A390929 Primes p such that, if q,r,s are the next three primes, both p*q*r*s - (p+q+r+s) and p*q*r*s + (p+q+r+s) are primes.

2, 3, 2657, 2741, 3769, 7193, 13997, 14561, 17077, 26501, 34721, 36151, 44917, 54983, 56237, 68447, 79979, 80599, 92849, 96167, 97213, 102931, 104959, 109579, 120851, 131783, 137573, 158771, 159389, 176417, 209159, 209381, 213611, 237563, 241079, 241781, 264739, 268267, 278233, 280603, 283277

Offset

1,1

Links

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

Example

a(3) = 2657 is a term because the four consecutive primes starting with 2657 are 2657, 2659, 2663, 2671, and  2657 * 2659 * 2663 * 2671 - (2657 + 2659 + 2663 + 2671) = 50252184558049 and 2657 * 2659 * 2663 * 2671 + (2657 + 2659 + 2663 + 2671) = 50252184579349 are prime.

Maple

q:= 2: r:= 3: s:= 5:
Res:= NULL: count:= 0:
for i from 1 while count < 100 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  a:= p*q*r*s; b:= p+q+r+s;
  if isprime(a+b) and isprime(a-b) then
    count:= count+1; Res:= Res, p
  fi
od:
Res;

Mathematica

Select[Partition[Prime[Range[25000]], 4, 1], AllTrue[Times @@ # + {Plus @@ #, -Plus @@ #}, PrimeQ] &][[All, 1]] (* Paolo Xausa, Dec 01 2025 *)

Crossrefs

Intersection of A390918 and A390930.

Sequence in context: A137321 A066848 A324310 * A125612 A185156 A235935

Adjacent sequences: A390926 A390927 A390928 * A390930 A390931 A390932

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 24 2025

Status

approved