Let the Difference of successive Primes be defined by
, and by

N. L. Gilbreath claimed that for all (Guy 1994). It has been verified for and all Primes up to , where is the Prime Counting Function.

**References**

Guy, R. K. ``Gilbreath's Conjecture.'' §A10 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, pp. 25-26, 1994.

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1999-05-25