Honaker's Problem

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for p<=2×10^(17) 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 M<199262 implies there are exactly three, and conjectured that these three are in fact the only such triplets.

See also

Cramér-Granville Conjecture, Prime Triplet

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Caldwell, 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., 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.

Referenced on Wolfram|Alpha

Honaker's Problem

Cite this as:

Weisstein, Eric W. "Honaker's Problem." From MathWorld--A Wolfram Web Resource.

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