M6 439 051 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	148.5209	68.0556%	4000000	18004726740	267.6241	12.0614%	416.1450	71.9085%
Target	2⁶⁶	2.2936	65.1515%	45000	8000000	0.1300	2.5752%	2.4236	66.0489%
Difference	+6	+146.2273	+2.9040%	+3955000	+17996726740	+267.4941	+9.4862%	+413.7214	+5.8596%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6439051	295095627354361527178361470416586246412087591	45	147.726	22914527882630649079993423752707211545 5 × 1949 × 12809 × 19417 × 161839 × 410659 × 1128823 × 126020539	2023-05-16	1128823	126020539	2.823e+10	2.1561	3.4851

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-10-06	ANONYMOUS	v4_computers	30000	247500		-		-	-	0.011	-	-	0.674%
2002-01-22	ANONYMOUS	v4_computers	30000	412500		-		-	-	0.014	-	-	0.795%
2002-05-11	ANONYMOUS	v4_computers	30000	292500		-		-	-	0.012	-	-	0.713%
2014-09-16	Nesowa	newfs	395000	9973750		-		-	-	0.249	-	-	3.222%
2022-01-03	Architects Cubed	gpu72ng	1000000	390677430		-		-	-	6.042	-	-	6.747%
2023-05-15	linament	U2K	3999900	3999900		-		-	-	1.087	-	-	3.018%
2023-05-16	linament	Cyber	4000000	18004726740			295095627354361527178361470416586246412087591	45	147.726	267.6	2.414	535.2	12.061%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.095	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.152	-	-
2014-08-02	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.305	-	-
2014-08-05	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.580	-	-
2015-10-24	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.161	-	-
2016-04-03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.321	-	-
2018-06-06	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.642	-	-
2020-05-17	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.284	-	-
2021-03-02	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	18.57	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	37.14	-	-
2021-10-11	SRBase	Manual testing	2⁷¹	2⁷²		-	-	74.27	-	-

ECM factoring results:

Total ECM effort:	1.710 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	1.710

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-12-13	sannerud.com	Jim2010	50000	5000000						3	0.855
2016-10-31	h0b0byter99	camserve	50000	5000000						3	0.855

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-10	ANONYMOUS	v4_computers	51A52111770191__	1.207
1999-04-13	ANONYMOUS	v4_computers	51A52111770191__	1.207
1999-09-30	ANONYMOUS	v4_computers	385D5D01D6178A5E	1.207
2002-05-18	ANONYMOUS	v4_computers	385D5D01D6178A5E	1.207

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 = 4000000, B2 = 18004726740 (P-1 stage 2)

B1 = 1000000, B2 = 390677430 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3999900 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 395000, B2 = 9973750 (P-1 stage 2)

B1 = 395000 (P-1 stage 1)

B1 = 30000, B2 = 412500 (P-1 stage 2)

B1 = 30000, B2 = 292500 (P-1 stage 2)

B1 = 30000, B2 = 247500 (P-1 stage 2)

B1 = 30000 (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

2⁶³

2⁶²

this exponent TF target: 66

TF double-checked to: 67.9

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

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