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.

## See also

Prime Difference Function,

Prime Gaps
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## 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." http://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." http://www.ift.uni.wroc.pl/~mwolf/.## Referenced
on Wolfram|Alpha

Shanks' Conjecture
## Cite this as:

Weisstein, Eric W. "Shanks' Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ShanksConjecture.html

## Subject classifications