Legendre's conjecture

The Legendre conjecture ( named after the mathematician Adrien -Marie Legendre ) is a number-theoretic conjecture, which states that there is at least one prime between and for every natural number.

The conjecture is one of the Landau - problems - named after Edmund Landau, who counted them at the International Congress of Mathematicians in Cambridge in 1912 to the four at the time, not attackierbaren conjectures about prime numbers.

The assumption is unproven. The analogous conjecture for cubic numbers proved Albert Ingham: For each sufficiently large is between and at least one prime number.

Examples

For n = 1, 2, 3, 4, 5, the prime numbers 29 confirm p = 2, 5, 11, 17, the presumption.

Modification

After Brocardschen conjecture ( named after Henri Brocard ) there are at least four for each primes between and The nth prime number (ie, ...). For example, are between and the five primes

Also this assumption is unproven.