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 2018-08-02, 10:08 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 6,323 Posts ecm-toy now called ecm-effort I've pushed ecm-toy to my GitHub, https://github.com/fivemack/factorisation-tools Happy to hear feature requests!
 2018-08-10, 03:48 #2 WraithX     Mar 2006 23×59 Posts I ran the script with the example line: ecm-effort.py G174 1000@11 tractor It ran for a while and then produced the following output: Code: And now NFS beats them [[43, 15400], [110, 1400], [260, 1500]] 30..34 0.0000 0.0000 35..39 0.0000 0.0000 40..44 0.0000 0.0000 45..49 0.0006 0.0006 50..54 0.0594 0.0599 55..59 0.1709 0.2308 60..64 0.1844 0.4152 65..69 0.1645 0.5797 70..74 0.1434 0.7231 75..79 0.1255 0.8486 80..84 0.1107 0.9593 85..89 0.0407 1.0000 When I plot the given recommended curves 15400@43e6, 1400@110e6, and 1500@260e6 on my ecm probabilities webpage I get the attached plot, which has much different probability curves. Maybe we're not plotting the same thing? Or, if we are, then I'm not understanding why our numbers are different. Can you help me understand what the numbers in the above table mean? Attached Thumbnails
2018-08-10, 07:57   #3
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

6,323 Posts

Quote:
 Originally Posted by WraithX I ran the script with the example line: ecm-effort.py G174 1000@11 tractor It ran for a while and then produced the following output: Code: And now NFS beats them [[43, 15400], [110, 1400], [260, 1500]] 30..34 0.0000 0.0000 35..39 0.0000 0.0000 40..44 0.0000 0.0000 45..49 0.0006 0.0006 50..54 0.0594 0.0599 55..59 0.1709 0.2308 60..64 0.1844 0.4152 65..69 0.1645 0.5797 70..74 0.1434 0.7231 75..79 0.1255 0.8486 80..84 0.1107 0.9593 85..89 0.0407 1.0000 When I plot the given recommended curves 15400@43e6, 1400@110e6, and 1500@260e6 on my ecm probabilities webpage I get the attached plot, which has much different probability curves. Maybe we're not plotting the same thing? Or, if we are, then I'm not understanding why our numbers are different. Can you help me understand what the numbers in the above table mean?
The second column is the probability of a *remaining* factor of the given size for the given input after following the recipe, whilst I think you're plotting the probability, given that a number has a factor of some size, of finding it using the recipe.

So if you try the same recipe on larger and larger inputs with my code you will find the probability shifts towards the large factors, which are entirely intractable by ECM but exist with higher probability for larger inputs.

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