Oppermann's conjecture is an unsolved problem in mathematics on the distribution of prime numbers.
It is named after Danish mathematician Ludvig Oppermann, who announced it in an unpublished lecture in March 1877.
[2] 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 prime-counting function must take unequal values at the endpoints of each range.
[1] Additionally, it would imply that the largest possible gaps between two consecutive prime numbers could be at most proportional to twice the square root of the numbers, as Andrica's conjecture states.
The conjecture also implies that at least one prime can be found in every quarter revolution of the Ulam spiral.