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Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap

School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
Mathematics 2019, 7(8), 691; https://doi.org/10.3390/math7080691
Received: 9 May 2019 / Revised: 19 July 2019 / Accepted: 28 July 2019 / Published: 1 August 2019
The Firoozbakht, Nicholson, and Farhadian conjectures can be phrased in terms of increasingly powerful conjectured bounds on the prime gaps g n : = p n + 1 - p n . While a general proof of any of these conjectures is far out of reach, I shall show that all three of these conjectures are unconditionally and explicitly verified for all primes below the as yet unknown location of the 81st maximal prime gap, certainly for all primes p < 2 64 . For the Firoozbakht conjecture itself this is a rather minor improvement on currently known results, but for the somewhat stronger Nicholson and Farhadian conjectures this may be considerably more interesting. Sequences: A005250 A002386 A005669 A000101 A107578 A246777 A246776. View Full-Text
Keywords: primes; prime gaps; Firoozbakht conjecture; Nicholson conjecture; Farhadian conjecture primes; prime gaps; Firoozbakht conjecture; Nicholson conjecture; Farhadian conjecture
MDPI and ACS Style

Visser, M. Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap. Mathematics 2019, 7, 691. https://doi.org/10.3390/math7080691

AMA Style

Visser M. Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap. Mathematics. 2019; 7(8):691. https://doi.org/10.3390/math7080691

Chicago/Turabian Style

Visser, Matt. 2019. "Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap" Mathematics 7, no. 8: 691. https://doi.org/10.3390/math7080691

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