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 2 terms appear at position 16.

14159265358979323846264338327950288419716…
position 16
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.