Possible values for k (in Mersenne factors)

[science_man_88]

Originally Posted by Batalov

"q I believe" is the new form of Q.E.D.?

I just wanted to make sure I wasn't forgetting any other possibility like a mod operation solution to the problem.

[Batalov]

Your post makes about as much sense as this test from Being John Malkovich, or closer to this forum these scribbles. Well, not much can be done about "Kathy", but can you before posting first shape your thoughts in some coherent form? hmm?

[science_man_88]

Originally Posted by Batalov

Your post makes about as much sense as this test from Being John Malkovich, or closer to this forum these scribbles. Well, not much can be done about "Kathy", but can you before posting first shape your thoughts in some coherent form? hmm?

okay let me put it this way:
1) Is there anything special above what is special about the k values in factors of normal mersenne factors, hidden within the k values of double mersenne factors ?

[pdazzl]

This is somewhat but not directly related to the topic; something I've noticed(checking mersenne.ca) is that it appears no mersenne prime (or primes that show up as factors in the Lucas Lehmer chain) are factors for any mersenne candidates. Is there a reason/property anyone can see for why this might be?


14
--- Factors
2
7

194
--- Factors
2
97


194^2-2
--- Factors
2
31
607


(194^2-2)^2-2
--- Factors
2
708158977


((194^2-2)^2-2)^2-2
--- Factors
2
127
7897466719774591


(((194^2-2)^2-2)^2-2)^2-2)
--- Factors
2
22783
265471
592897
2543310079
220600496383


((((194^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
113210499946729046527
71510428488234435849323250891975205208728978040847871


(((((194^2-2)^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
3867637345756894712411491994657791
4141173562324283362391211134773751434933274141271057666869711137355139870107549772907161419207982079



((((((194^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
1049179854847
27293256153178849431531258375109421840383

[science_man_88]

Originally Posted by pdazzl

This is somewhat but not directly related to the topic; something I've noticed(checking mersenne.ca) is that it appears no mersenne prime (or primes that show up as factors in the Lucas Lehmer chain) are factors for any mersenne candidates. Is there a reason/property anyone can see for why this might be?


14
--- Factors
2
7

194
--- Factors
2
97


194^2-2
--- Factors
2
31
607


(194^2-2)^2-2
--- Factors
2
708158977


((194^2-2)^2-2)^2-2
--- Factors
2
127
7897466719774591


(((194^2-2)^2-2)^2-2)^2-2)
--- Factors
2
22783
265471
592897
2543310079
220600496383


((((194^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
113210499946729046527
71510428488234435849323250891975205208728978040847871


(((((194^2-2)^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
3867637345756894712411491994657791
4141173562324283362391211134773751434933274141271057666869711137355139870107549772907161419207982079



((((((194^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2
--- Factors
2
1049179854847
27293256153178849431531258375109421840383

Yes, simply put, since s at that point has remainder of 0 when divided by these factors the next s will have 0^2-2 = factor-2 remainder from this factor, the next s after that has (-2)^2-2 which gets you to 2, 2^2-2 = 2 so you never move from 2 like the mersenne primes themselves so only sequences that hit 2 remainder a mersenne can possibly be have that mersenne divide by it but the only scenario I know that causes this is when the mersenne is prime and hence has no prime factors other than itself. it would have to divide the lower mersennes if that.

[science_man_88]

I know if we could factor any residue mod Mp we probably wouldn't need the LL test but is this feasible for low p values:

a = LL residue mod Mp

factor a and then eliminate k values based on k*p = (prime factors -1)/2 mod prime factors so if p is x mod prime factors k is y or z mod the prime factors ?

edit: I'm just realizing this again probably

[pdazzl]

Something I was trying out today was running an LL just on the factors without the embedded 2, was doing some compares against the original LL
(Doing this via ^2, *2, -1 instead of ^2-2), seems to result in smaller residues to calculate overall but unfortunately an extra operation.


2*(2^2)-1=7

2*(7^2)-1=97

2*(97^2)-1=18817

[TheMawn]

Originally Posted by science_man_88

I know if we could factor any residue mod Mp we probably wouldn't need the LL test but is this feasible for low p values:

I believe the residue is already mod M_P

[LaurV]

Channeling my inner RDS, why is this stuff in the math forum?

[science_man_88]

Originally Posted by TheMawn

I believe the residue is already mod M_P

I know , I did however end up writing it with an assumption I don't know why I made and that was a= 0 mod 2kp+1.

[Qubit]

Originally Posted by pdazzl

This is somewhat but not directly related to the topic; something I've noticed(checking mersenne.ca) is that it appears no mersenne prime (or primes that show up as factors in the Lucas Lehmer chain) are factors for any mersenne candidates. Is there a reason/property anyone can see for why this might be?

Other ways to see this are:
1. Recall that every two prime-exponent Mersenne numbers are coprime (that is, they share no common factor greater than 1). What you noticed follows.
or 2. Recall that if M(p) divides M(q) (p, q are odd primes) then , which is a contradiction since q cannot divide an even number.

(Also, unrelated, notice that p never divides .)