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Help me prove the Riemann Hypothesis

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1 Help me prove the Riemann Hypothesis on Mon Jun 19, 2017 2:23 pm

Kyx

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The Riemann Hypothesis states that:

All non-trivial zeroes of the zeta function have real part 1/2


But there is a much easier way to prove it, and win $1,000,000. Here's how:

Write a list of all the natural numbers, not including 1. The following uses all the natural numbers up to 20, not including 1:

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Remove each number that is divisible by a square number (not including 1^2)

2 3 5 6 7 10 11 13 14 15 17 19

With the following numbers, write all of their prime factors.

2-(2) 3-(3) 5-(5) 6-(3,2) 7-(7) 10-(5,2) 11-(11) 13-(13) 14-(7,2) 15-(5,3) 17-(17) 19-(19)


Replace each number that has an odd number of prime factors with the letter A. Replace each number that has an even number of prime factors with the letter B.

A A A B A B A A B B A A


If you can prove that the distribution of As and Bs is statistically random, you will have proved the Riemann Hypothesis, and won $1,000,000 from the Clay Institute (provided the results are published in a paper, you will win the $1,000,000 after two years of your work being scrutinised by mathematicians to make sure it is correct)

Why don't we try and do this?

Find the prime factors of numbers here: https://www.calculatorsoup.com/calculators/math/prime-factors.php

I will find the prime factors of the numbers 2 to 100

2 - 100: Kyx
101 - 200: spotify95
201 - 300: spotify95
301 - 400:Kyx
401 - 500:

Targets (will turn green once reached):

First 1,000 Numbers
First 10,000 Numbers
First 100,000 Numbers
First 1,000,000 Numbers
First 1,000,000,000 Numbers
ALL NUMBERS UP TO INFINITY


Please post your As and Bs below and state which numbers they are for, for example

This is for the numbers 2-20: A A A B A B A A B B A A

EDIT: It should be noted that this will not prove the Reimann hypothesis unless we can do it for all positive numbers, which is impossible using this method. This is designed to have some fun and to get more people interested in mathematics Very Happy

You can find all our results in one post here: http://quantumquasar.forumotion.com/t122-riemann-hypothesis-our-proof-so-far#1294



Last edited by Kyx on Thu Nov 23, 2017 12:17 am; edited 3 times in total

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2 Re: Help me prove the Riemann Hypothesis on Mon Jun 19, 2017 6:05 pm

Kyx

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This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA

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3 Re: Help me prove the Riemann Hypothesis on Wed Jun 21, 2017 1:38 pm

Kyx wrote:This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA


Awesome stuff Smile

Just to ask, if I come across with 2 or more prime factors that are the same (e.g. 2, 2, 17), would I have to list both of the 2's, and would they both be counted in the prime factors of the number (to determine the A or B)?

Thanks!

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4 Re: Help me prove the Riemann Hypothesis on Wed Jun 21, 2017 9:04 pm

Kyx

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spotify95 wrote:
Kyx wrote:This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA


Awesome stuff Smile

Just to ask, if I come across with 2 or more prime factors that are the same (e.g. 2, 2, 17), would I have to list both of the 2's, and would they both be counted in the prime factors of the number (to determine the A or B)?

Thanks!

You shouldn't come across two prime factors that are the same, because then that number would be divisible by a square number. We get rid of all numbers divisible by a square number (not including 1^2) Smile

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5 Re: Help me prove the Riemann Hypothesis on Wed Jul 05, 2017 11:16 pm

Kyx wrote:
spotify95 wrote:
Kyx wrote:This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA


Awesome stuff Smile

Just to ask, if I come across with 2 or more prime factors that are the same (e.g. 2, 2, 17), would I have to list both of the 2's, and would they both be counted in the prime factors of the number (to determine the A or B)?

Thanks!

You shouldn't come across two prime factors that are the same, because then that number would be divisible by a square number. We get rid of all numbers divisible by a square number (not including 1^2) Smile

Okay, thanks for clarifying. Silly me forgetting about the square numbers!

