M12574579 Mersenne number exponent details

Residue

Status

L-L

D42999371802CA4A

double-checked

PRP

3D967E4521201BD5

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	2.3630	64.1791%	155000	2751250	0.1655	3.9628%	2.5285	65.5986%	1.4195%
PrimeNet	2⁶⁴	0.2831	62.5000%	55000	1700000	0.0807	4.2536%	0.3638	64.0951%	1.5951%
GPU72	2⁶⁸	4.7401	64.7059%	90000	2200000	0.1144	3.0930%	4.8545	65.7975%	1.0917%
Difference	-1	-2.3771	-0.5268%	+65000	+551250	+0.0511	+0.8698%	-2.3260	-0.1989%	-0.1989%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.3630

64.1791%

155000

2751250

0.1655

3.9628%

2.5285

65.5986%

1.4195%

PrimeNet

2⁶⁴

0.2831

62.5000%

55000

1700000

0.0807

4.2536%

0.3638

64.0951%

1.5951%

GPU72

2⁶⁸

4.7401

64.7059%

90000

2200000

0.1144

3.0930%

4.8545

65.7975%

1.0917%

Difference

-1

-2.3771

-0.5268%

+65000

+551250

+0.0511

+0.8698%

-2.3260

-0.1989%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12574579	199232394469926213905617	24	77.399	7922030410319352 2³ × 3 × 43 × 7676386056511	2016-04-05	43	7676386056511	4,432.0	233,477	436,071

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12574579

199232394469926213905617

77.399

7922030410319352
2³ × 3 × 43 × 7676386056511

2016-04-05

7676386056511

4,432.0

233,477

436,071

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-22T00:00:00	ANONYMOUS	v4_computers	155000	2751250		-		-	-	0.165	-	-	3.963%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.000	-	-
2000-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.283	-	-
2013-06-18T11:18:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.297	-	-
2014-03-28T12:19:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.594	-	-
2015-03-25T10:52:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.189	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.585 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.585 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	199232394469926213905617	1	0.585

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-04-05T02:32:51	Bruce	Desk7	50000	5000000	199232394469926213905617	77.399	1	2		1	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-01-15T00:00:00	ANONYMOUS	v4_computers	D42999371802CA4A	4.841
2004-11-22T00:00:00	ANONYMOUS	v4_computers	D42999371802CA4A	4.841

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-04-19T21:58:55

XZT

800G5Mini1

199232394469926213905617

3D967E4521201BD5

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 155000, B2 = 2751250 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront