faster than LL?

[paulunderwood]

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:

? 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 ...

[science_man_88]

Originally Posted by paulunderwood

? 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

is your intent for D/d to get the largest one's out of the way first as D/2 will be the biggest exponent and will also be a divisor of D.

[paulunderwood]

Originally Posted by science_man_88

is your intent for D/d to get the largest one's out of the way first as D/2 will be the biggest exponent and will also be a divisor of D.

Some order is possible, I guess.