Periodicity of the congruence 1666667 mod 666667 - Page 2

enzocreti · 2018-11-30, 17:35

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?

science_man_88 · 2018-11-30, 17:39

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 ...

LaurV · 2018-11-30, 17:41

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???

science_man_88 · 2018-11-30, 17:47

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.

enzocreti · 2018-11-30, 17:48

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!

science_man_88 · 2018-11-30, 17:53

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

LaurV · 2018-11-30, 18:03

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??

science_man_88 · 2018-11-30, 18:04

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 ...

LaurV · 2018-11-30, 18:07

Quote:

Originally Posted by science_man_88

Fermat and Euler ...

it beats me... sorry...

science_man_88 · 2018-11-30, 18:10

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.

LaurV · 2018-11-30, 18:18

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...

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?

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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, 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...