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A124587 Primes p such that q-p >= 16, where q is the next prime after p. 1

%I #15 Dec 10 2023 19:02:16

%S 523,887,1069,1129,1259,1327,1381,1637,1669,1759,1831,1913,1933,1951,

%T 2113,2161,2179,2221,2251,2311,2477,2503,2557,2593,2803,2861,2971,

%U 3089,3121,3137,3229,3271,3373,3391,3413,3433,3469,3643,3739,3803,3889,3947,3967

%N Primes p such that q-p >= 16, where q is the next prime after p.

%H Charles R Greathouse IV, <a href="/A124587/b124587.txt">Table of n, a(n) for n = 1..10000</a>

%H K. Soundararajan, <a href="https://doi.org/10.1090/S0273-0979-06-01142-6">Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim</a>, Bull. Amer. Math. Soc., 44 (2007), 1-18.

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%F a(n) = n log n + O(n log^2 n). - _Charles R Greathouse IV_, May 05 2017

%t Prime[#]&/@Flatten[Position[Differences[Prime[Range[600]]],_?(#>14&)]] (* _Harvey P. Dale_, Dec 10 2023 *)

%o (PARI) is(n)=isprime(n) && nextprime(n+2)-n > 15 \\ _Charles R Greathouse IV_, May 05 2017

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 19 2006

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)