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Old 2020-07-10, 15:39   #353
garambois
 
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Yes, I'm still interested in the abundance/deficiency charts. But until base 28, that will be more than enough, no need to go any further.
Thank you very much !

Please, can you check with some base 2 exponents if you get the same thing as me, see in the attached file. That would reassure me for the future work !
Attached Files
File Type: gz base_2.tar.gz (733.9 KB, 1 views)
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Old 2020-07-10, 17:02   #354
EdH
 
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Quote:
Originally Posted by garambois View Post
Yes, I'm still interested in the abundance/deficiency charts. But until base 28, that will be more than enough, no need to go any further.
Thank you very much !

Please, can you check with some base 2 exponents if you get the same thing as me, see in the attached file. That would reassure me for the future work !
I added the prefix you used to my output lines and ran the entire base 2 as you did. My result file was identical to yours according to diff. I would say, both our programs have been validated, or at least, they both have the same error(s).

I'll upload the other abundance/deficiency files later today.
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Old 2020-07-10, 17:42   #355
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Quote:
Originally Posted by garambois View Post
Yes, I'm still interested in the abundance/deficiency charts. But until base 28, that will be more than enough, no need to go any further.
Thank you very much !
. . .
Here are bases 10 through 14:
Attached Files
File Type: txt 10-Stats.txt (8.6 KB, 2 views)
File Type: txt 11-Stats.txt (5.0 KB, 2 views)
File Type: txt 12-Stats.txt (7.3 KB, 2 views)
File Type: txt 13-Stats.txt (4.2 KB, 3 views)
File Type: txt 14-Stats.txt (7.5 KB, 2 views)
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Old 2020-07-10, 17:45   #356
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Quote:
Originally Posted by garambois View Post
Yes, I'm still interested in the abundance/deficiency charts. But until base 28, that will be more than enough, no need to go any further.
Thank you very much !
. . .
Here are bases 15 through 28:
Attached Files
File Type: txt 15-Stats.txt (4.4 KB, 2 views)
File Type: txt 17-Stats.txt (3.9 KB, 2 views)
File Type: txt 21-Stats.txt (3.4 KB, 2 views)
File Type: txt 24-Stats.txt (5.9 KB, 2 views)
File Type: txt 28-Stats.txt (6.5 KB, 2 views)
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Old 2020-07-11, 09:29   #357
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Many thanks for all Ed !

I downloaded all the files.
And I'm very happy to learn that our programs are giving the same results !

But what surprises me is that the data analysis I'm doing for a single database takes a lot of time. I must have underestimated the amount of work the computer would need to do all the tests I planned to do.
Base 2 analysis : 8 hours.
Base 3 analysis : I started 12 hours ago and it's not finished.
I will let you know the first results before I leave, as I'm not sure I'll be able to obtain everything before my trip at this pace !
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Old 2020-07-11, 11:39   #358
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I think I've come up with a new conjecture ! But I would be very surprised if the experts working on the factorization of Mersenne numbers did not know this conjecture !
Thank you for keeping me informed !



Unless I'm mistaken, I'm almost certain that the prime number 68625988504811774259364670661552948915363901845035416371912463477873783063 factors all numbers of the form 2^(269*i)-1 if i is an integer. I tried on factordb to factorize 2^2690000 and 2^(2690000-269) and it worked !
It's up to you to try again.

In the same way, I think I can affirm that the prime number 160619474372352289412737508720216839225805656328990879953332340439 factorizes all numbers of the form 2^(241*i) with i integer.

And I have several more like this, see the attached file.

The attached file starts like this :

base 2 prime 10567201 exponent 75
base 2 prime 10567201 exponent 150
base 2 prime 10567201 exponent 225
base 2 prime 10567201 exponent 300
base 2 prime 10567201 exponent 375
base 2 prime 10567201 exponent 450
base 2 prime 10567201 exponent 525

This means that the prime 10567201 is a prime factor that appears in the aliquot sequences 2^75, 2^150, 2^225... and more generally 2^(75*i) with integer i. And I don't know why, but this prime number always appears in the decomposition of the number at index 1 of the sequence. So it factors the numbers 2^(75*i)-1.

I didn't check with all the prime numbers in the file, but for the ones I did, it worked like this...

So the same should happen with all the prime numbers in the file...

12112549 should factor every 2^(164*i)-1.
13264529 should factor every 2^(47*i)-1.
...
...
...
68625988504811774259364670661552948915363901845035416371912463477873783063 should factor every 2^(269*i)-1.


I'll try to do the same work with the other bases...
Attached Files
File Type: gz Conjecture 2^i-1 factors.tar.gz (7.6 KB, 2 views)
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Old 2020-07-11, 15:40   #359
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Not conjecture, theorem. If p = ab (a, b > 1), then 2^a-1 and 2^b-1 both divide 2^p-1. Ergo, any number that divides 2^n-1 will also divide 2^(ni)-1, for any i ≥ 1. That's why exponents for Mersenne primes must themselves also be prime.

Last fiddled with by Happy5214 on 2020-07-11 at 15:45
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Old 2020-07-11, 16:21   #360
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Thank you very much Happy5214.
I suspected it was already known !

I continue my analysis to try to find something else on the other bases and also on a number of iterations greater than 1 to go further in the sequences ...
But I'm stuck, the data analysis by my programs for base 3 is still not finished after 20 hours of operation !
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Old 2020-07-11, 17:51   #361
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OK, page updated.
Base 30 added.

A lot of thanks to all.

The next update will not occur until early August.
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Old 2020-07-11, 18:16   #362
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Have a great trip! I'll see if I can form some intriguing questions while you're away.
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Old 2020-07-11, 19:39   #363
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Quote:
Originally Posted by EdH View Post
Have a great trip! I'll see if I can form some intriguing questions while you're away.

Thank you very much !
Good luck in your quest.


And don't forget to look at the Neowise Comet, it can be seen with the naked eye (but it's very low on the horizon !) : https://theskylive.com/c2020f3-info


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