- for all
Equivalently: for all
Another equivalent statement, for all is the motivating reason for the sequence A205827.
The conjecture is named after Farideh Firoozbakht, from the University of Isfahan, who stated it in 1982. If this conjecture is true, then the prime gap function satisfies which is sharper than Cramér's conjecture Currently, the largest stated verification was done by using "Maximal gaps between consecutive primes less than 4.444 * 1012" by Firoozbakht. Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended to all primes below 4×1018.
- Prime number theorem
- Andrica's conjecture
- Cramér's conjecture
- Legendre's conjecture
- Oppermann's conjecture
- Paulo Ribenboim 2004, p. 185
- Rivera, Carlos. "Conjecture 30. The Firoozbakht Conjecture". Retrieved 22 August 2012.
- Sinha, Nilotpal Kanti. "On a new property of primes that leads to a generalization of Cramer's conjecture". preprint. Retrieved 22 August 2012.
- Gaps between consecutive primes
- Ribenboim, Paulo (2004). The Little Book of Bigger Primes Second Edition. Springer-Verlag. ISBN 0-387-20169-6.