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.
Honaker's Problem
See also
Cramér-Granville Conjecture, Prime TripletExplore with Wolfram|Alpha
References
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. 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.Referenced on Wolfram|Alpha
Honaker's ProblemCite this as:
Weisstein, Eric W. "Honaker's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HonakersProblem.html