With the international Congress of mathematics of 1912 with Cambridge, Edmund Landau draws up a list of four basic problems in connection with the Prime numbers. These problems were characterized in its speech as being " unattackable in the actual position of the connaissances" and are from now on known as being the Problèmes of Pram . These problems are the following:

1. the Conjecture of Goldbach: can each entirety higher than 2 be written as the sum of two prime numbers?

2. the Conjecture of the prime numbers twins: does there exist an infinity of prime numbers p such as p +2 is first?
3. the Conjecture of Legendre: does there exist always at least a prime number between two square perfect consecutive?
4. Exists there an infinity of prime numbers p such as p − 1 is a perfect Square ? In other words: does there exist an infinity of prime numbers (called the prime number of Fermat generalized) of the form N ² + 1?

In 2007, the four problems are always unsolved.

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