A322748Primes p such that q=p^2+p+1 is prime and (q^2+q+1)/3 is prime.

2, 3, 5, 41, 71, 383, 827, 1217, 1931, 2729, 2969, 3491, 3671, 4751, 5039, 6551, …

The first 3 terms appear at position 698.

…495853710507922796892589235420199561121290219608640…
position 698
termsstringfirst positionoccurrences
126100,002,410
2231610,000,834
3235698999,505
42354129,3449,885
5235417115,803,259115
62354171383not within 1,000,000,0000

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.