M1 726 667 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	34.5202	69.1176%	17000000	272007836100	1,167.0220	19.3703%	1,201.5422	75.0997%
Target	2⁶¹	0.1779	65.5738%	7000	550000	0.0029	1.3448%	0.1808	66.0367%
Difference	+7	+34.3423	+3.5439%	+16993000	+272007286100	+1,167.0191	+18.0256%	+1,201.3614	+9.0629%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1726667	157553984883828940632859211085827331584111	42	136.855	45623731988805293850192078462676165 5 × 7 × 11 × 5237 × 10223 × 10247 × 21067 × 770261 × 13311647311	2023-06-22	770261	13311647311	7.745e+10	57.108	106.55

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-11	Carsten Kossendey	leela	90000	1530000		-		-	-	0.013	-	-	2.095%
2014-04-04	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.768%
2014-05-04	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.012	-	-	0.970%
2014-10-03	Jocelyn Larouche	Manual testing	187172	187172		-		-	-	0.015	-	-	1.094%
2015-01-09	Jocelyn Larouche	Manual testing	280758	280758		-		-	-	0.022	-	-	1.345%
2015-02-11	Jocelyn Larouche	Manual testing	373687	373687		-		-	-	0.029	-	-	1.541%
2015-02-21	Jocelyn Larouche	Manual testing	411055	411055		-		-	-	0.032	-	-	1.610%
2015-03-08	Jocelyn Larouche	Manual testing	452160	452160		-		-	-	0.036	-	-	1.681%
2015-03-15	Jocelyn Larouche	Manual testing	497376	497376		-		-	-	0.039	-	-	1.754%
2015-04-08	Jocelyn Larouche	Manual testing	601824	601824		-		-	-	0.047	-	-	1.905%
2015-05-01	Jocelyn Larouche	Manual testing	728206	728206		-		-	-	0.057	-	-	2.062%
2015-05-07	Jocelyn Larouche	Manual testing	801026	801026		-		-	-	0.063	-	-	2.144%
2015-05-22	Jocelyn Larouche	Manual testing	881128	881128		-		-	-	0.069	-	-	2.227%
2015-05-26	Jocelyn Larouche	Manual testing	969240	969240		-		-	-	0.076	-	-	2.312%
2015-06-08	Jocelyn Larouche	Manual testing	1066164	1066164		-		-	-	0.084	-	-	2.399%
2015-06-25	Jocelyn Larouche	Manual testing	1172780	1172780		-		-	-	0.092	-	-	2.488%
2015-07-07	Jocelyn Larouche	Manual testing	1290058	1290058		-		-	-	0.101	-	-	2.578%
2015-07-21	Jocelyn Larouche	Manual testing	1419063	1419063		-		-	-	0.112	-	-	2.671%
2015-07-24	Jocelyn Larouche	Manual testing	1560969	1560969		-		-	-	0.123	-	-	2.765%
2015-09-05	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.964%
2018-10-03	Jocelyn Larouche	low 4M	1726667	17266670	12	-		-	-	0.202	-	-	5.311%
2018-10-07	Jocelyn Larouche	low 4M	1726667	69066680	12	-		-	-	0.424	-	-	6.829%
2018-10-12	Jocelyn Larouche	low 4M	1726667	172666700	12	-		-	-	0.868	-	-	7.852%
2018-10-17	Jocelyn Larouche	low 4M	1726667	189933370	12	-		-	-	0.942	-	-	7.959%
2023-01-04	Jocelyn Larouche	Manual testing	1726667	1254200640		-		-	-	5.504	-	-	10.099%
2023-03-20	Jocelyn Larouche	Manual testing	1726667	3382777860		-		-	-	14.63	-	-	11.232%
2023-06-22	linament	Cyber	17000000	272007836100			157553984883828940632859211085827331584111	42	136.855	1,167	0.187	2,334	19.370%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2022-07-30	masser	Manual testing	1700000	61200000	160	43			-	-	0.393

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	m1_76l	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	-	-
2018-04-02	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.656	-	-
2019-06-24	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.31	-	-

ECM factoring results:

Total ECM effort:	36.088 GHz-days
Estimated T-Level:	25.667

Digits	B1	Complete	FacMiss
20	11000	14.300	0.000%
25	50000	1.597	20.247%
30	250000	0.133	87.511%
35	1000000	0.009	99.098%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		260	17.84
250000	40000000		43	18.24

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-08	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-09-28	SubPrime	abd0	50000	5000000						3	0.206
2010-07-28	ANONYMOUS		50000	5000000						3	0.206
2011-12-10	S36049	Wolle5	50000	5000000						3	0.206
2013-05-02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-01	Sara	Sara	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						12	0.824
2016-09-22	Bruce	DESK3	50000	5000000						3	0.206
2016-11-23	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-01-16	Bruce	DESK3	50000	5000000						3	0.206
2017-05-12	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-03	Bruce	DESK3	50000	5000000						3	0.206
2018-02-03	Bruce	DESK3	50000	5000000						3	0.206
2019-07-12	storm5510	7700_Kaby_Lake	50000	5000000						3	0.206
2019-11-01	nordi	nordiputer	50000	5000000						50	3.432
2019-11-18	mnd9	50869	50000	5000000						3	0.206
2020-01-29	Sergey Nosov	TS140-02	50000	5000000						3	0.206
2020-02-10	DRMEDESY	hm02	50000	5000000						3	0.206
2020-02-15	mnd9	eileen	50000	5000000						3	0.206
2020-02-23	daveward2005	Davy	50000	5000000						3	0.206
2020-02-29	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.206
2020-03-06	EricP	Cannonfodder	50000	5000000						3	0.206
2020-03-14	EricP	Cannonfodder	50000	5000000						3	0.206
2020-03-22	kracker	O0	50000	5000000						3	0.206
2020-04-22	S04803	lfmcal	50000	5000000						3	0.206
2020-04-26	mnd9	fb	50000	5000000						3	0.206
2020-05-04	TJAOI	Manual testing	50000	5000000						120	8.236
2023-07-14	TJAOI	Manual testing	250000	40000000						43	18.24

date	userid	compid	res64	spent (GHz-days)
1997-01-01	John Lloyd		4B42ED5C5720235D	0.094
1999-01-02	ANONYMOUS	v4_computers	4B42ED5C5720235D	0.094
2015-06-29	MadPoo	Manual testing	4B42ED5C5720235D	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 = 17000000, B2 = 272007836100 (P-1 stage 2)

B1 = 1726667, B2 = 3382777860 (P-1 stage 2)

B1 = 1726667, B2 = 1254200640 (P-1 stage 2)

B1 = 17000000 (P-1 stage 1)

B1 = 1726667, B2 = 189933370 (P-1 stage 2)

B1 = 1726667, B2 = 172666700 (P-1 stage 2)

B1 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 1726667, B2 = 69066680 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1726667, B2 = 17266670 (P-1 stage 2)

B1 = 1726667 (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)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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