content:mathematics:brocards_conjecture

# Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

# Brocard's conjecture

Brocard's conjecture asserts that there are at least four prime numbers between (*p _{n}*)

^{2}and (

*p*p

_{n+1})^{2}, where_{n}is the

*n*

^{th}prime number, for every

*n*â‰¥ 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.

**Show another (random) article**

Suggestions for corrections and ideas for articles are welcomed :

**Get in touch!**

Further resources :