[seqfan] Primes in primes

[Tomasz Ordowski]

Dear SeqFans!

Primes of the form 1+2^1+2^2+...+2^(p-1) are Mersenne primes 2^p-1 for p =
2,3,5,7,13,17,19,...

Let's rise higher and define:

Primes p such that q =
1+2^(2-1)+2^(3-1)+2^(5-1)+2^(7-1)+2^(11-1)+...+2^(p-1) is prime.

Data: 2, 3, 5, 19, 2039, 2879, ... The last two primes I have from Robert
Israel.

The prime p = 19 gives the prime q = 332887 = 1010001010001010111.

The positions of 1's (read from the end): 1, 2, 3, 5, 7, 11, 13, 17, 19.

Cf. https://oeis.org/A080355

Best regards.

Thomas