M12 549 751 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	76.2034	66.6667%	3000000	12241447680	373.9071	11.9704%	450.1105	70.6568%
Target	2⁶⁸	4.7495	64.7059%	90000	2200000	0.1144	3.0921%	4.8639	65.7972%
Difference	+4	+71.4539	+1.9608%	+2910000	+12239247680	+373.7927	+8.8783%	+445.2466	+4.8596%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12549751	546231265546629815484751235630196528418001	42	138.649	21762633599129967418666363803959000 2³ × 5³ × 7³ × 13 × 251 × 1249 × 29201 × 52627 × 1293983 × 7828939	2023-03-03	1293983	7828939	1.317e+10	0.9211	1.4701

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-05-11	dave_0273	v4_computers	75000	1368750		-		-	-	0.081	-	-	1.633%
2019-01-14	riccardo uberti	Nomad2C	430000	8500000	12	-		-	-	0.485	-	-	3.440%
2023-03-03	Naegi Makoto	5950X	3000000	12241447680			546231265546629815484751235630196528418001	42	138.649	373.9	9.66	747.8	11.970%

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	2⁵⁵		-	-	0.000	-	-
2000-03-28	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.284	-	-
2013-06-19	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.298	-	-
2014-03-28	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.595	-	-
2015-03-23	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.191	-	-
2017-12-16	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.382	-	-
2017-12-16	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.764	-	-
2021-08-07	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	9.53	-	-
2021-08-28	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	19.05	-	-
2021-10-29	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	38.11	-	-

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
2016-04-01	Bruce	Desk2	50000	5000000						1	0.585
2018-12-20	kracker	center	50000	5000000						1	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-06-03	twmoss	v4_computers	5AB3B53ACFA8680B	4.832
2004-09-02	ANONYMOUS	v4_computers	5AB3B53ACFA8680B	4.832
2004-11-30	ANONYMOUS	v4_computers	5AB3B53ACFA8680B	4.832

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 = 12241447680 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 430000, B2 = 8500000 (P-1 stage 2)

B1 = 430000 (P-1 stage 1)

B1 = 75000, B2 = 1368750 (P-1 stage 2)

B1 = 75000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁵

this exponent TF target: 68

TF double-checked to: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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