Honaker's problem asks for all consecutive prime number triples with such that . Caldwell and Cheng (2005) showed that the only Honaker triplets for are (2, 3, 5), (3, 5, 7), and (61, 67, 71). In addition, Caldwell and Cheng (2005) showed that the Cramér-Granville conjecture implies that there can only exist a finite number of such triplets, that implies there are exactly three, and conjectured that these three are in fact the only such triplets.
See alsoCramér-Granville Conjecture, Prime Triplet
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ReferencesCaldwell, C. K. and Cheng, Y. "Determining Mills' Constant and a Note on Honaker's Problem." J. Integer Sequences 8, Article 05.4.1, 1-9, 2005. http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Caldwell/caldwell78.html.Crandall, R. and Pomerance, C. Prime Numbers: A Computational Perspective. New York: Springer-Verlag, p. 73, 2001.Koshy, T. Elementary Number Theory with Applications. San Diego, CA: Harcourt/Academic Press, p. 121, 2001.
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Weisstein, Eric W. "Honaker's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HonakersProblem.html