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Cramér's conjecture

Cramér's conjecture is stated as :

$${\displaystyle \limsup _{n\rightarrow \infty }{\frac {p_{n+1}-p_{n}}{(\log p_{n})^{2}}}=1,}$$

It was provided by the Swedish mathematician Harald Cramér in 1936, and provides a formula related to estimating the size of the spaces between consecutive prime numbers.

To date, there is no formal proof regarding whether or not the formula holds for all possible groups of prime numbers.

An archived copy of Cramér's original paper for Acta Arithmetica, 2: 23–46 can be found here.


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