mersenne.ca

[Uncwilly]

And there are things like the table comparing the Prime95 factoring levels to GPU72 levels. And some other assorted items that I can't think of at the moment.

[James Heinrich]

Originally Posted by Viliam Furik

TJAOI report is not there.

Thanks, added.

Originally Posted by Uncwilly

And there are things like the table comparing the Prime95 factoring levels to GPU72 levels.

I'm not sure I remember what/where this is?

Let me know if you think of anything else missing from the list (I haven't yet had a chance to review it myself).

[Prime95]

Originally Posted by James Heinrich

I'm not sure I understand what you're trying to do with that lookup table in your code. But I don't speak Python well (or at all).

This is what I have in PHP:

function ECMeffortExpected() {
	return array(
		20 => array(    11000,    100),
		25 => array(    50000,    280),
		30 => array(   250000,    640),
		35 => array(  1000000,   1580),
		40 => array(  3000000,   4700),
		45 => array( 11000000,   9700),
		50 => array( 44000000,  17100),
		55 => array(110000000,  46500),
		60 => array(260000000, 112000),
		65 => array(800000000, 360000),
	);
}
function ECMeffort($curves) {
	// https://www.mersenneforum.org/showpost.php?p=573887&postcount=569
	// https://github.com/sethtroisi/misc-scripts/blob/main/mersenne/ecm_progress/test.py
	// Try to convert list of <B1, B2, number_of_curves> to t40, t45, t50 progress
	// original code by SethTro <https://www.mersenneforum.org/member.php?u=15870> 2021-03-16
	// translated to PHP by James Heinrich <james@mersenne.ca> 2021-03-17
	$completed = array();
	foreach (ECMeffortExpected() as $digits => $B1curvesNeeded) {
		$complete = 0;
		$curvecount = 0;
		list($min_B1, $curves_needed) = $B1curvesNeeded;
		foreach ($curves as $curvedata) {
			list($B1, $B2, $count) = $curvedata;
			if (($B1 >= $min_B1) && ($B2 >= (20 * $min_B1))) {
				$complete += ($count / $curves_needed);
				$curvecount += $count;
			}
		}
		if ($complete > 0.001) {
			$completed[$digits] = array($complete, $curvecount);
		}
	}
	return $completed;
}

function ECMprobabilityMissedSmallerFactor($curves_complete, $needed_curves) {
	// https://www.mersenneforum.org/showpost.php?p=573952&postcount=574
	// Probability of missed (smaller) factor is
	// (1 - 1/needed_curves) ^ curves_complete
	// which can be transformed to
	// math.exp(curve_count * math.log(1 - 1/curve_count))
	// or approximated by
	// (1/e)^(complete)
	//return exp($curves_complete * log(1 - (1 / $needed_curves)));
	return pow(1 - (1 / $needed_curves), $curves_complete);
}

If you could, please explain in more detail what your new code is doing, and what the bits of the lookup table are for. If you're real ambitious, feel free to rewrite your code in PHP so I can just plug it in.

I'm not happy with the above. My reading of this code is that B2 is practically ignored. Clearly B2=150*B1 is worth more than B2=70*B1. Someday we may well see B2=thousands*B1. IIUC the replacement PHP code has more B1/B2 data points but there are still lots of gaps leading to accumulated error.

What is needed is a way to convert odd B1/B2 combos into an equivalent number of "standard" curves.
This is what the PrimeNet server does to translate a curve where B2 != 100*B1. This came from Alex Kruppa who knows more about ECM than just about anyone.

// Our total_ECM_effort tracks curves assuming a B2 value of 100 * B1.
// If B2 is not 100 * B1, then adjust the reported B1 value up or down
// to reflect the increased or decreased chance of finding a factor.
//
// From Alex Kruppa, master of all things ECM, the following formula
// compensates for using B2 values that are not 100 * B1.
// 0.11 + 0.89 * (log_10(B2 / B1) / 2) ^ 1.5

function normalized_B1( $B1, $B2 )
{
	if ($B2 == 100 * $B1) return $B1;
	return $B1 * (0.11 + 0.89 * pow (log10 ($B2 / $B1) * 0.5, 1.5));
}

Alex did indicate this is an approximation... not sure over what range of B2/B1 that it is decently accurate.

