Journal of Integer Sequences, Vol. 18 (2015), Article 15.11.2

Upper Bounds for Prime Gaps Related to Firoozbakht's Conjecture

Alexei Kourbatov
15127 NE 24th St., #578
Redmond, WA 98052


We study two kinds of conjectural bounds for the prime gap after the kth prime pk: (A) pk+1 < pk1+1/k 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 → ∞ .

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(Concerned with sequences A002386 A005250 A111943 A182134 A182514 A182519 A205827 A233824 A235402 A235492 A245396 A246776 A246777 A246778 A246810 A249669.)

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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