A031132 Record differences between n-th prime and (n+2)-nd prime.

3, 4, 6, 10, 12, 14, 18, 24, 28, 40, 42, 44, 48, 50, 56, 58, 72, 76, 80, 82, 100, 114, 116, 126, 138, 140, 160, 190, 200, 234, 236, 246, 248, 270, 306, 328, 330, 336, 340, 372, 376, 410, 436, 438, 450, 476, 502, 506, 524, 540, 546, 594, 600, 624, 678, 690, 700, 760, 780, 838, 900, 944, 972, 1014, 1016, 1032, 1152

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Examples

			The difference a(49) = 524 first occurs at prime(2158173265) - prime(2158173263) = 50949283633 - 50949283109 = 524. - _Jon E. Schoenfield_, Aug 29 2006
		

Crossrefs

Cf. A031131, A031132, A031133, A031134, A122412, A122413.

See A031133 for lower primes and A031134 for upper primes.

Programs

Mathematica

d = 0; lst = {}; {p, q, r} = {1, 2, 3}; Do[{p, q, r} = {q, r, Prime@n}; If[r - p > d, d = r - p; AppendTo[lst, {p, r}]; Print[{p, r-p, r}]], {n, 212550893}]; Last /@ lst - First /@ lst (* Robert G. Wilson v, May 17 2006 *)
dist = 0; n = 0; While[n<250000000, n++; tmp = Prime[n + 2] - Prime[n]; If[tmp > dist, dist = tmp; Print[tmp]];]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 08 2006 *)

Formula

a(n) = A031134(n) - A031133(n). - Robert G. Wilson v

Extensions

Extended (and first term added) by Patrick De Geest, Oct 15 2000

Further extended by Jud McCranie, Jan 03 2001 and again on May 18 2006

a(50)-a(52) from Jon E. Schoenfield, Sep 02 2006

a(53)-a(55) from Dmitry Kamenetsky, Jul 28 2008

a(55) corrected, a(56)-a(62) added by Dmitry Petukhov, Sep 22 2015

a(63)-a(67) added by Vladimir Chirkov and Natalia Makarova, Sep 24 2015, Sep 29 2015