Let 
be the first prime which follows a prime
gap of 
between consecutive primes. Shanks' conjecture holds
that
 |
Wolf conjectures a slightly different form
 |
which agrees better with numerical evidence.
Shanks' Conjecture
See also
Prime Difference Function, Prime GapsExplore with Wolfram|Alpha
References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 21, 1994.Rivera, C. "Problems & Puzzles: Conjecture 009.-Shanks' Conjecture." https://www.primepuzzles.net/conjectures/conj_009.htm.Shanks, D. "On Maximal Gaps between Successive Primes." Math. Comput. 18, 646-651, 1964.Wolf, M. "First Occurrence of a Given Gap between Consecutive Primes." https://mwolf.pracownicy.uksw.edu.pl/firstocc.pdf.Referenced on Wolfram|Alpha
Shanks' ConjectureCite this as:
Weisstein, Eric W. "Shanks' Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ShanksConjecture.html