304259

This number is a prime.

The smallest prime expressible as the sum of 45 consecutive terms of k{prime(k)}, which occurs for k = 15 to 59 (see A268467). It is simultaneously a Sophie Germain prime and a sexy prime. Additionally, the sums of the 1st, 3rd, and 5th powers of its digits yield three distinct primes: 23, 953, and 63473. [Ahmed]

The smallest prime p such that 120(p + n) + 1 is prime for the symmetric set n ∈ {0, 1, 3, 4, 5, 7, 8} (palindromic gaps 1, 2, 1, 1, 2, 1). [Ahmed]