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Old 2018-11-30, 17:35   #12
enzocreti
 
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Default 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?
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Old 2018-11-30, 17:39   #13
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Quote:
Originally Posted by enzocreti View Post
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 ...
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Old 2018-11-30, 17:41   #14
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Quote:
Originally Posted by science_man_88 View Post
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???
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Old 2018-11-30, 17:47   #15
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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.
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Old 2018-11-30, 17:48   #16
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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!
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Old 2018-11-30, 17:53   #17
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Quote:
Originally Posted by enzocreti View Post
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
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Old 2018-11-30, 18:03   #18
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(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
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Old 2018-11-30, 18:04   #19
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Quote:
Originally Posted by LaurV View Post
We got that, but where did you take "3 mod 6" from, and generally, where did you take "mod 6" from?
Fermat and Euler ...
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Old 2018-11-30, 18:07   #20
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Originally Posted by science_man_88 View Post
Fermat and Euler ...
it beats me... sorry...
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Old 2018-11-30, 18:10   #21
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Quote:
Originally Posted by LaurV View Post
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
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Old 2018-11-30, 18:18   #22
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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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