1. This is a contradiction, because each Fermat number is clearly odd. 2. At this point we present the Fermat number transform ( FNT ). 3. The fermat number transform is given by 4. Mersenne and Fermat numbers are just special situations of \ Phi _ n ( 2 ). 5. He later factored the tenth and eleventh Fermat numbers using Lenstra's elliptic curve factorisation algorithm. 6. In 1854 he factored the sixth Fermat number as 2 64 + 1 = 67280421310721 ?274177. 7. ,331 prime factors of Fermat numbers are known, and 288 Fermat numbers are known to be composite. 8. ,331 prime factors of Fermat numbers are known, and 288 Fermat numbers are known to be composite. 9. In 1980 he and John Pollard factored the eighth Fermat number using a variant of the Pollard rho algorithm. 10. At this date, not only the 20th but also the 37th Fermat number is known to be composite.
