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Colbert Number

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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 numberdecimal digits
5359×2^(5054502)+11521561
19249×2^(13018586)+13918990
27653×2^(9167433)+12759677
28433×2^(7830457)+12357207
33661×2^(7031232)+12116617

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 numberdecimal 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 Kind

This 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 Number

Cite this as:

Helm, Louis. "Colbert Number." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ColbertNumber.html

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