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Old 2009-09-26, 08:31   #1
fivemack
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Default YA aliquot-sequence-chasing script

Here's the python script I've been using to chase aliquot sequences.

The input file is

<number> <index in sequence>

then a long list of primes that turned out to be useful (order doesn't matter); just run python aliquot.py <input filename>, and it will add new useful primes to the bottom.

Features: incremental ECM, self-timing GNFS with recovery from not having enough relations, reasonably optimised crossover GNFS/MPQS and between different GNFS sizes, nice and small and written in fairly clear Python. Can be stopped at any point in ECM or GNFS and will restart at the same place; I haven't bothered tracking where the temporary directory for msieve is so it doesn't restart msieve MPQS jobs, but it should never run one of those for more than about half an hour.

Set the PROG_ variables at the top to something appropriate; you need ecm, msieve and a directory with gnfs-lasieve4I11e through gnfs-lasieve4I13e in it.
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File Type: txt aliquot.py.txt (8.9 KB, 361 views)

Last fiddled with by fivemack on 2009-09-26 at 08:33
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Old 2009-09-26, 09:30   #2
Andi47
 
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Default 11e vs. 12e?

Quote:
Originally Posted by fivemack View Post
gnfs-lasieve4I11e through gnfs-lasieve4I13e
For which ranges of input size (GNFS resp. SNFS) do you use 11e; where is the approx. crossover between 11e and 12e?

Last fiddled with by Andi47 on 2009-09-26 at 09:31
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Old 2009-09-26, 09:40   #3
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This is a pure-GNFS script; I found that 11e was better than MPQS-with-msieve or than 12e from about 85 to about 93 digits. Though I may be confounding things by using 23-bit large primes with 11e and 24-bit with 12e. Just not enough data points to be certain.
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Old 2009-09-26, 10:24   #4
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Quote:
Originally Posted by fivemack View Post
This is a pure-GNFS script; I found that 11e was better than MPQS-with-msieve or than 12e from about 85 to about 93 digits. Though I may be confounding things by using 23-bit large primes with 11e and 24-bit with 12e. Just not enough data points to be certain.
Consistent with my experience. See here
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Old 2009-09-28, 16:30   #5
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I am not understanding exactly what this does. Are you giving a list of primes you want to run ggnfs and ecm on? what does the aliqueit part do? Or are the primes, the known primes of that index of the given seq?
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Old 2009-09-28, 16:40   #6
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You give it the starting point, and you give it a list of primes which divide some numbers in the sequence after that starting point; it refactorises everything, it's just that the first method it uses is trial division by a set of primes known to include the factors, which is really quick.

And then having done the factorisation it computes sigma(n)-n and continues.
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