A137869 Primes p with property that (p - previous prime) >= 6 and (next prime - p) >= 6.

53, 89, 157, 173, 211, 251, 257, 263, 293, 331, 337, 359, 367, 373, 389, 409, 449, 479, 509, 541, 547, 557, 563, 577, 587, 593, 607, 631, 653, 683, 691, 701, 709, 719, 727, 733, 751, 787, 797, 839, 919, 929, 947, 953, 977, 983, 991, 997, 1039, 1069, 1103, 1109, 1117

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

M:=1000; t1:=[];
for i from 2 to M do
p:=ithprime(i); o:=prevprime(p); q:=nextprime(p);
if p-o >= 6 and q-p >= 6 then t1:=[op(t1), p]; fi; od:
t1; # N. J. A. Sloane

Mathematica

lst={}; Do[p=Prime[n]; If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 20 2009 *)
Select[Partition[Prime[Range[200]], 3, 1], Min[Differences[#]]>5&][[;; , 2]] (* Harvey P. Dale, Oct 29 2023 *)

Prog

(PARI) p=q=2; forprime(r=2, 999, r-q>4 & q-p>4 & print1(q", "); p=q; q=r) \\ M. F. Hasler, May 02 2009
(Magma) [p:p in PrimesInInterval(3, 1200)|p-PreviousPrime(p) ge 6 and NextPrime(p)-p ge 6]; // Marius A. Burtea, Aug 11 2019

Crossrefs

These are the primes not in A167773.

Cf. A053070.

Sequence in context: A272367 A119289 A124282 * A096697 A033234 A266845

Adjacent sequences: A137866 A137867 A137868 * A137870 A137871 A137872

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 29 2008

Extensions

Edits and more terms from N. J. A. Sloane, May 02 2009

Status

approved