M1 726 691 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	17.2086	68.6567%	3642200	123456789	0.8000	8.6245%	18.0086	71.3599%
Target	2⁶¹	0.1779	65.5738%	7000	550000	0.0029	1.3448%	0.1808	66.0367%
Difference	+6	+17.0307	+3.0829%	+3635200	+122906789	+0.7971	+7.2797%	+17.8278	+5.3232%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1726691	154404023423760648799	21	67.065	44710959697989 3 × 13 × 1223 × 937395637	2015-12-17	1223	937395637	22.863	4.0175	7.5035

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-09	Carsten Kossendey	leela	90000	1530000		-		-	-	0.013	-	-	2.366%
2014-04-04	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.885%
2014-05-04	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.012	-	-	1.111%
2014-10-03	Jocelyn Larouche	Manual testing	187172	187172		-		-	-	0.015	-	-	1.248%
2015-01-09	Jocelyn Larouche	Manual testing	280758	280758		-		-	-	0.022	-	-	1.525%
2015-02-11	Jocelyn Larouche	Manual testing	373687	373687		-		-	-	0.029	-	-	1.741%
2015-02-21	Jocelyn Larouche	Manual testing	411055	411055		-		-	-	0.032	-	-	1.816%
2015-03-08	Jocelyn Larouche	Manual testing	452160	452160		-		-	-	0.036	-	-	1.894%
2015-03-15	Jocelyn Larouche	Manual testing	497376	497376		-		-	-	0.039	-	-	1.973%
2015-04-08	Jocelyn Larouche	Manual testing	601824	601824		-		-	-	0.047	-	-	2.137%
2015-05-01	Jocelyn Larouche	Manual testing	728206	728206		-		-	-	0.057	-	-	2.309%
2015-05-07	Jocelyn Larouche	Manual testing	801026	801026		-		-	-	0.063	-	-	2.397%
2015-05-22	Jocelyn Larouche	Manual testing	881128	881128		-		-	-	0.069	-	-	2.488%
2015-05-26	Jocelyn Larouche	Manual testing	969240	969240		-		-	-	0.076	-	-	2.580%
2015-06-08	Jocelyn Larouche	Manual testing	1066164	1066164		-		-	-	0.084	-	-	2.674%
2015-06-25	Jocelyn Larouche	Manual testing	1172780	1172780		-		-	-	0.092	-	-	2.770%
2015-07-07	Jocelyn Larouche	Manual testing	1290058	1290058		-		-	-	0.101	-	-	2.868%
2015-07-21	Jocelyn Larouche	Manual testing	1419063	1419063		-		-	-	0.112	-	-	2.967%
2015-07-24	Jocelyn Larouche	Manual testing	1560969	1560969		-		-	-	0.123	-	-	3.068%
2015-09-05	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	8.624%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-23	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.178	-	-
2010-10-27	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.924	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.569	-	-
2015-05-04	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.137	-	-
2015-05-04	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.164	-	-
2015-09-02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.328	-	-

ECM factoring results:

Total ECM effort:	38.441 GHz-days
Estimated T-Level:	25.718

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.674	18.740%
30	250000	0.144	86.623%
35	1000000	0.010	99.005%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		240	16.47
50000	5000000	154404023423760648799	11	0.755
250000	40000000		50	21.21

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-18	Scott Kurowski	LM-Dell4700	50000	5000000						3	0.206
2009-09-28	ekrumme	nuanceH2	50000	5000000						3	0.206
2010-08-02	Wolfgang Fluck	C91F72025	50000	5000000						3	0.206
2012-01-16	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.206
2013-05-02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-01-29	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-07	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-07	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-17	mikr	MSI	50000	5000000	154404023423760648799	67.065	11	2		11	0.755
2020-05-18	TJAOI	Manual testing	50000	5000000						216	14.82
2023-07-14	TJAOI	Manual testing	250000	40000000						50	21.21

date	userid	compid	res64	spent (GHz-days)
1997-01-01	John Lloyd		2CA2250FCEC30D11	0.094
1998-11-21	bezahar	v4_computers	2CA2250FCEC30D11	0.094
2015-07-18	MadPoo	Manual testing	2CA2250FCEC30D11	0.094

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 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1560969 (P-1 stage 1)

B1 = 1419063 (P-1 stage 1)

B1 = 1290058 (P-1 stage 1)

B1 = 1172780 (P-1 stage 1)

B1 = 1066164 (P-1 stage 1)

B1 = 969240 (P-1 stage 1)

B1 = 881128 (P-1 stage 1)

B1 = 801026 (P-1 stage 1)

B1 = 728206 (P-1 stage 1)

B1 = 601824 (P-1 stage 1)

B1 = 497376 (P-1 stage 1)

B1 = 452160 (P-1 stage 1)

B1 = 411055 (P-1 stage 1)

B1 = 373687 (P-1 stage 1)

B1 = 280758 (P-1 stage 1)

B1 = 187172 (P-1 stage 1)

B1 = 90000, B2 = 1530000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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