A074259 Gaps between primes p such that 2p+1 is also prime, i.e., Sophie-Germain primes A005384.

1, 2, 6, 12, 6, 12, 12, 30, 6, 24, 18, 42, 6, 12, 42, 6, 12, 30, 12, 66, 60, 12, 12, 48, 18, 84, 48, 12, 6, 24, 36, 24, 18, 48, 102, 42, 60, 6, 12, 18, 54, 120, 6, 60, 120, 30, 12, 30, 18, 12, 48

Offset: 1

Author

Jon Perry, Sep 20 2002

Keywords

• nonn

Comments

The first two consecutive identical gaps are 12, 12 between A005384(6..8) = (29, 41, 53).

The first three, four and five identical gaps in a row are equal to 30, 150 and 420, respectively, and occur after A005384(85) = 3299, A005384(29952) = 4866623, and A005384(32361449747) = 22081407211439. These were found by N. Fernandez and G. Resta, see link to discussion on the SeqFan mailing list. - M. F. Hasler, Sep 18 2016

Links

• M. F. Hasler, Table of n, a(n) for n = 1..7745
• Giovanni Resta, in reply to Harvey P. Dale and others, Re: Consecutive Sophie Germain primes with the same gap, SeqFan mailing list, Sep. 2016. (Click "Previous message" to see Neil Fernandez' earlier results.)

Crossrefs

First differences of A005384.

Programs

Mathematica

Select[Prime[Range[500]],PrimeQ[2#+1]&]//Differences (* Harvey P. Dale, Jul 15 2019 *)

PARI

c=0; forprime(p=1+L=2,10^6,if(isprime(2*p+1),write("primegap.txt",c++," "p-L); L=p)) \\ Edited by M. F. Hasler, Sep 16 2016

Extensions

Edited (name, offset, more terms) by M. F. Hasler, Sep 16 2016