A033919 Odd k for which k+2^m is composite for all m < k.

773, 2131, 2491, 4471, 5101, 7013, 8543, 10711, 14717, 17659, 19081, 19249, 20273, 21661, 22193, 28433, 35461, 37967, 39079, 40291, 41693, 48527, 60443, 60451, 60947, 64133, 75353, 78557

Offset: 1

Author

Dan Hoey

Keywords

• nonn

Comments

Related to the Sierpiński number problem.

In an archived website, Payam Samidoost gives these numbers and other results about the dual Sierpiński problem. It is conjectured that, for each of these k<78557, there is an m such that k+2^m is prime. Then a covering argument would show that 78557 is the least odd number such that 78557+2^m is composite for all m. The impediment in the "dual" problem is that it is currently very difficult to prove the primality of large numbers of the form k+2^m. It is much easier to prove the Proth primes of the form k*2^m+1 which occur in the usual Sierpiński problem. According to the distributed search project "Five or Bust", 40291 is the only value of k < 78557 for which there is currently no m known making k + 2^m a prime or probable prime. - T. D. Noe, Jun 14 2007 and Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009

Links

• Mersenneforum, Five or Bust
• Payam Samidoost, The dual Sierpinski problem search (Archive of the site at the Wayback Machine, original link is dead)
• Eric Weisstein's World of Mathematics, Sierpiński Number of the Second Kind.

Crossrefs

Cf. A067760, A076336.

Programs

Mathematica

t={}; Do[k=1; While[kT. D. Noe, Jun 14 2007 *)

Extensions

More terms from David W. Wilson

More terms from T. D. Noe, Jun 14 2007

Out-of-date information from Payam Samidoost's website corrected, using the current status on the dual Sierpiński problem from "Five or Bust," by Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009

Broken link to Payam Samidoost's website replaced with link to archive in the Wayback Machine by Felix Fröhlich, Jul 11 2014

26213 removed from sequence following an email message from Maximilian Pacher, who reports that 2^1271+26213 is prime. - N. J. A. Sloane, Dec 31 2015