Fermat number

However, little is known about Fermat numbers with large "n".

It is generally believed that all but the first few Fermat numbers are composite.

In these papers, he proved that the 12th and 23rd Fermat numbers are composite:

A Fermat number is a special positive number.

However, F is composite and so are all other Fermat numbers that have been verified as of 2011.

Yves Gallot's proth.exe has been used to find factors of large Fermat numbers.

Distributed computing project 'Fermatsearch' has successfully found some factors of Fermat numbers.

If proven true, this would mean it is possible to generate infinitely many strong pseudoprimes to base 2 from the Fermat numbers.

No two Fermat numbers have common divisors.

Mathematics: The search for mathematically interesting prime numbers and Fermat numbers.

He also proved a result concerning Fermat numbers that is called Goldbach's theorem.

Today, Fermat numbers can be used to generate random numbers, between 0 and some value N, which is a power of 2.

The first few Fermat numbers are:

The Fermat numbers satisfy the following recurrence relations:

Factorizations of the first twelve Fermat numbers are:

He also gave his name to Pépin's test, a test of primality for Fermat numbers.

Let be the nth Fermat number.

Because of the size of Fermat numbers, it is difficult to factorize or to prove primality of those.

The next twenty-eight Fermat numbers, F through F, are known to be composite.

Fermat numbers are named after Pierre de Fermat.

This pattern breaks down after there, as the 6th Fermat number is composite, so the following rows do not correspond to constructible polygons.

Like composite numbers of the form 2'p' 1, every composite Fermat number is a strong pseudoprime to base 2 .

The rho algorithm's most remarkable success has been the factorization of the eight Fermat number by Pollard and Brent.

In mathematics, Pépin's test is a primality test, which can be used to determine whether a Fermat number is prime.

He later factored the tenth and eleventh Fermat numbers using Lenstra's elliptic curve factorisation algorithm.