mersenneforum.org Periodicity of the congruence 1666667 mod 666667
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 2018-11-30, 17:35 #12 enzocreti   Mar 2018 10000011112 Posts Not random It is too difficult to predict which is the next. Simple questions sometimes require very complex explanations. Even Goldbach conjecture is simple to state, but to proof it it is extremely difficult...so how can I predict which is the next?
2018-11-30, 17:39   #13
science_man_88

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Quote:
 Originally Posted by enzocreti It is too difficult to predict which is the next. Simple questions sometimes require very complex explanations. Even Goldbach conjecture is simple to state, but to proof it it is extremely difficult...so how can I predict which is the next?
Using actual math, even Goldbach has heuristic arguments. You have a form of a number prove something about the form it Also has to take to be prime ...

2018-11-30, 17:41   #14
LaurV
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Jun 2011
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Quote:
 Originally Posted by science_man_88 for a pair of consecutive Mersennes mod 7, to create 6 mod 7 we have: (1,0) d=3 mod 6 (3,1) d=4 mod 6 (0,3) d does not exist.

Huh???

2018-11-30, 17:47   #15
science_man_88

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Quote:
 Originally Posted by LaurV Huh???
(1,0) means first Mersenne is 1 mod 7, second is 0 mod 7 d is a relationship for the number of digits for the second Mersenne.

similar for the others.

 2018-11-30, 17:48 #16 enzocreti   Mar 2018 52710 Posts 2,3,4,7,8,12,19,22,36,46,51,67,79,215,359,394,451,1323,2131,3336,3371,6231,19179=9*2131,39699,51456,56238,69660,75894,79798,92020,174968, 176006,181015,285019,331259,360787,366770,...,541456 these are the exponents found with Pfwg leading to a prime...look at them...if they are random, I am superman!
2018-11-30, 17:53   #17
science_man_88

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Quote:
 Originally Posted by enzocreti these are the exponents found with Pfwg leading to a prime...look at them...if they are random, I am superman!
define random ... https://en.m.wikipedia.org/wiki/Randomness

Last fiddled with by science_man_88 on 2018-11-30 at 17:53

2018-11-30, 18:03   #18
LaurV
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Quote:
 Originally Posted by science_man_88 (1,0) means first Mersenne is 1 mod 7, second is 0 mod 7 d is a relationship for the number of digits for the second Mersenne. similar for the others.
We got that, but where did you take "3 mod 6" from, and generally, where did you take "mod 6" from? Shouldn't that be "6 mod 7" and respective "4 mod 7" there??

Last fiddled with by LaurV on 2018-11-30 at 18:04

2018-11-30, 18:04   #19
science_man_88

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Quote:
 Originally Posted by LaurV We got that, but where did you take "3 mod 6" from, and generally, where did you take "mod 6" from?
Fermat and Euler ...

2018-11-30, 18:07   #20
LaurV
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Quote:
 Originally Posted by science_man_88 Fermat and Euler ...
it beats me... sorry...

2018-11-30, 18:10   #21
science_man_88

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Quote:
 Originally Posted by LaurV it beats me... sorry...
10 is coprime with 7, therefore an extension of Fermat's little theorem says that (10^6)^k for arbitrary natural number k will have remainder 1 on division by 7.

Last fiddled with by science_man_88 on 2018-11-30 at 18:11

 2018-11-30, 18:18 #22 LaurV Romulan Interpreter     Jun 2011 Thailand 23×5×229 Posts Right. Thanks. Just now I realized you were talking about d being 3 or 4 (mod 6). I was talking about 10^d being 4 or 6 (mod 7), which is the same thing. I have to remember not to read the forum at 1:15 AM, after a company party... I am going to bed now...

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