Verification of the Firoozbakht conjecture for primes up to four quintillion

Abstract

If $p_k$ is the k-th prime, the Firoozbakht conjecture states that the sequence $(p_k{)}^{1/k}$ is strictly decreasing. We use the table of first-occurrence prime gaps in combination with known bounds for the prime-counting function to verify the Firoozbakht conjecture for primes up to four quintillion $(4\times 10^{18})$.

6 pages, 1 table. Endnotes added, URL ref.[5] updated

References in corpus (2)

• Estimates of Some Functions Over Primes without R.H.
• The distribution of maximal prime gaps in Cramer's probabilistic model of primes

Cited by in corpus (4)

• Strong version of Andrica's conjecture
• Some consequences of the Firoozbakht's conjecture
• Upper bounds for prime gaps related to Firoozbakht's conjecture
• Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap