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 $(4\times10^{18})$.