1,1

Related to the Sierpinski number problem.

In an archived website, Payam Samidoost gives these numbers and other results about the dual Sierpinski 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 Sierpinski problem. According to the archived website, there is no m known that makes k+2^m a probable prime for the following eight k: 2131, 8543, 28433, 37967, 40291, 41693, 60451, 75353. - T. D. Noe (noe(AT)sspectra.com), Jun 14 2007

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Payam Samidoost, The dual Sierpinski problem search

t={}; Do[k=1; While[k<n && !PrimeQ[n+2^k], k++ ]; If[k==n, AppendTo[t, n]], {n, 3, 78557, 2}]; t - T. D. Noe (noe(AT)sspectra.com), Jun 14 2007

Cf. A067760, A076336.

Sequence in context: A114543 A133963 A133964 this_sequence A055521 A077077 A043519

Adjacent sequences: A033916 A033917 A033918 this_sequence A033920 A033921 A033922

nonn

Dan Hoey (Hoey(AT)aic.nrl.navy.mil)

More terms from David W. Wilson (davidwwilson(AT)comcast.net)

More terms from T. D. Noe (noe(AT)sspectra.com), Jun 14 2007