Primes p at which (nextprime(p) - p) / (p - prevprime(p)) is a new record high.
3, 31, 113, 139, 199, 523, 1669, 2971, 7759, 12163, 16141, 25471, 40639, 79699, 149629, 173359, 265621, 404851, 838249, 1349533, 1895359, 5826001, 10343761, 19918753, 37369531, 42082303, 79167733, 151931911, 191186251, 192983851, 390932389, 516540163
1
In the paper below, Pintz proves theorems about these numbers, but does not display them. The ratio (nextprime(p) - p) / (p - prevprime(p)) for these 32 primes varies from 2 to 125.
T. D. Noe, Plot of 32 terms
Janos Pintz, On the ratio of consecutive gaps between primes, arXiv 1406.2658, Jun 10 2014.
(Mma) mn = 0; t = {}; Do[f = (Prime[n + 1] - Prime[n])/(Prime[n] - Prime[n - 1]); If[f > mn, mn = f; AppendTo[t, {Prime[n], f}]], {n, 2, 1000000}]; Transpose[t][[1]]
Cf. S000081 (record lows), S000082 (highs and lows).
nonn
T. D. Noe, Jun 12 2014