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Legendre's Conjecture

Legendre's Conjecture concerns the distribution of Prime Numbersplugin-autotooltip__plain plugin-autotooltip_bigPrime Numbers

Since all other whole numbers (except 0) can be produced by multiplying together primes – they must be considered fundamental.

(1), 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 &etc

There are an infinite number of primes - as proved by Euclid around 300B.C. (

It asks : "Is there is a prime number between n2 and (n + 1)2 for every positive integer n. squares?"

It was first presented by French mathematician Adrien-Marie Legendre in the early 1800s - and to date has neither been proved or disproved.

Technical discussion here On Legendre’s Conjecture Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 2, 117–125


Also see : Oppermann's conjectureplugin-autotooltip__plain plugin-autotooltip_bigOppermann's conjecture

Oppermann's Conjecture concerns the distribution of Prime Numbers.

It was first suggested in 1877, and has not been proved or disproved since then.

The conjecture states that : for every integer x > 1, there is at least one prime number between


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