M10 011 851 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	2⁷⁴	382.1337	67.5676%	5000000	150000000	5.4556	6.1659%	387.5893	69.5673%
Target	2⁶⁸	5.9534	64.7059%	65000	12000000	0.3025	2.5683%	6.2559	65.6123%
Difference	+6	+376.1803	+2.8617%	+4935000	+138000000	+5.1531	+3.5976%	+381.3334	+3.9550%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10011851	210791680260653377709070461321	30	97.412	10527108336942558259660 2² × 5 × 526355416847127912983	2023-04-04	5	526355416847127912983	4.482e+9	1.213e+13	2.265e+13

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-11	ANONYMOUS	v4_computers	135000	135000		-		-	-	0.057	-	-	0.544%
2000-09-08	ANONYMOUS	v4_computers	110000	1045000		-		-	-	0.068	-	-	1.237%
2001-05-20	ANONYMOUS	v4_computers	110000	1320000		-		-	-	0.074	-	-	1.323%
2011-12-12	bcp19	acer-Q8200	150000	4000000		-		-	-	0.152	-	-	1.882%
2020-09-10	ViliamF	Manual testing	1000000	30000000		-		-	-	1.091	-	-	3.949%
2020-10-02	ViliamF	Manual testing	5000000	150000000		-		-	-	5.456	-	-	6.166%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2023-04-04	JacobZ	Desktop-Neon	2000000	150000000	2	7	210791680260653377709070461321	P+1	30	97.412	4.628

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-10-15	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.356	-	-
2011-09-14	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.373	-	-
2015-04-19	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.746	-	-
2015-11-05	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.493	-	-
2016-03-14	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	2.986	-	-
2017-09-21	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	5.971	-	-
2017-12-07	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	11.94	-	-
2021-01-06	ViliamF	Manual testing	2⁷⁰	2⁷¹		-	-	23.88	-	-
2021-04-28	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	47.77	-	-
2021-04-28	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	95.54	-	-
2021-05-06	-Anonymous-	Manual testing	2⁷³	2⁷⁴		-	-	191.1	-	-

ECM factoring results:

Total ECM effort:	1.331 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	1.331

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-03-29	taffa	xenor	50000	5000000						1	0.444
2016-06-12	Bruce	test	50000	5000000						1	0.444
2019-01-29	arnaud	snd-15-157	50000	5000000						1	0.444

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-10-06	ANONYMOUS	v4_computers	79A518DCF9BF506F	2.920
2004-03-08	ANONYMOUS	v4_computers	79A518DCF9BF506F	2.920

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 = 5000000, B2 = 150000000 (P-1 stage 2)

B1 = 2000000, B2 = 150000000 (P+1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 2000000 (P+1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 150000, B2 = 4000000 (P-1 stage 2)

B1 = 110000, B2 = 1320000 (P-1 stage 2)

B1 = 110000, B2 = 1045000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 68

TF double-checked to: 67.8

ECM T-Level=0.58 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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