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Old 2018-07-18, 21:57   #9
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Sep 2003

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Originally Posted by a1call View Post
I would appreciate if someone would confirm that F33 is the smallest Fermat number with unknown primality status.
Yes. Factors are known for all Fermat numbers smaller than that, other than F20 and F24, but those two are known to be composite by the Pépin test, which is the counterpart to the Lucas-Lehmer test.

I would also appreciate if someone would work out the number of decimal-digits of F33.
Well, 233 is 8,589,934,592, so that's how many binary digits F33 has. To get the number of decimal digits, multiply that by log10(2) to get 2,585,827,973.

Are F31 and F32 known to be composite?
Yes, they have known small factors.

F31 has the factor 5463561471303 × 233 + 1

F32 has the factor 1479 × 234 + 1
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