M1754309 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	33.9763	69.1176%	1754309	192973990	0.9575	8.0021%	34.9338	71.5889%	2.4712%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8038%	0.0121	64.1909%	1.0330%
GPU72	2⁶¹	0.1751	65.5738%	8000	110000	0.0011	1.4134%	0.1762	66.0603%	0.4866%
Difference	+7	+33.8012	+3.5439%	+1746309	+192863990	+0.9565	+6.5887%	+34.7576	+5.5285%	+5.5285%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1754309	212985509198402796885847	24	77.495	60703533185545647 3³ × 2248279006872061	2020-07-14	27	2248279006872061	21,855	9,635,562	17,996,546

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:36:00	Carsten Kossendey	leela	95000	1567500		-		-	-	0.014	-	-	2.137%
2014-04-08T23:00:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.770%
2014-05-06T21:04:00	Jocelyn Larouche	Manual testing	136587	136587		-		-	-	0.011	-	-	0.923%
2014-09-16T20:52:00	ANONYMOUS	Manual testing	173174	173174		-		-	-	0.014	-	-	1.052%
2015-04-25T12:47:00	Squeeky_Squirrel	P4_2600	130000	3640000		-		-	-	0.025	-	-	2.773%
2015-07-04T12:23:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.976%
2018-10-02T11:45:36	Jocelyn Larouche	low 4M	1754309	140344720	12	-		-	-	0.732	-	-	7.644%
2018-10-03T11:47:46	Jocelyn Larouche	low 4M	1754309	157887810	12	-		-	-	0.807	-	-	7.776%
2018-10-07T10:38:35	Jocelyn Larouche	low 4M	1754309	175430900	12	-		-	-	0.882	-	-	7.895%
2018-10-19T02:38:28	Jocelyn Larouche	low 4M	1754309	192973990	12	-		-	-	0.958	-	-	8.002%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2010-04-21T12:38:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.088	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.175	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.910	-	-
2016-02-23T16:28:50	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.560	-	-
2015-05-13T21:10:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.119	-	-
2015-05-13T21:10:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.130	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.260	-	-
2018-06-04T13:10:08	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.519	-	-
2019-06-24T09:36:07	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.04	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.287 GHz-days
Estimated T-Level:	24.750

Digits	B1	Curves	Complete	FacMiss
20	11000	266 / 100	2.660	6.902%
25	50000	266 / 280	0.950	38.608%

New Calculation Method

Total ECM effort:	18.287 GHz-days
Estimated T-Level:	24.750

Digits	B1	Complete	FacMiss
20	11000	8.581	0.019%
25	50000	0.776	46.047%
30	250000	0.048	95.337%
35	1000000	0.002	99.782%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		263	18.08
50000	5000000	212985509198402796885847	3	0.206