Please can you check this for me to make sure I am doing it right? This is for numbers 201 - 220. (Any crossed out are divisible by a square number.)

Of course, I will add the As and Bs (A for odd number of factors, B for even, am I right?) once I've done them all, and from now on I shall do it on scrap paper rather than my whiteboard, but this is just to check that I'm doing it properly!


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6 Re: Help me prove the Riemann Hypothesis on Thu Jul 06, 2017 9:17 am

Kyx

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spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA


Awesome stuff Smile

Just to ask, if I come across with 2 or more prime factors that are the same (e.g. 2, 2, 17), would I have to list both of the 2's, and would they both be counted in the prime factors of the number (to determine the A or B)?

Thanks!

You shouldn't come across two prime factors that are the same, because then that number would be divisible by a square number. We get rid of all numbers divisible by a square number (not including 1^2) Smile

Okay, thanks for clarifying. Silly me forgetting about the square numbers!

Please can you check this for me to make sure I am doing it right? This is for numbers 201 - 220. (Any crossed out are divisible by a square number.)

Of course, I will add the As and Bs (A for odd number of factors, B for even, am I right?) once I've done them all, and from now on I shall do it on scrap paper rather than my whiteboard, but this is just to check that I'm doing it properly!



All good yep Smile

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7 Re: Help me prove the Riemann Hypothesis on Thu Jul 06, 2017 9:40 pm

Kyx wrote:
spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:This is for the numbers 2 to 100: AAABABAABBAABBABAAABBBABBAAABABABBBAABBAABAAABBAABABBBABBBBA


Awesome stuff Smile

Just to ask, if I come across with 2 or more prime factors that are the same (e.g. 2, 2, 17), would I have to list both of the 2's, and would they both be counted in the prime factors of the number (to determine the A or B)?

Thanks!

You shouldn't come across two prime factors that are the same, because then that number would be divisible by a square number. We get rid of all numbers divisible by a square number (not including 1^2) Smile

Okay, thanks for clarifying. Silly me forgetting about the square numbers!

Please can you check this for me to make sure I am doing it right? This is for numbers 201 - 220. (Any crossed out are divisible by a square number.)

Of course, I will add the As and Bs (A for odd number of factors, B for even, am I right?) once I've done them all, and from now on I shall do it on scrap paper rather than my whiteboard, but this is just to check that I'm doing it properly!



All good yep Smile

Thanks Smile

Please can you check this as well? This is the complete set of numbers (201-300).
After a while, it becomes quite easy to remember, that anything divisible by 4 goes, anything divisible by 9 goes, anything divisible by 25 goes etc.

Note, I have used my phone to take the photo this time but in the future I will use my scanner on my printer.



Numbers from 201 to 300: BBBBBBBABBBBBBBAABAAAAABBAAAABBABBAAABBABABAAABABAAAAABABABBB. (If this doesn't match what is on the paper, the paper one is correct, as I checked that - can't guarantee if this has typos or not)

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8 Re: Help me prove the Riemann Hypothesis on Fri Jul 07, 2017 8:21 am

Kyx

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If you use the prime factor website in the OP, it should be correct Very Happy Smile

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9 Re: Help me prove the Riemann Hypothesis on Fri Jul 07, 2017 9:26 am

Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

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10 Re: Help me prove the Riemann Hypothesis on Fri Jul 07, 2017 11:17 am

Kyx

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spotify95 wrote:
Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

Then it should be perfect Very Happy Cool Razz

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11 Re: Help me prove the Riemann Hypothesis on Fri Jul 21, 2017 11:55 pm

Kyx wrote:
spotify95 wrote:
Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

Then it should be perfect Very Happy Cool Razz

Awesome!

