fond of a factor? Urn yourself to become remains

[phillipsjk]

TIL my largest factor is not even in the top 300.


https://www.mersenne.ca/exponent/99797147


(32 digits, 105 bits)


https://www.mersenne.ca/pm1user/1


(need 27 digits, 121 bits to get in top 300).

[James Heinrich]

Originally Posted by phillipsjk

TIL my largest factor is not even in the top 300.

It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it!

[storm5510]

Originally Posted by James Heinrich

It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it!

It's clear you're not referring to the Top P-1 Factoring Producers list. I am #61 on that list. 117 factors in 5,569 tests. My largest factor, do date, is 39 digits. I didn't find it with P-1 though, but with ECM. I found that rather amazing.

[Miszka]

Originally Posted by James Heinrich

It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it!

I've found 1400+ P-1 factors, and 9 of them are in the top-300. My biggest factor is in 23rd position.

[Jwb52z]

P-1 found a factor in stage #1, B1=723000.
UID: Jwb52z/Clay, M100271917 has a factor: 77514042504246954650663761 (P-1, B1=723000)

86.003 bits.

[nordi]

2020-09-29 00:19 M235871 has a factor: 1354753690999656789045256961
2020-09-29 02:32 M339331 has a factor: 167369080256159138493834809
2020-09-29 06:29 M289789 has a factor: 75593232163993815783204345943
2020-09-29 07:45 M1871603 has a factor: 470279274234060910537


Individually they are nothing special, but 4 factors in 8 hours is really lucky. Normally I get 1 per day if things go well.

[James Heinrich]

M44053 has a 119.154 bit factor: 739364366231468476552737013655785457

Notable in that it's the first ECM factor I've found in 8 years (mostly for lack of trying).

Also an excellent segue to introduce the reworking of the Top Factors section of my site:
https://www.mersenne.ca/userfactors
This replaces the Top P-1 Factors section but now adds ECM factors as well.

[mathwiz]

Originally Posted by James Heinrich

Also an excellent segue to introduce the reworking of the Top Factors section of my site:
https://www.mersenne.ca/userfactors
This replaces the Top P-1 Factors section but now adds ECM factors as well.

Were all the factors here actually found by ECM?

[James Heinrich]

Originally Posted by mathwiz

Were all the factors here actually found by ECM?

Short answer: maybe.

Longer answer: PrimeNet thinks they were. Many of them certainly were. Unfortunately, back in the old days (2010 and older, perhaps more recently) PrimeNet didn't keep nearly as much data as it should about submissions -- in the early days PrimeNet would just "guess" on how a factor was found based on the size of the factor (if <xx-bit then TF, elseif <yy-bit then P-1, else ECM) so many older factors are incorrectly credited to ECM when they were actually found by P-1 or even TF. In generating the lists on mersenne.ca I have already filtered out the F-ECM results where the factor is smaller than the PrimeNet-default TF level. I'm fairly certain that all these are false-ECM results, but I'm also fairly certain that there are some false-ECM results still in there. The data has long since been lost (it was never recorded) so it's not easy to know for certain. Certainly small ones should likely be found by TF, very large ones by ECM, smooth ones by P-1, etc, but there's always a boundary area between the methods where a factor could conceivably be found by several methods.
But recent results (last... 5? years) should (nearly) all be accurate in terms of the correct factoring method, date of discovery, etc.

[LaurV]

5 or 6 of the first 10 are (S)NFS factors. They made big news at their times (see 1061, the most recent, it was discussed on this forum and acclaimed a lot when it came. When sieving was started (it was announced), people here were betting on how large the factors will be, or even on the fact that it will be a 2-way or 3-way split (in fact, I think I was the only one betting on 3-way split, for fun, just to be "different" haha, even if all the odds were against ). Maybe the others 3 or 4 are NFS, too. But PrimeNet doesn't record NFS stuff, so it recorded the factors like ECM. Maybe a mention is in order. The ECM all times records (for all types of numbers) are somewhere at 83 digits (if my memory serves right) and the first positions in tops are NOT mersenne numbers, so, for sure, those factors in top of your list aren't ECM.

[James Heinrich]

Originally Posted by LaurV

...so, for sure, those factors in top of your list aren't ECM.

If you want to provide me a sublist of factors from that list that cannot possibly be ECM, or perhaps some criteria that I could walk through the database and weed out the non-ECM ones (as I did with the below-TF-limit ones) I'd be happy to trim the database.