In 1982, Farideh Firoozbakht made an interesting conjecture that the sequence decreases i.e. for all ,

.

I present a stronger form of Firoozbakht’s conjecture.

**Conjecture**: *Let be the n-th prime and let* .

If the above conjecture is true than we can have explicit bounds on in terms of .

**Corollary 1**: *For every , there exists a sufficiently large natural number , which depends only on , such that for all ,*

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The above inequality would imply Cramer’s conjecture and in fact we have a stronger bound on the gap between consecutive primes.

**Corollary 2**: *For all sufficient large* ,

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**References**

[1] http://arxiv.org/abs/1010.1399

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