Legendre's conjecture [SEP] named after
Legendre's conjecture
Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between "n" and ("n" + 1) for every positive integer "n". The conjecture is one of Landau's problems (1912) on prime numbers; , the conjecture has neither been proved nor disproved.
Prime gaps.
Legendre's conjecture is one of a family of results and conjectures related to prime gaps, that is, to the spacing between prime numbers
Oppermann's conjecture
Oppermann's conjecture is an unsolved problem in mathematics on the distribution of prime numbers. It is closely related to but stronger than Legendre's conjecture, Andrica's conjecture, and Brocard's conjecture. It is named after Danish mathematician Ludvig Oppermann, who posed it in 1882.
Statement.
The conjecture states that, for every integer "x"  1, there is at least one prime number between 
and at least another prime between 
It can also be phrased equivalently as stating that the