A086977 Increasing peaks in the prime gap sequence A000230.

199, 1831, 5591, 30593, 81463, 82073, 162143, 173359, 404597, 542603, 544279, 1100977, 1444309, 2238823, 5845193, 6752623, 6958667, 11981443, 13626257, 49269581, 83751121, 147684137, 166726367, 378043979, 895858039, 1872851947

Offset: 1

Author

Harry J. Smith, Jul 26 2003

Keywords

• nonn

Comments

a(n) is the smaller of the two consecutive primes having a late occurring prime gap g = p_k+1 - p_k. All even gaps smaller than g occur at a smaller prime. Also, the next even gap g+2 also occurs earlier.

Examples

			1831 is in this list because the next prime is 1847, giving a prime gap of 16. All even gaps less than 16 occur before this (for smaller primes) and the next even gap, 18, also occurs earlier.
		

References

• P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.

Links

• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
• Eric Weisstein's World of Mathematics, Prime Gaps

Crossrefs

Cf. A000230, A001223, A001632, A038664, A086978, A086979, A086980, A002386.

Programs

Mathematica

lst={};b=max=2;Do[a=2;While[NextPrime@a-a!=2n,a=NextPrime@a];If[a=max,AppendTo[lst,b]];b=a;If[b>max,max=b],{n,40}];lst (* Giorgos Kalogeropoulos, Aug 18 2021 *)