Verification of the Firoozbakht conjecture for primes up to four quintillion

TL;DR

This paper verifies the Firoozbakht conjecture for all primes up to four quintillion by analyzing prime gaps and applying bounds on the prime-counting function, providing computational evidence for the conjecture.

Contribution

It extends the verified range of the Firoozbakht conjecture up to four quintillion using computational methods and prime gap analysis.

Findings

Firoozbakht conjecture holds for primes up to 4×10^18

Utilizes prime gap data and prime-counting bounds for verification

Provides computational evidence supporting the conjecture's validity in large ranges

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