A082890 Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.

19609, 25471, 31397, 34061, 35617, 40289, 40639, 43331, 44293, 58831, 79699, 85933, 89689, 102701, 107377, 110359, 124367, 134513, 142993, 149629, 155921, 156157, 162143, 173359, 175141, 186481, 188029, 190409, 203461, 212701, 218287

Offset: 1

Author

Labos Elemer, Apr 17 2003

Keywords

• nonn

Examples

			If p = 492113 then r = 492227 and (r-p)/log(p) = 114/log(492113) = 8.69799..., so 492113 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082862, A082884, A082885, A082886, A082888, A082889, A082891.

Programs

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>5, Print[Prime[n]]], {n, 1, 50000}]
seq[len_] := Module[{p = 2, s = {}, c = 0}, While[c < len, q = NextPrime[p]; If[q - p > 5*Log[p], AppendTo[s, p]; c++]; p = q]; s]; seq[31] (* Amiram Eldar, Nov 04 2024 *)

Formula

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 5.