mersenne.ca

[James Heinrich]

Originally Posted by Viliam Furik

it's more important for a table to have correct data than to look pretty.

However in this case, it both looks ugly and probably contains a good deal of incorrect data.

Also, the URL has changed to https://www.mersenne.ca/factored_counts_report_tf/

[Viliam Furik]

Originally Posted by James Heinrich

However in this case, it both looks ugly and probably contains a good deal of incorrect data.

Also, the URL has changed to https://www.mersenne.ca/factored_counts_report_tf/

You may be right about the incorrect data. In the 999M range, there are supposed to be 27515 factored exponents, however, the table row sums to only about 500.

Is it possible, that your query ignores the ones with factors less than 67, instead of making them appear like they are TFed to 67, and thus not making the 67 range be <=67?

[masser]

Originally Posted by Viliam Furik

Yes, that's what I am looking for.

I think the problem with no TF data can be solved by trusting the user TJAOI, that there are no more factors under 67 bits (technically he is at 66.990, but in a week or two he is done). Maybe some check-box "I trust TJAOI" could be made, such that when checked, considers all exponents to be TFed to at least 67 bits (or the current TJAOI-TF integer bit-level achieved), and when not, takes what is in the database. Or no check-box with a disclaimer that data is based on TJAOI's work.

Are you planning to TF some exponents that have known factors to higher bit levels? Besides TJAOI's efforts, you should also keep in mind the P-1 bounds (if you trust them; there are reasons why you might not) will occasionally make TF irrelevant at lower bit levels. For the very low exponents (say, < 3M or so), ECM makes additional TF even more non-productive.

[James Heinrich]

Originally Posted by Viliam Furik

For the P-1, yes, that is pretty much what I imagined.

Now available at https://www.mersenne.ca/factored_counts_report_pm1/ with separate reports for factored and unfactored exponents.

You can again access the latest report via
https://www.mersenne.ca/factored_cou..._pm1/?latest=f and/or
https://www.mersenne.ca/factored_cou..._pm1/?latest=n respectively.

Originally Posted by Viliam Furik

You may be right about the incorrect data. In the 999M range, there are supposed to be 27515 factored exponents, however, the table row sums to only about 500.

I will investigate this.

[Viliam Furik]

Originally Posted by masser

Are you planning to TF some exponents that have known factors to higher bit levels?

Yes, mostly the easy-to-do ones (for me that's <10 GHz-D).

Originally Posted by masser

Besides TJAOI's efforts, you should also keep in mind the P-1 bounds (if you trust them; there are reasons why you might not) will occasionally make TF irrelevant at lower bit levels.

Yes, I know. From my experience with factoring of the 10M range, I know that about half of the factors are easier to find by TF than P-1 if we compare the two methods. The other half is easier to find by P-1. Easy is defined by the GHz-D amount.

The ratio is most probably not 1:1, but close enough, I would say.

Originally Posted by masser

For the very low exponents (say, < 3M or so), ECM makes additional TF even more non-productive.

In this range, there are not many TFable exponents that fit my work criterion. I also have this weird uncomfortability with ECM, because I don't have a complete idea of how it works, only a rough idea.

[petrw1]

Originally Posted by Viliam Furik

Yes, I know. From my experience with factoring of the 10M range, I know that about half of the factors are easier to find by TF than P-1 if we compare the two methods. The other half is easier to find by P-1. Easy is defined by the GHz-D amount.

The ratio is most probably not 1:1, but close enough, I would say.

Some stats:
Top 500 totals in each of TF, P1 and ECM.
Interestingly the last column (GhzDays/Factor) does NOT vary a whole lot.

Work   GhzDays   Attempts    Succ.   GD/Att   GD/Succ
TF   134655501   34272856   710178     3.93    189.61
P1      790280     114778     3811     6.89    207.37
ECM     181452     356771     1150     0.51    157.78

[James Heinrich]

Originally Posted by Viliam Furik

I also have this weird uncomfortability with ECM, because I don't have a complete idea of how it works, only a rough idea.

A (very) rough analogy is the game Battleship -- you guess a random square/curve and see if it hits something. The more attempts you make in a particular area the more likely you are to find something hiding there. You might get lucky and get a hit on your very first attempt, there's also a chance you could use all your guesses and miss every one. Overall it allows finding factors larger than is practical for TF and that don't fit the rules for being found by P-1.

[Viliam Furik]

Originally Posted by petrw1

Interestingly the last column (GhzDays/Factor) does NOT vary a whole lot.

If I am interpreting the numbers correctly, that means I am about right. Is that correct?

Maybe the best way to test would be to parse the list of known factors and compare the minimal work amount for TF and P-1, as there is a bias towards the TF in the factoring process because the TF is done first.

[Viliam Furik]

Originally Posted by James Heinrich

A (very) rough analogy is the game Battleship -- you guess a random square/curve and see if it hits something. The more attempts you make in a particular area the more likely you are to find something hiding there. You might get lucky and get a hit on your very first attempt, there's also a chance you could use all your guesses and miss every one. Overall it allows finding factors larger than is practical for TF and that don't fit the rules for being found by P-1.

That I understand, but the part not clear to me is how do the bounds affect the outcome of the ECM, and how exactly is the factor found by the elliptic curve.

Bounds in the P-1 are pretty straightforward, but because ECM is based on chance, the straightforwardness goes away.

[James Heinrich]

Originally Posted by Viliam Furik

You may be right about the incorrect data. In the 999M range, there are supposed to be 27515 factored exponents, however, the table row sums to only about 500.

The bulk of the exponents in the upper ranges have known factors but no record of what factoring effort was done (makes sense, the small factors are trivial to find) so the field that tracks factoring on factored exponents wasn't set. I've set them all now to the assumption that TJAOI has found everything up to 2⁶⁷ (right now he's working between 66.987 and 66.990 so I'm jumping the gun slightly).

[VBCurtis]

Originally Posted by Viliam Furik

That I understand, but the part not clear to me is how do the bounds affect the outcome of the ECM, and how exactly is the factor found by the elliptic curve.

Bounds in the P-1 are pretty straightforward, but because ECM is based on chance, the straightforwardness goes away.

While I cannot speak to the "how is the factor found", I find it helpful to think of ECM as similar to P-1, except that ECM is sort of checking P - sigma (where sigma is the random seed). The effect of bounds on ECM and P-1 are just about the same. This is, to be sure, more analogy than mathematically-accurate representation.