cp's OEIS Frontend

The first 16 terms correspond to n from 0 to 15, which makes 25*n^2 + 25*n + 47 a prime-generating polynomial (see the link).

This is a prime-generating polynomial of the form s*n^2 + s*n + p, where s=k^2 and p is prime with s and p containing at most two digits. Prime-generating polynomials of this kind arise for k=1,2,3,5,7. This is the case of k=5; it generates most primes in a row out of the prime k's listed, with 12 for k=3,7, and 14 for k=2. See also A005846 and A007635 (k=1), and A048988 (k=2).

All terms are of the form 10m+7, with their next-to-last digits being 4 or 9.

The first 14 terms correspond to n from 0 to 13, which makes 8*n^2+8*n+31 a prime-generating polynomial (see the link).

This is a prime-generating polynomial of the form c*n^2+c*n+p, where c=2^k (k=0,1,2...) and p is prime with c and p containing at most two digits. Prime-generating polynomials of this kind arise for k=0,1,2,3 - see A005846 and A007635 (k=0), A007639 (k=1), and A048988 (k=2).

All terms are of the form 4m+3. Terms 1 and 4 are Mersenne primes (A000668).