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