Book World Record for the most number of simultaneous matches in October 2010. [McCranie] The smallest prime formed by concatenating three distinct consecutive Fibonacci primes, i.e., 2, 3, 5. [Loungrides] Negative 5 plus 23 added to 523 is the next prime after 523. [Silva] The smallest prime formed from two adjacent primes with their difference inserted between them. [Loungrides] The only distinct-digit prime-digit prime that is a sum of mountain primes, i.e., 523=151+181+191. [Loungrides] The smallest prime-digit prime that is the sum of three consecutive primes in the sequence of prime-digit primes, i.e., 73+223+227=523. [Loungrides] The only distinct-digit prime-digit prime that can be represented as sum of successive mountain primes, i.e., 151+181+191. [Loungrides] The long-abiding abstruseness behind Ramanujan's mysterious partition congruences such as p(5n + 4) = 0 (mod 5), i.e., that 5 (= 2 + 3) divides p(n) for any n ending in prime square digits 22 and 32, got cracked down finally thanks to a 2011 major breakthrough by Ken Ono's team revealing the underlying fractal nature of p(n). [Beedassy] The smallest prime of the form x^x+n, where x is a positive integer and n a perfect number, i.e., 3^3+496. [Loungrides] 523 = 520*10^0+3 is prime. Note that 520*10^n+3 is not prime again until n = 826. [Sariyar] The only prime-digit prime that can be represented as sum of two successive narcissistic numbers, i.e., 153+370. [Loungrides] The ordered concatenation of the 3-digit prime-digit primes, without 523, is prime. [Loungrides]