M10 290 209 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	92.9363	66.6667%	7000000	10459345050	273.0559	12.4997%	365.9921	70.8332%
Target	2⁶⁸	5.7924	64.7059%	70000	8000000	0.2378	2.6587%	6.0302	65.6442%
Difference	+4	+87.1439	+1.9608%	+6930000	+10451345050	+272.8180	+9.8411%	+359.9619	+5.1890%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10290209	1073794618247417347831873	25	79.829	52175549507663904 2⁵ × 3 × 7 × 185177 × 419286341	2022-12-18	185177	419286341	21,849	10.903	20.209
10290209	180361320679128301734184528719388449839439623	45	147.016	8763734569391559575426724992630783779 19 × 283 × 479 × 157427 × 330907 × 547901 × 2808101 × 42453517	2022-12-18	2808101	42453517	1.526e+10	2.3532	2.7070

exponent	prime factors	composite factor	digits	bits*
10290209	1073794618247417347831873 180361320679128301734184528719388449839439623	19367101548524459494753128916274168274167091549444 9569422624338503879	69	226.845

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23	ANONYMOUS	v4_computers	55000	825000		-		-	-	0.046	-	-	1.274%
2003-12-23	ANONYMOUS	v4_computers	55000	825000		-		-	-	0.046	-	-	1.274%
2004-10-03	ANONYMOUS	v4_computers	55000	825000		-		-	-	0.046	-	-	1.274%
2013-06-20	Nesowa	EPC	125000	2531250		-		-	-	0.121	-	-	2.067%
2022-12-18	mikr	G111	7000000	10459345050			1073794618247417347831873 180361320679128301734184528719388449839439623	69	226.845	273.1	6.723	546.1	12.500%

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		-	-	0.346	-	-
1999-10-21	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.346	-	-
2013-09-20	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.363	-	-
2015-04-28	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.726	-	-
2015-12-02	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.452	-	-
2017-09-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.905	-	-
2017-12-07	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	5.810	-	-
2020-08-05	ViliamF	Manual testing	2⁶⁹	2⁷⁰		-	-	11.62	-	-
2021-09-29	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	23.24	-	-
2022-08-27	Architects Cubed	GPU72_TF	2⁷¹	2⁷²		-	-	46.48	-	-

ECM factoring results:

Total ECM effort:	0.993 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	0.993

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-07	William Wallace		50000	5000000						1	0.497
2016-09-17	arnaud	snd-15-157	50000	5000000						1	0.497

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-06-29	ANONYMOUS	v4_computers	8BD7FDA296DA866E	3.361
2003-12-13	ANONYMOUS	v4_computers	8BD7FDA296DA866E	3.361
2003-12-23	ANONYMOUS	v4_computers	8BD7FDA296DA866E	3.361
2004-10-03	ANONYMOUS	v4_computers	8BD7FDA296DA866E	3.361

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-12-24

Funky Waddle

main

1073794618247417347831873

180361320679128301734184528719388449839439623

240BA1CBEE73057C

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 = 7000000, B2 = 10459345050 (P-1 stage 2)

B1 = 7000000 (P-1 stage 1)

B1 = 125000, B2 = 2531250 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 55000, B2 = 825000 (P-1 stage 2)

B1 = 55000 (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

this exponent TF target: 68

TF double-checked to: 67.9

ECM T-Level=0.38 ~= -15-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