[James Heinrich]

Originally Posted by Prime95

I'm not happy with the above....
What is needed is a way to convert odd B1/B2 combos into an equivalent number of "standard" curves.

I'm not sure what/how you suggest I integrate Alex's function?

[Prime95]

Originally Posted by James Heinrich

I'm not sure what/how you suggest I integrate Alex's function?

Something along the lines of replacing

			if (($B1 >= $min_B1) && ($B2 >= (20 * $min_B1))) {
				$complete += ($count / $curves_needed);
				$curvecount += $count;
			}

with

        // Normalize curvedata to B2 = B1 * 100
	$count *= $B1 * (0.11 + 0.89 * pow (log10 ($B2 / $B1) * 0.5, 1.5));
        // Adjust curve count if B1 > min_B1
        $count *=  $B1/$min_B1;
        // Add curve data to totals
	$complete += ($count / $curves_needed);
	$curvecount += $count;

I do not recommend implementing that willy-nilly. I think it deserves some further study. For example, if you run the suggested change with the GMP-ECM recommended curve counts for large B2/B1 ratios, does it report ~100% complete.

[SethTro]

Originally Posted by Prime95

I'm not happy with the above. My reading of this code is that B2 is practically ignored. Clearly B2=150*B1 is worth more than B2=70*B1. Someday we may well see B2=thousands*B1. IIUC the replacement PHP code has more B1/B2 data points but there are still lots of gaps leading to accumulated error.

What is needed is a way to convert odd B1/B2 combos into an equivalent number of "standard" curves.
This is what the PrimeNet server does to translate a curve where B2 != 100*B1. This came from Alex Kruppa who knows more about ECM than just about anyone.

Alex did indicate this is an approximation... not sure over what range of B2/B1 that it is decently accurate.

Thanks for suggesting the improvement!

You understand version two of the PHP code correctly in that it finds the largest curve with precomputed (B1, B2) less than the curves' (B1, B2) from a set of ~100 B1/B2 pairs with precomputed ECM effort.

At the time the vast majority of curves were done with only this small set of bounds (see #594)

A short term fix could be to augment more pre-computed pairs (with B2=100*B1, 200*B1, 400*B1, ...) the instructions are in #595

Alternatively I can compute a bunch of ECM-effort from (B1,B2) and compare with Alex's heuristic.

[Prime95]

Originally Posted by SethTro

Alternatively I can compute a bunch of ECM-effort from (B1,B2) and compare with Alex's heuristic.

Please do. If the heuristic is inaccurate, I'll need to change the server's PHP code.

[SethTro]

I coded up Alex's normalize_B1 and it's not great

https://colab.research.google.com/dr...Fq5tmL_k02wMuA

First attachment shows number of curves needed at various B1/B2 with B2 = {1,3,10,30,100,300,1000} * B1

Second attachment shows the predicted number of curves using B1 = normalized_B1(B1, B2), B2 = 100 * B1

Third attachment removes the B2=B1 points which have very high error

Fourth attachment I bounded the error and added a green dot if abs(error) < 10%

---

You can clone my colab (please share your version if you do) and play with this if you want.

It's possible the heuristic can be easily tweaked by adding a term based on B1

[Zhangrc]

Originally Posted by James Heinrich

Please elaborate with settings used, screenshot, etc to help me track down what you're seeing.

That's easy to reproduce:
https://www.mersenne.ca/prob.php?exp...bits=77&prob=4

[James Heinrich]

Originally Posted by Zhangrc

P-1 probability calculator on mersenne.ca seems to have been broken.
It now shows only 1x and 5x bounds.

Thanks, fixed.

[alpertron]

I've found a glitch in the GIMPS process visualization.

If you sum the numbers in the column <71 of the page https://www.mersenne.ca/status/tf/0/0/0/100000, the result does not match the number in the total row.

The same problem occurs on https://www.mersenne.ca/status/tf/0/0/1/400000