Upper Bounds for Prime Gaps Related to Firoozbakht's Conjecture
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We study two kinds of conjectural bounds for the prime gap after the
kth prime pk: (A) pk+1
and (B) pk+1 - pk <
log2pk - log pk - b for
k > 9.
The upper bound (A) is equivalent to Firoozbakht's conjecture. We
prove that (A) implies (B) with b = 1;
on the other hand, (B) with b = 1.17
implies (A). We also give other sufficient conditions for (A) that
have the form (B) with b → 1 as k → ∞ .
Full version: pdf,
(Concerned with sequences
Received June 18 2015;
revised versions received September 26 2015; October 1 2015.
Published in Journal of Integer Sequences, November 24 2015.
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