OFFSET
1,1
COMMENTS
Also, primes for which residue of (p-1)!+1 modulo p+d equals 1 if d=2,4,6,8,10 and 12. It is evident that all terms p in this sequence have that property, since p+d is composite for d in D = {2, 4, 6, 8, 10, 12}, and so with the least prime q dividing p+d, q <= (p+d)/q <= (p+d)/2 <= (p+12)/2 < p for p > 12 (smaller primes can easily be checked), so q divides (p-1)!. Hence it suffices to show that all p having that property are in this sequence. If not, then p+d is prime but p+d divides (p-1)!, a contradiction. - Charles R Greathouse IV, May 05 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18.
FORMULA
a(n) = n log n + O(n log^2 n). - Charles R Greathouse IV, May 05 2017
MATHEMATICA
Select[Partition[Prime@ Range@ 430, 2, 1], First@ Differences@ # >= 14 &][[All, 1]] (* Michael De Vlieger, May 12 2017 *)
PROG
(PARI) is(n)=isprime(n) && !isprime(n+2) && !isprime(n+4) && !isprime(n+6) && !isprime(n+8) && !isprime(n+10) && !isprime(n+12) && n>2 \\ Charles R Greathouse IV, Sep 14 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 19 2006
STATUS
approved