M6 480 869 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	147.5626	68.0556%	4000000	18004726740	267.6241	12.0678%	415.1867	71.9106%
Target	2⁶⁶	2.2788	65.1515%	45000	8000000	0.1300	2.5779%	2.4088	66.0499%
Difference	+6	+145.2838	+2.9040%	+3955000	+17996726740	+267.4941	+9.4900%	+412.7779	+5.8607%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6480869	31131586810646648709661978407462193386355890442817	50	164.413	2401806517817799488746183452208507330294432 2⁵ × 397 × 787 × 21013 × 25357 × 84521 × 1206941 × 2166319 × 2040157961	2023-05-27	2166319	2040157961	2.314e+10	30.765	56.421

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-25	ANONYMOUS	v4_computers	30000	247500		-		-	-	0.011	-	-	0.675%
2001-06-17	MadPoo	v4_computers	30000	247500		-		-	-	0.011	-	-	0.675%
2014-08-31	Nesowa	newfs	395000	10072500		-		-	-	0.251	-	-	3.231%
2022-08-17	takahashi	vaio	2500000	50028510		-		-	-	1.383	-	-	5.446%
2023-05-27	linament	Cyber	4000000	18004726740			31131586810646648709661978407462193386355890442817	50	164.413	267.6	2.429	535.2	12.068%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.095	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.151	-	-
2014-08-02	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.303	-	-
2014-08-09	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.577	-	-
2015-10-26	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.153	-	-
2016-04-14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.306	-	-
2018-06-06	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.612	-	-
2019-11-30	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	9.224	-	-
2021-03-18	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	18.45	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	36.90	-	-
2021-10-17	SRBase	Manual testing	2⁷¹	2⁷²		-	-	73.79	-	-

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
2011-12-29	sannerud.com	Jim2010	50000	5000000						3	0.855
2017-02-13	WileECoyote	penny	50000	5000000						3	0.855

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15	George Vaughan	v4_computers	D6DEB2ECEC5995F5	1.215
2001-08-18	MadPoo	v4_computers	D6DEB2ECEC5995F5	1.215

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 = 2500000, B2 = 50028510 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 2500000 (P-1 stage 1)

B1 = 395000, B2 = 10072500 (P-1 stage 2)

B1 = 395000 (P-1 stage 1)

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

2¹⁶⁰

2¹⁷⁰

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