Brocard's conjecture asserts that there are at least four prime numbers between (p_n)² and (p_n+1)², where p_n is the n^th prime number, for every n ≥ 2.

It was first suggested by French mathematician Henri Brocard in the late 19th century.

As yet, it has neither been proved or disproved.

For technical details see : Wolfram Mathworld

Also see : Brocard's problemplugin-autotooltip__plain plugin-autotooltip_bigBrocard's problem

Brocard's problem asks to find integer values of n and m for which n! + 1 = m2, where n is the factorial.

Put another way:

Does the equation n!+1 = m2 have integer solutions other than 4, 5, 7?

It was first proposed by French mathematician Henri Brocard 1876.