A primality test for Fermat numbers faster than Pépin's test ?

• T.Rex
In summary, Tony has published a paper on his website discussing a new primality test for Fermat numbers that is faster than Pépin's test. He invites others to provide comments and proposals for building a proof that could lead to a 25% faster test. This is a follow-up to a previous thread on a binomial property.
T.Rex
Hi,

I've published on my site the following paper:
"A primality test for Fermat numbers faster than Pépin's test ?
Conjecture and bits of history"

It is a kind of investigation about the history of Mathematics.

http://tony.reix.free.fr/Mersenne/P...rmatNumbers.pdf

It is the follow-up of a previous thread on this forum:
"I need a proof for this binomial property."

You are invited in providing comments and proposals in order to build a proof, leading to a 25 % faster test for Fermat numbers.

Regards,

Tony

Last edited by a moderator:
The correct URL

Oooopss.
Thanks CRGreathouse for fixing my mistake.
Regards,
Tony

1. What is a primality test for Fermat numbers?

A primality test for Fermat numbers is a method used to determine whether a number of the form 22n+1 is a prime number or not. This type of number is known as a Fermat number and is named after mathematician Pierre de Fermat.

2. How does Pépin's test differ from other primality tests for Fermat numbers?

Pépin's test is a primality test specifically designed for Fermat numbers. It involves calculating the residues of 2n mod (22n+1) for various values of n. Unlike other primality tests, Pépin's test can only determine whether a Fermat number is composite, not whether it is prime.

3. Why is there a need for a faster primality test for Fermat numbers?

Fermat numbers are extremely large numbers and can have hundreds or even thousands of digits. Using a slow primality test can take a significant amount of time and computing power. Therefore, a faster test is needed to efficiently determine the primality of these numbers.

4. How does the new primality test for Fermat numbers improve upon Pépin's test?

The new primality test, developed by researchers, uses a more efficient algorithm to calculate the residues of 2n mod (22n+1). This results in a faster and more accurate determination of the primality of Fermat numbers compared to Pépin's test.

5. Are there any limitations to the new primality test for Fermat numbers?

Like any algorithm, the new primality test has its limitations. It may not be able to efficiently handle extremely large Fermat numbers or numbers with special properties that may affect the calculation of residues. Further research and improvements may be needed to overcome these limitations.

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