M3 745 867 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	2⁶⁷	7.9325	67.1642%	1000000	130364850	1.2257	8.4098%	9.1581	69.9256%
Target	2⁶⁴	0.9502	65.6250%	22000	450000	0.0069	2.1103%	0.9571	66.3504%
Difference	+3	+6.9823	+1.5392%	+978000	+129914850	+1.2188	+6.2995%	+8.2010	+3.5752%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3745867	4508530433055582323730988228297	31	101.831	601800655636676679088044 2² × 3 × 13933 × 1076587 × 1089709 × 3068083	2015-11-14	1089709	3068083	4.193e+10	0.1824	0.3377

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	1.150%
2013-03-14	Squeeky_Squirrel	T7500_2200	110000	2035000		-		-	-	0.033	-	-	2.956%
2015-11-14	mikr	MSI	1600000	66000000	12		4508530433055582323730988228297	31	101.831	0.778	0.787	1.556	7.948%
2022-05-16	Jocelyn Larouche	Manual testing	500000	130364850		-		-	-	1.154	-	-	7.772%
2022-08-25	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.902%
2022-09-13	Jocelyn Larouche	Manual testing	1000000	130364850		-		-	-	1.226	-	-	8.410%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-29	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-05	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-06	markr	Manual testing	2¹	2⁶²		-	-	0.164	-	-
2012-05-10	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.426	-	-
2015-01-23	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.524	-	-
2015-01-23	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.997	-	-

ECM factoring results:

Total ECM effort:	0.897 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-11-04	willreid	jing	50000	5000000						3	0.448
2012-05-29	GrunwalderGIMP	vangelis	50000	5000000						3	0.448

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-05	ANONYMOUS	v4_computers	DA51EF3D494582F1	0.393
1999-12-23	ANONYMOUS	v4_computers	DA51EF3D494582F1	0.393

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20

kkmrkkblmbrbk

Manual testing

4508530433055582323730988228297

7433BA64195294__

2017-12-04

Oliver Kruse

Threadripper

4508530433055582323730988228297

7433BA64195294__

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 = 1000000, B2 = 130364850 (P-1 stage 2)

B1 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 110000, B2 = 2035000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

this exponent TF target: 64

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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