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Corrigendum: Upper Bounds for Prime Gaps Related to Firoozbakht’s Conjecture

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Corrigendum: Upper Bounds for Prime Gaps Related to Firoozbakht’s Conjecture

Alexei Kourbatov www.JavaScripter.net/math

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

USA

[email protected]

1 Corrigendum

The proof of Theorem 3 in [K], as well as subsequent discussion, should reflect the true range of applicability of Eq. (11), necessitating the following changes (see [A]):

In inequality (11), replace “x≥5.43” with “x≥2634800823”

Remove “Let k >9.” after inequality (11).

In inequalities (12) and (13), remove “for pk≥29”.

Replace the last two sentences of the proof of Theorem 3 with

Now, exponentiation with base pk yields (1) for pk ≥ 2634800823. This completes the proof since for pk ∈[29,2634800823] both (1) and (10) hold unconditionally.

In the 2nd display formula on p. 5, replace “x≥5.43” with “x≥2634800823” . These changes have been incorporated in the arxiv paper arXiv:1506.03042v4.

References

[K] A. Kourbatov, Upper bounds for prime gaps related to Firoozbakht’s conjecture,Journal of Integer Sequences,18 (2015), Article 15.11.2.

[A] C. Axler, Corrigendum to “New bounds for the prime counting function”, Integers 16 (2016), A22, 15 pp. http://math.colgate.edu/~integers/vol16.html

http://math.colgate.edu/~integers/vol16.html

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