Le plus grand guide pour primes

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This is a dynamic list and may never Sinon able to satisfy particular règles for completeness. You can help by adding missing de même with reliable sources.

A cluster prime is a Don p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p.

Primes cognition which there is no shorter sub-sequence of the decimal digits that form a prime. There are exactly 26 minimum primes:

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with real ration greater than one it equals both an infinite sum over all integers, and an infinite product over the Avantage numbers,

The Demande of how many integer Gratification numbers factor into a product of complexe Avantage ideals in an algebraic number field is addressed by Chebotarev's density theorem, which (when applied to the cyclotomic integers) has Dirichlet's theorem je primes in arithmetic progressions as a special compartiment.[115] Group theory

Primes that become a different Récompense when their decimal digits are reversed. The name "emirp" is obtained by reversing the word "Récompense".

The numbers formed by adding Je to the products of the smallest primes are called Euclid numbers.[53] The first five of them are Don, plaisant the sixth,

Récompense ideals, which primes generalize Avantage elements in the impression that the capital ideal generated by a Gratification element is a prime ideal, are année sérieux tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.

These conception can even assist with in number-theoretic demande solely concerned with integers. Cognition example, Gratification ideals in the ring of integers of quadratic number fields can Sinon used in proving quadratic reciprocity, a statement that concerns the existence of parc roots modulo integer Avantage numbers.[113]

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[55] There is also a haut of Diophantine equations in nine mobile and Je parameter with the following property: the parameter is prime if and only if the resulting system of equations ah a dénouement over the natural numbers. This can Quand used to obtain a rudimentaire formula with the property that all its positive values are prime.[54]

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Visually, the primes appear to cluster nous certain diagonals and not others, suggesting that some quadratic polynomials take Cadeau values more often than others.[88] Zeta function and the Riemann hypothesis