M12 564 193 Mersenne number exponent details

Residue

Status

L-L

7213AA0FA5540815

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	76.1158	66.6667%	3000000	12199971630	372.6456	11.9678%	448.7614	70.6559%
Target	2⁶⁸	4.7440	64.7059%	90000	11000000	0.3821	3.0927%	5.1261	65.7974%
Difference	+4	+71.3718	+1.9608%	+2910000	+12188971630	+372.2636	+8.8752%	+443.6353	+4.8585%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

76.1158

66.6667%

3000000

12199971630

372.6456

11.9678%

448.7614

70.6559%

Target

2⁶⁸

4.7440

64.7059%

90000

11000000

0.3821

3.0927%

5.1261

65.7974%

Difference

+71.3718

+1.9608%

+2910000

+12188971630

+372.2636

+8.8752%

+443.6353

+4.8585%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22	ANONYMOUS	v4_computers	155000	2751250		-		-	-	0.165	-	-	2.268%
2023-03-26	Naegi Makoto	5950X	3000000	12199971630		-		-	-	372.6	-	-	11.968%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-22	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.000	-	-
2000-03-22	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2000-04-05	lalera	v4_computers	2¹	2⁶²		-	-	0.049	-	-
2000-04-12	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.283	-	-
2013-06-18	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.297	-	-
2014-03-28	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.595	-	-
2015-03-24	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.190	-	-
2017-12-16	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.379	-	-
2017-12-16	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.758	-	-
2021-08-07	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	9.52	-	-
2021-08-30	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	19.03	-	-
2021-10-29	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	38.06	-	-

ECM factoring results:

Total ECM effort:	1.171 GHz-days
Estimated T-Level:	0.385

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		2	1.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-04-03	Walter van Boer	Z87-I7-4790K	50000	5000000						1	0.585
2018-12-22	tottenhoff	i3-8100-01	50000	5000000						1	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-04-28	ANONYMOUS	v4_computers	7213AA0FA5540815	4.837
2005-01-20	lozcs	v4_computers	7213AA0FA5540815	4.837

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 = 3000000, B2 = 12199971630 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

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

B1 = 155000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶²

2⁵⁶

2⁵⁴

this exponent TF target: 68

TF double-checked to: 67.9

ECM T-Level=0.38 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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