Most people use only a fraction of the potential processing power of their computer. Many use a Screen Saver program making their computer an expensive room heater 95% of the time. We offer you the ability not only to warm your room but also to possibly find a place in history. The well-known project GIMPS conducts a search for huge Mersenne prime numbers. By joining our project, you will greatly increase the probability of being entered in the record books by finding a unique Fermat Number factor. We think that you will want to take advantage of our particular mathematics project: "Search for Fermat Number Divisors."

Fermat numbers have a very beautiful mathematical form: 2^2m+1. The first 5 numbers F₀=3, F₁=5, F₂=17, F₃=257, F₄=65537 are all prime. Having discovered this fact, Pierre de Fermat assumed that all numbers of this type were prime. But he was wrong. In 1732 after almost a century, Euler elegantly proved that F₅ had a factor: 641 and was therefore not prime. That year can be considered as the beginning of the search for divisors of other Fermat numbers. For 3 centuries more than 200 divisors were found. It has been proven that all divisors of Fermat numbers have the simple form: k.2ⁿ+1, where n > m+2. This corollary is being used for discovery of Fermat number divisors. Because of the scarcity and difficulty of finding these divisors, the person who discovers a new factor takes his place in history. Wilfrid Keller keeps a current, detailed account of all known Fermat factors and their discoverers. Professor Richard E. Crandall carried on a search project for factors of small Fermat numbers.

If you have some new results to submit to this search, please email the .LOG file to me.

Caution about WinPFGW usage for Fermat factor searching.