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-28T17:28:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-10-06T14:01:00	SubPrime	mysql0	50000	5000000						3	0.206
2010-08-25T10:18:00	James Classen	towerofart	50000	5000000						3	0.206
2012-01-08T20:14:00	S36049	Wolle5	50000	5000000						3	0.206
2013-05-29T13:45:00	Bruce	yoyodyne	50000	5000000						3	0.206
2014-02-15T13:41:00	Bruce	snowflake	50000	5000000						3	0.206
2014-12-30T11:51:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-08-18T00:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-30T06:12:51	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-16T05:31:03	Bruce	DESK3	50000	5000000						3	0.206
2016-05-03T02:40:28	Dennis Schreiber	z800	50000	5000000						3	0.206
2016-07-30T17:07:28	Bruce	DESK3	50000	5000000						3	0.206
2016-10-05T19:07:33	Bruce	DESK3	50000	5000000						3	0.206
2016-12-03T17:01:30	Bruce	DESK3	50000	5000000						3	0.206
2017-01-29T16:39:35	Bruce	DESK3	50000	5000000						3	0.206
2017-09-05T22:55:11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-26T09:10:28	Bruce	DESK3	50000	5000000						3	0.206
2018-02-18T19:47:46	Bruce	DESK3	50000	5000000						3	0.206
2019-11-17T23:54:13	mnd9	dlounge	50000	5000000						3	0.206
2019-11-18T05:33:26	George Woltman	kaggle1	50000	5000000						3	0.206
2019-11-22T01:34:38	Keysarecool	Boat_Anchor	50000	5000000						3	0.206
2019-11-24T23:46:33	mnd9	50869b	50000	5000000						3	0.206
2019-11-26T08:38:44	Nesowa	6700T	50000	5000000						3	0.206
2019-11-29T23:58:15	IanGlencross	glenx24	50000	5000000						3	0.206
2019-12-06T16:41:02	cappy95833	HomePC	50000	5000000						3	0.206
2019-12-08T00:45:55	mnd9	50871b	50000	5000000						3	0.206
2019-12-16T21:26:05	TheJudger	Sinope	50000	5000000						3	0.206
2019-12-17T06:40:20	mnd9	75211cornerb	50000	5000000						3	0.206
2019-12-22T21:57:35	Sergey Nosov	TS140-02	50000	5000000						3	0.206
2019-12-28T16:51:57	TheJudger	myECM	50000	5000000						3	0.206
2020-01-02T05:27:37	TheJudger	myECM	50000	5000000						3	0.206
2020-01-08T10:51:10	Keysarecool	Boat_Anchor	50000	5000000						3	0.206
2020-01-18T09:14:22	Claude Portenier	Petit-Idiot	50000	5000000						3	0.206
2020-01-19T06:04:25	Bommer	2600X	50000	5000000						3	0.206
2020-01-22T11:27:04	Brett Walker	brain	50000	5000000						3	0.206
2020-01-31T10:22:05	Yxinity	Olga	50000	5000000						3	0.206
2020-02-07T09:30:19	Keysarecool	Boat_Anchor	50000	5000000						3	0.206
2020-02-14T23:14:21	mnd9	office2	50000	5000000						3	0.206
2020-02-22T12:42:47	mnd9	50871	50000	5000000						3	0.206
2020-02-29T02:15:02	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.206
2020-03-08T22:19:43	Nesowa	6700T	50000	5000000						3	0.206
2020-03-13T13:59:46	Keysarecool	Boat_Anchor	50000	5000000						3	0.206
2020-03-21T11:34:07	mnd9	office2	50000	5000000						3	0.206
2020-04-02T16:13:08	Keysarecool	HPLaptop	50000	5000000						3	0.206
2020-04-16T12:52:52	daveward2005	Davy	50000	5000000						3	0.206
2020-04-26T04:30:51	Brett Walker	brain	50000	5000000						3	0.206
2020-05-04T10:51:59	mnd9	27016b	50000	5000000						3	0.206
2020-05-16T07:23:05	mnd9	50871b	50000	5000000						3	0.206
2020-06-01T23:40:01	daveward2005	Davy	50000	5000000						3	0.206
2020-06-21T15:35:10	GAN	LMS-03	50000	5000000						3	0.206
2020-07-01T07:36:08	GAN	OSB-02	50000	5000000						3	0.206
2020-07-08T04:38:07	daveward2005	Davy	50000	5000000						3	0.206
2020-07-14T16:25:46	mnd9	25836b	50000	5000000	212985509198402796885847	77.495	3	2	5408548564720314	3	0.206
2020-07-27T11:05:22	TJAOI	Manual testing	50000	5000000						107	7.356

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	MadPoo	v4_computers	3636740CA190405B	0.095
2015-07-18T19:04:00	MadPoo	Manual testing	3636740CA190405B	0.095

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 = 1754309, B2 = 192973990 (P-1 stage 2)

B1 = 1754309, B2 = 175430900 (P-1 stage 2)

B1 = 1754309, B2 = 157887810 (P-1 stage 2)

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

B1 = 1754309, B2 = 140344720 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1754309 (P-1 stage 1)

B1 = 130000, B2 = 3640000 (P-1 stage 2)

B1 = 95000, B2 = 1567500 (P-1 stage 2)

B1 = 173174 (P-1 stage 1)

B1 = 136587 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10⁰

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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