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

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2010

Keywords

• nonn

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

Crossrefs

Cf. A000040, A001359, A002144, A006512, A176131, A176132.

Programs

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 *)