A176133 Pythagorean primes p (primes of form 4*k + 1) such that 6*p -+ 1 are twin primes.
5, 17, 137, 313, 373, 397, 577, 593, 653, 773, 1033, 1117, 1433, 1613, 2137, 2153, 2293, 2333, 2677, 3257, 3413, 3593, 3673, 4153, 4217, 4597, 4657, 5197, 5693, 5717, 6373, 6673, 6857, 6997, 7297, 8377, 8573, 9277, 9413, 9433, 10357, 10973, 11813
Offset: 1
Keywords
Examples
5 is a term since 5 = 4*1 + 1, and 6*5 - 1 = 29 and 6*5 + 1 = 31 are twin primes.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
lst={};Do[If[PrimeQ[p=4*n+1]&&PrimeQ[6*p-1]&&PrimeQ[6*p+1],AppendTo[lst,p]],{n,0,8!}];lst Select[4*Range[3000]+1,AllTrue[{#,6#+1,6#-1},PrimeQ]&] (* Harvey P. Dale, May 29 2025 *)