Honaker,s Problem
المؤلف:
Crandall, R. and Pomerance, C.
المصدر:
Prime Numbers: A Computational Perspective. New York: Springer-Verlag,
الجزء والصفحة:
...
26-6-2020
981
Honaker's Problem
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.
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. https://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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