MM43112609

[antimath]

Imagine MM43112609...we cant even prove MM127's primality...try seeing if MM(largest prime known) is prime!

[ewmayer]

Originally Posted by antimath

Imagine MM43112609...we cant even prove MM127's primality...try seeing if MM(largest prime known) is prime!

Both numbers could be trial-factored using the same kind of sieving approach to search for factors q = 2.k.p+1. The key differences are the number of candidates (distinct k's) one could try for a given computational effort, and method one would use to do the modmuls - MM127 calls for highly-optimized several-integer-word-based MUL, whereas M[any M-prime large enough to need a transform-based LL test] would also need a high-efficiency transform-based modmul, since each individual k-candidate is going to need effort of similar order as the full primality test of the M-prime exponent required. So for MM127 it's no big deal for an average PC to test all k's up to (say) 2^50, whereas for MM43112609 you'd need close a PC-year to test just one or two k's.

[Edit: Note we now have a subforum dedicated to testing double-Mersennes.]

[NBtarheel_33]

Originally Posted by antimath

Imagine MM43112609...we cant even prove MM127's primality...try seeing if MM(largest prime known) is prime!

You are interested in multiple-Mersenne numbers, yet you post under the name "antimath"?

[jasong]

Originally Posted by NBtarheel_33

You are interested in multiple-Mersenne numbers, yet you post under the name "antimath"?

lol, a few hours ago a new guy on Machinima Youtube channel tried to say his Youtube name, makesammichwoman, wasn't intended to be sexist, but just humorous.

Impulsiveness can be a real problem on the Internet, and I probably suffer from it more than the average 37 year old.

sorry for the off-topic, another thing I am pro at.

Oh, fun question: Could the final calculation of a Mersenne Primality test be used to more easily find a factor for the Mersenne number? And if not that calculation, what about the others? Like maybe the very first one? I barely comprehend the math, just thought I'd throw this out there.

[science_man_88]

Originally Posted by jasong

lol, a few hours ago a new guy on Machinima Youtube channel tried to say his Youtube name, makesammichwoman, wasn't intended to be sexist, but just humorous.

Impulsiveness can be a real problem on the Internet, and I probably suffer from it more than the average 37 year old.

sorry for the off-topic, another thing I am pro at.

Oh, fun question: Could the final calculation of a Mersenne Primality test be used to more easily find a factor for the Mersenne number? And if not that calculation, what about the others? Like maybe the very first one? I barely comprehend the math, just thought I'd throw this out there.

I could see how because if Mn=x*y then Mn=0 mod x and 0 mod y that's just my two cents I may come back with examples:

1736 mod 89 =45 so we'd expect 45 as the answer we get using 89 instead of M11 and I believe it's what we get. note that z mod x or z mod y is what you want.

[science_man_88]

Originally Posted by science_man_88

I could see how because if Mn=x*y then Mn=0 mod x and 0 mod y that's just my two cents I may come back with examples:

1736 mod 89 =45 so we'd expect 45 as the answer we get using 89 instead of M11 and I believe it's what we get. note that z mod x or z mod y is what you want.

(10:20)>4
%81 = 4
(10:20)>(%^2-2)%89
%82 = 14
(10:20)>(%^2-2)%89
%83 = 16
(10:20)>(%^2-2)%89
%84 = 76
(10:20)>(%^2-2)%89
%85 = 78
(10:20)>(%^2-2)%89
%86 = 30
(10:20)>(%^2-2)%89
%87 = 8
(10:20)>(%^2-2)%89
%88 = 62
(10:20)>(%^2-2)%89
%89 = 15
(10:20)>(%^2-2)%89
%90 = 45
(10:20)>4
%91 = 4
(10:20)>(%^2-2)%2047
%92 = 14
(10:20)>(%^2-2)%2047
%93 = 194
(10:20)>(%^2-2)%2047
%94 = 788
(10:20)>(%^2-2)%2047
%95 = 701
(10:20)>(%^2-2)%2047
%96 = 119
(10:20)>(%^2-2)%2047
%97 = 1877
(10:20)>(%^2-2)%2047
%98 = 240
(10:20)>(%^2-2)%2047
%99 = 282
(10:20)>(%^2-2)%2047
%100 = 1736
(10:20)>1736%89
%101 = 45

they match so 89 is a factor of 2047 it also works for 23. however this is slower than trial factoring because the residue is near Mn.

[ewmayer]

Originally Posted by jasong

Could the final calculation of a Mersenne Primality test be used to more easily find a factor for the Mersenne number?

No, although as with the Pe'pin test for Fermat numbers, the LL test residue can be used to effect an efficient probable-prime test on the remaining cofactor of a Mersenne number with 1 or more known factors.

To understand that, you need to learn to comprehend at least some basic math, as opposed to just do quasi-random numerical computations like some folks around here are so fond of. (Probably because plugging numbers into some compute software is so much easier than trying to 'comprehend' things.)