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:

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by F. Firoozbakht, dating from about 1982, was communicated to me by the author; as far as I know, it remains unpublished.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.

My question is about the new developpements in this direction.