A137670 Prime numbers p such that p-b < p-a < p < p+a < p+b are prime for some a and b.

17, 23, 29, 37, 41, 43, 47, 53, 59, 61, 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, 313

Offset: 1

Author

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

Keywords

• nonn

Comments

It seems highly likely that all primes other than 2,3,5,7,19 are in this sequence. There are no further exceptions to 4 billion. - Charles R Greathouse IV, Apr 19 2010

Crossrefs

Cf. A071681.

Programs

Mathematica

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

Extensions

New name from Charles R Greathouse IV, Apr 19 2010