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Old 2018-07-18, 04:03   #3
ATH
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Quote:
Originally Posted by siegert81 View Post
I'm assuming that various researchers have attempted to factor them and that their attempts have been considerably deep. Given they have effectively ruled out many small potential factors, what are the "probabilities" that these numbers are prime?
It might have been "deep" factoring considering the amount of work it took, but comparing to the size of F33, F34 and F35 it is close to nothing:
http://www.prothsearch.com/fermat.html#Search

For F33: k*235 searched to k=4.8*1017 and k*236 searched to k=7*1017 and lower for k*237, k*238 etc.

Now: 7*1017 * 236 is about 295 so 95 bits. Compare that to F33 = 28,589,934,592 + 1. So it has been factored (almost) up to the 90,000,000th root of F33.
For a Mersenne number in the 90M range the 90,000,000th root is 2, so that would correspond to no factoring at all on a 90M exponent.

For F34 and F35 it is even worse: ~295 vs 217,179,869,184 and 234,359,738,368

Last fiddled with by ATH on 2018-07-18 at 04:05
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