A137675 Prime numbers p such that p +- a, p +- b, p +- c and p +- d are prime numbers, where a, b, c and d are distinct positive integers with p > d, d > c, c > b and b > a.

37, 41, 43, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset

1,1

Comments

Conjecture: includes all primes > 61. - Robert Israel, May 24 2026

Contains all primes p such that 2*p can be written as the sum of 2 distinct primes in at least 5 ways (cf. A002375).

Links

Table of n, a(n) for n=1..52.

Maple

filter:= proc(p) local a, t;
  if not isprime(p) then return false fi;
  if isprime(2*p-3) then t:= 1 else t:= 0 fi:
  for a from 6 to p-4 by 6 do
    if isprime(p+a) and isprime(p-a) then
      t:= t+1; if t = 4 then return true fi fi od;
  false
end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, May 24 2026

Mathematica

s=""; q=1; For[i=2, i<10^2, p=Prime[i]; For[a=2, a<p, If[PrimeQ[p-a]&&PrimeQ[p+a], For[b=a+2, b<p, If[PrimeQ[p-b]&&PrimeQ[p+b], For[c=b+2, c<p, If[PrimeQ[p-c]&&PrimeQ[p+c], For[d=c+2, d<p, If[p>q&&PrimeQ[p-d]&&PrimeQ[p+d], (*Print[p, ":", a, ", ", b, ", ", c, ", ", d]; *)s=s<>ToString[p]<>", "; q=p]; d=d+2]]; c=c+2]]; b=b+2]]; a=a+2]; i++ ]; Print[s]

Crossrefs

Cf. A002375.

Sequence in context: A081645 A069963 A071855 * A161725 A100722 A093690

Adjacent sequences: A137672 A137673 A137674 * A137676 A137677 A137678

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2008; corrected May 02 2008

Status

approved