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Old 2021-08-16, 01:18   #1
LOBES
 
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Default Factor Found P-1 Question

I don't find many factors using P-1, but when I do I always find it interesting. I have a question when looking at the results:

See: https://www.mersenne.ca/exponent/107731187

In the "P-1 results:" section, where it says "bits (76.408)", does this mean that if someone had simply TF'ed it from 76-77 that it would have found that same factor?
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Old 2021-08-16, 01:52   #2
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That is correct.
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Old 2021-08-16, 02:27   #3
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I've even found a factor like this.
M107599963 has a factor: 118142113851371427649409 (76.645 bits)
k: 2^6 × 83 × 179 × 13187 × 43783
I TFed to find this one, but it's really P-1-smooth
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Old 2021-08-16, 02:58   #4
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Quote:
Originally Posted by Uncwilly View Post
That is correct.
Thanks...because when I look at one like this:

https://www.mersenne.ca/exponent/107934373

And I see bits is 122.960, I think "Damn, that would take a LONG time to TF".
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Old 2021-08-16, 04:47   #5
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It takes quite a lot of P-1 to get one or more in the top 100 (>131.75 bits) of https://www.mersenne.ca/userfactors/pm1/1/bits
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Old 2021-08-16, 22:25   #6
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Quote:
Originally Posted by kriesel View Post
It takes quite a lot of P-1 to get one or more in the top 100 (>131.75 bits) of https://www.mersenne.ca/userfactors/pm1/1/bits
or quite a lot of luck
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Old 2021-08-17, 02:12   #7
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Quote:
Originally Posted by Uncwilly View Post
That is correct.
Indeed. All x.zzzz bits factors found by P-1 will be found also by TF, if you TF from x to x+1 bits.

However, viceversa is not true. If you find a factor by TF from x to x+1 bits, this factors will be found by suitable P-1 to some B1/B2 limit, only if the factors is B1/B2 smooth.

TF finds all factors between x and x+1 bits (unless you stop after the first factor found, obviously).

P-1 finds only "smooth" factors, regardless of their "bit" size.

So, the two methods have a non-void intersection, and a non-void non-intersection (i.e. there exist factors that will be found by both methods, and there exists factors that are very easy to find by one method, but close-to-impossible to find with the other - otherwise we won't use both methods here).

Last fiddled with by LaurV on 2021-08-17 at 02:17
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