Let $(p\_{n})\_{n∈ℕ}$ be the sequence of consecutive primes. In P. Ribenboim, *The New Book of Prime Number Records*, Springer-Verlag, 1995, page 185, the author says:



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> A new conjecture by F. Firoozbakht, dating from about 1982, was communicated to me by the author; as far as I know, it remains unpublished. The conjecture is that the sequence $(p\_{n}^{(1/n)})\_{n≥2}$ is strictly decreasing.
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Have there been any new developments in this direction?



Have there been any new developments in the Firoozbakht conjecture?
The status as of 2010 is summarized in [On a new property of primes that leads to a generalization of Cramer's conjecture](http://arxiv.org/abs/1010.1399) . ([Firoozbakht's](http://en.wikipedia.org/wiki/Firoozbakht%27s_conjecture) conjecture is slightly stronger than [Cramér's,](http://en.wikipedia.org/wiki/Cramer%27s_conjecture) as explained [here.](http://www.primepuzzles.net/conjectures/conj_030.htm))


I find it noteworthy that [Farideh Firoozbakht](http://www.primepuzzles.net/thepuzzlers/Firoozbakht.htm) proposed this conjecture as an undergraduate student.


