mersenneforum.org Factordb and aliquot sequences with useless size terms
 Register FAQ Search Today's Posts Mark Forums Read

 2017-08-28, 15:09 #1 garambois     "Garambois Jean-Luc" Oct 2011 France 24×43 Posts Factordb and aliquot sequences with useless size terms I recently worked on aliquot sequences with record size terms. The works are visible on this page, but sorry, in french : http://www.aliquotes.com/suite_terme...le_record.html Brief explanations of the principle before my two questions about factordb : It is quite easy to calculate several hundred terms of a strictly increasing aliquot sequence, each of those terms has more than 10 ^ 7 digits. If p is a prime and M=2^p-1 is a prime too (a Mersenne prime), N = 2^(p-1) * M, and N is a perfect number. So we have an aliquot sequence which starts on the number : j0 = N * z0 = 2^(p-1) * M * z0. PGCD(M,z0)=1 because z0 zi as long as zi
 2017-08-28, 17:43 #2 firejuggler     "Vincent" Apr 2010 Over the rainbow 22×11×61 Posts The db has no idea of what a perfect number is, or what to do with it Last fiddled with by firejuggler on 2017-08-28 at 17:44
2017-08-29, 07:16   #3
garambois

"Garambois Jean-Luc"
Oct 2011
France

68810 Posts

Quote:
 Originally Posted by firejuggler The db has no idea of what a perfect number is, or what to do with it

I assumed that it would be possible for db "to know" the Mersenne prime numbers in their "condensed" form.
For example, in the form :
2 ^ 74207281 - 1
Instead of that form which is written with more than 44 million digits :
451129962706 ... 557930315776
And especially that db is not obliged to check again the primality of this huge number first already known and famous.

But it must be very difficult to program things like that.

 2017-08-29, 07:28 #4 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2017-08-30, 08:04 #5 garambois     "Garambois Jean-Luc" Oct 2011 France 24×43 Posts OK, thank you for your answers !
2017-08-30, 08:11   #6
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

22×32×179 Posts

Quote:
 Originally Posted by garambois I recently worked on aliquot sequences with record size terms.
Given that the cofactors are the same whatever perfect number you're looking at (at least until you start getting the Mersenne prime as an accidental cofactor), why not compute the series of cofactors explicitly and just label the perfect number something symbolic?

 2017-08-30, 11:03 #7 garambois     "Garambois Jean-Luc" Oct 2011 France 24·43 Posts This is exactly what I did to get for example this aliquot sequence whose terms have more than 44677235 digits in base 10 : http://www.aliquotes.com/parfait_74207281_3.txt My problem is that I can not inform the database factordb with this aliquot sequence because factordb does not know the "symbolic" representation of the large prime numbers of Mersenne.
2017-08-30, 11:47   #8
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by garambois This is exactly what I did to get for example this aliquot sequence whose terms have more than 44677235 digits in base 10 : http://www.aliquotes.com/parfait_74207281_3.txt My problem is that I can not inform the database factordb with this aliquot sequence because factordb does not know the "symbolic" representation of the large prime numbers of Mersenne.
the real problem, is that it expands the numbers. it technically knows the mersenne primes up to the 35th but can't learn any more because the rest are over the expanded limit of 10 million characters. you can type any form into factordb search and it will find number of that form in theory. just not over a certain length.

2017-08-31, 19:03   #9
garambois

"Garambois Jean-Luc"
Oct 2011
France

24×43 Posts

Quote:
 Originally Posted by science_man_88 the real problem, is that it expands the numbers. it technically knows the mersenne primes up to the 35th but can't learn any more because the rest are over the expanded limit of 10 million characters. you can type any form into factordb search and it will find number of that form in theory. just not over a certain length.

OK, thank you !

You are right, I tried with success for the 35th Mersenne prime.
But no success for the 36th Mersenne prime !

I didn't know.

2^1398268*(2^1398269-1)*3 : SUCCESS

2^2976220*(2^2976221-1) * 3 : NO SUCCESS

2017-09-01, 00:06   #10
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2·4,813 Posts

Quote:
 Originally Posted by garambois If we look at the 3 previous aliquot sequences (2^520 * (2^521-1) * 3 and 2^74207280 * (2^74207281-1) * 3 and 2^216090 * (2^216091-1) * 3), we note that the sequence of the numbers zi are identical : only the perfect number N changes.
Of course they are identical. It is a bloody trivial result.

By uploading uselessly large algebraically trivial results into factordb, you are sabotaging users who use factordb for proper reasons.

2017-09-02, 00:21   #11
garambois

"Garambois Jean-Luc"
Oct 2011
France

12608 Posts

Quote:
 Originally Posted by Batalov Of course they are identical. It is a bloody trivial result. By uploading uselessly large algebraically trivial results into factordb, you are sabotaging users who use factordb for proper reasons.
Sorry, that was not my intention at all : I was not aware of it !

 Similar Threads Thread Thread Starter Forum Replies Last Post fivemack FactorDB 46 2021-02-21 10:46 fivemack Aliquot Sequences 4 2018-03-23 11:54 schickel FactorDB 18 2013-06-12 16:09 yoyo FactorDB 6 2012-01-12 20:58 schickel mersennewiki 0 2008-12-30 07:07

All times are UTC. The time now is 11:16.

Tue Dec 7 11:16:23 UTC 2021 up 137 days, 5:45, 0 users, load averages: 1.64, 1.76, 1.60