Colbert Number
A Colbert number is any prime number with more than 1000000 decimal digits whose discovery contributes to the long-sought after proof that k=78557 is the smallest Sierpiński number of the second kind. Colbert Numbers are named to honor Stephen T. Colbert.
There are currently five known Colbert numbers, as summarized in the following table.
Colbert number decimal digits
5359×2^(5054502)+1 1521561
19249×2^(13018586)+1 3918990
27653×2^(9167433)+1 2759677
28433×2^(7830457)+1 2357207
33661×2^(7031232)+1 2116617
The Seventeen or Bust distributed computing effort is conducting a search for the remaining six Colbert numbers (where x indicates the exponent is unknown).
unknown Colbert number decimal digits
10223×2^x+1 ?
21181×2^x+1 ?
22699×2^x+1 ?
24737×2^x+1 ?
55459×2^x+1 ?
67607×2^x+1 ?
See also
Sierpiński Number of the Second KindThis entry contributed by Louis Helm
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References
Caldwell, C. "The Prime Glossary: Colbert Numbers". http://primes.utm.edu/glossary/xpage/ColbertNumber.html.Helm, L.; Moore, P.; Samidoost, P.; and Woltman, G. "Resolution of the Mixed Sierpinski Problem." Integers: Elec. J. Combin. Numb. Th. 8, No. A61, 2008.Helm, L. and Norris, D. "Seventeen or Bust: A Distributed Attack on the Sierpinski Problem." http://www.seventeenorbust.com/.Referenced on Wolfram|Alpha
Colbert NumberCite this as:
Helm, Louis. "Colbert Number." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ColbertNumber.html