I developed a mathematical algorithm to generate prime numbers (tested as high as 10^60), that is ten times faster than any of known analogues. Is there any commercial application for that?

3answers

Cryptography: Look up the RSA encryption algorithm, it's used all over the place to protect financial transactions, etc.

Answered 7 years ago

A search of the web found that cryptography is the best use of prime numbers, you could contact RSA, the are one of the biggest security companies in cryptography, here are just two sites I found using this as my search term:

uses for prime number generation

http://math.stackexchange.com/questions/43119/real-world-applications-of-prime-numbers

if you algorithm is really as great as you claim, someone will be interested in it I am sure.

Answered 7 years ago

Generating primes

From Wikipedia, the free encyclopedia

In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers.

For relatively small numbers, it is possible to just apply trial division to each successive odd number. Prime sieves are almost always faster.

Prime sieves

A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin[1] (2004), and various wheel sieves[2] are most common.

A prime sieve works by creating a list of all integers up to a desired limit and progressively removing composite numbers (which it directly generates) until only primes are left. This is the most efficient way to obtain a large range of primes; however, to find individual primes, direct primality tests are more efficient[citation needed]. Furthermore, based on the sieve formalisms, some integer sequences (sequence A240673 in the OEIS) are constructed which they also could be used for generating primes in certain intervals.

Large primes[edit]

For the large primes used in cryptography, it is usual to use a modified form of sieving: a randomly chosen range of odd numbers of the desired size is sieved against a number of relatively small primes (typically all primes less than 65,000). The remaining candidate primes are tested in random order with a standard probabilistic primality test such as the Baillie-PSW primality test or the Miller-Rabin primality test for probable primes.

Alternatively, a number of techniques exist for efficiently generating provable primes. These include generating prime numbers p for which the prime factorization of p − 1 or p + 1 is known, for example Mersenne primes, Fermat primes and their generalizations.

Answered 4 years ago

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