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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 ≥ 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 Br…
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