[seqfan] Primes in primes
Tomasz Ordowski
tomaszordowski at gmail.com
Fri Oct 26 19:05:57 CEST 2018
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
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