Thread: faster than LL?
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Old 2016-08-01, 22:56   #12
paulunderwood
 
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Sep 2002
Database er0rr

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I have extended the nub of this thread a little further, but it still seems to be computationally useless.

For example b = 3 and p = 61 so that mp = 2^61 - 1, I ran this:

Code:
? p=61;mp=2^p-1;D=mp-1;V=factor(D,1000000);forbigdiv(D,d -> r=lift(Mod(3,mp)^(D/d));if(2^logint(r,2)==r,print(">>>"d))) 
>>>1
>>>61
>>>3
>>>183
>>>9
>>>549
Where "forbigdiv" is given here

This means 3^((mp-1)/549) == 2^n for some n OR 3^4200078341008550 == 2^n for some n, thus implying M61 is prime.

I will experiment with other bases b, for example p ...

Last fiddled with by paulunderwood on 2016-08-01 at 23:21
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