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Brocard's conjecture

Brocard's conjecture asserts that there are at least four prime numbers between (pn)2 and (pn+1)2, where pn is the nth prime number, for every n โ‰ฅ 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.


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