Paul Leyland is a British number theorist who has studied

integer factorization In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are suf ...

and

primality test A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whet ...

ing. He has contributed to the factorization of

RSA-129 In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories ...

, RSA-140, and

RSA-155 In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories i ...

, as well as potential

factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! +&n ...

s as large as 400! + 1. He has also studied Cunningham numbers,

Cullen number In mathematics, a Cullen number is a member of the integer sequence C_n = n \cdot 2^n + 1 (where n is a natural number). Cullen numbers were first studied by James Cullen in 1905. The numbers are special cases of Proth numbers. Properties In 1 ...

Woodall number In number theory, a Woodall number (''W'n'') is any natural number of the form :W_n = n \cdot 2^n - 1 for some natural number ''n''. The first few Woodall numbers are: :1, 7, 23, 63, 159, 383, 895, … . History Woodall numbers were first st ...

s, etc., and numbers of the form

x^y + y^x

, which are now called

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, 177, ...

s. He was involved with the

NFSNet In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than . Heuristically, its complexity for factoring an integer (consisting of bits) is of the form :\exp\left ...

project to use

distributed computing A distributed system is a system whose components are located on different computer network, networked computers, which communicate and coordinate their actions by message passing, passing messages to one another from any system. Distributed com ...

on the

Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, pub ...

from 2005 to 2008.

References

External links

Paul Leyland's home page
Living people Year of birth missing (living people) Number theorists 20th-century British mathematicians 21st-century British mathematicians {{UK-mathematician-stub