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A033919
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Odd k for which k+2^m is composite for all m < k.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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, Jun 14 2007 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Out-of-date information from Payam Samidoost's website corrected, using the current status on the dual Sierpiński problem from "Five or Bust," by Phil Moore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
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STATUS
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approved
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