Has anyone else decided to take this further with a few more numbers? Or do we need to do some more ourselves? Smile

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12 Re: Help me prove the Riemann Hypothesis on Sat Jul 22, 2017 10:47 am

Kyx

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spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

Then it should be perfect Very Happy Cool Razz

Awesome!

Has anyone else decided to take this further with a few more numbers? Or do we need to do some more ourselves? Smile

I think we'll have to do it ourselves Smile

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13 Re: Help me prove the Riemann Hypothesis on Sat Jul 22, 2017 2:24 pm

Kyx wrote:
spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

Then it should be perfect Very Happy Cool Razz

Awesome!

Has anyone else decided to take this further with a few more numbers? Or do we need to do some more ourselves? Smile

I think we'll have to do it ourselves Smile

That's fine; I don't know whether anyone else (such as ThatsAGoodOne349 or S2M) will chime in, if not then I'll do TAGO's 100-199 and we'll carry on from there Smile

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14 Re: Help me prove the Riemann Hypothesis on Sat Jul 22, 2017 3:00 pm

Kyx

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Admin
spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:
spotify95 wrote:
Kyx wrote:If you use the prime factor website in the OP, it should be correct Very Happy Smile

Yeah I did use the prime factor thing that you linked me to, otherwise I would have not had a clue!

Then it should be perfect Very Happy Cool Razz

Awesome!

Has anyone else decided to take this further with a few more numbers? Or do we need to do some more ourselves? Smile

I think we'll have to do it ourselves Smile

That's fine; I don't know whether anyone else (such as ThatsAGoodOne349 or S2M) will chime in, if not then I'll do TAGO's 100-199 and we'll carry on from there Smile

If you could ask them to go on here more often, that would be great. If not, then I'll do the next one Smile

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15 Re: Help me prove the Riemann Hypothesis on Sat Aug 19, 2017 9:18 pm

Okay I'm claiming 101 - 200 if that's okay Smile
Kyx, we'll have to get it done between the two of us (unless someone else will help us).

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16 Re: Help me prove the Riemann Hypothesis on Sun Aug 20, 2017 2:31 pm

Kyx

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spotify95 wrote:Okay I'm claiming 101 - 200 if that's okay Smile
Kyx, we'll have to get it done between the two of us (unless someone else will help us).

yep

And I'm claiming 301-400 then

Might not be done very soon sinc I'm busy but I'll try and get it snuck in sometime :p

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17 Re: Help me prove the Riemann Hypothesis on Mon Aug 28, 2017 10:54 pm

Kyx wrote:
spotify95 wrote:Okay I'm claiming 101 - 200 if that's okay Smile
Kyx, we'll have to get it done between the two of us (unless someone else will help us).

yep

And I'm claiming 301-400 then

Might not be done very soon sinc I'm busy but I'll try and get it snuck in sometime :p

Awesome stuff. I'm going to be busy tomorrow but if I get a moment soon then I'll do it. Might have to get used to how to do it!

Btw, how do we manage to get the "numbers up to infinity" bit done? How is that even possible?

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18 Re: Help me prove the Riemann Hypothesis on Thu Nov 23, 2017 2:45 am

Kyx

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For the numbers 301 - 400:

BBBBABAAABAABBABBBBBABBABBABAAAABABABBAAABAABABBAABABBBBBABA


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19 Re: Help me prove the Riemann Hypothesis on Fri Nov 24, 2017 3:46 pm

Kyx

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Admin
spotify95 wrote:
Kyx wrote:
spotify95 wrote:Okay I'm claiming 101 - 200 if that's okay Smile
Kyx, we'll have to get it done between the two of us (unless someone else will help us).

yep

And I'm claiming 301-400 then

Might not be done very soon sinc I'm busy but I'll try and get it snuck in sometime :p

Awesome stuff. I'm going to be busy tomorrow but if I get a moment soon then I'll do it. Might have to get used to how to do it!

Btw, how do we manage to get the "numbers up to infinity" bit done? How is that even possible?

It isn't. I have edited the OP to make this clear :p

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