content:mathematics:cramers_conjecture

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# CramĂ©r's conjecture

CramĂ©r'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 CramĂ©r 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 CramĂ©r's original paper for *Acta Arithmetica*, 2: 23â€“46 can be found here.

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