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 mnd9 2020-02-04 01:47

Lucky ECM results

Just curious is there a page listing "luckiest" ECM results i.e. factors found with more digits than typical for B1 value?

It came to my mind when I recently noticed I found a 36 digit factor with a curve at B1=50k

[url]https://www.mersenne.ca/exponent/1732831[/url]

I'm not a probability expert, so just curious how unlikely (or not) this is?

 VBCurtis 2020-02-04 02:32

The gratuitous factors thread has notable (?) achievements like these.

Finding a factor 10 digits larger than the bounds "aim" for isn't too difficult, provided enough curves are run. You can get a sense of how many curves it would be expected to take by invoking ecm with -v flag, and looking at the number of curves for 35 digits.

You can think of "how lucky" as the fraction of the expected number of curves compared to how many curves it took you.
As a wild guess, I would say that a t25 run at B1=50k has on the order of 2% chance to find a 36 digit factor (provided one is there to be found, of course).

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