X-Nico

4 unusual facts about prime number

Benaloh cryptosystem

Like many public key cryptosystems, this scheme works in the group $(\mathbb{Z}/n\mathbb{Z})^*$ where n is a product of two large primes.

Generalized inversive congruential pseudorandom numbers

A generalization for arbitrary composite moduli $m=p 1,\dots p r$ with arbitrary distinct primes $p 1,\dots ,p r \ge 5$ will be present here.

Okamoto–Uchiyama cryptosystem

The system works in the group $(\mathbb{Z}/n\mathbb{Z})^*$ , where n is of the form p²q and p and q are large primes.

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A fundamental difference of this cryptosystem is that here n is a of the form p²q, where p and q are large primes.

Andrzej Schinzel

A conjecture of his on the prime values of polynomials, known as Schinzel's hypothesis H, has attracted the attention of many number theorists.

In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A Horn, of The University of Utah, who proposed it in 1962.

Elliptic curve primality proving

Elliptic Curve Primality Proving (ECPP) is a method based on elliptic curves to prove the primality of a number (see Elliptic curve primality testing).

Fortunate number

A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that p_n# + m is a prime number, where the primorial p_n# is the product of the first n prime numbers.

Lemoine's conjecture

In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.

RSA problem

The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.