M1731929 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	34.4153	69.1176%	1890916	190512190	0.9571	8.0355%	35.3724	71.5992%	2.4815%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7970%	0.0123	64.1884%	1.0305%
GPU72	2⁶¹	0.1774	65.5738%	7000	110000	0.0010	1.3457%	0.1784	66.0370%	0.4633%
Difference	+7	+34.2379	+3.5439%	+1883916	+190402190	+0.9561	+6.6898%	+35.1941	+5.5622%	+5.5622%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1731929	1253414493813527420471	22	70.086	361855045389715 5 × 14717 × 4917510979	2020-05-13	14717	4917510979	166.51	21.076	39.363

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:44:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.124%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.768%
2014-05-06T10:52:00	Jocelyn Larouche	Manual testing	137059	137059		-		-	-	0.011	-	-	0.923%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	174118	174118		-		-	-	0.014	-	-	1.053%
2014-12-02T21:55:00	Jocelyn Larouche	Manual testing	211177	211177		-		-	-	0.017	-	-	1.166%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	255523	255523		-		-	-	0.020	-	-	1.284%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	281075	281075		-		-	-	0.022	-	-	1.346%
2015-02-12T12:33:00	Jocelyn Larouche	Manual testing	340100	340100		-		-	-	0.027	-	-	1.476%
2015-02-20T16:56:00	Jocelyn Larouche	Manual testing	374110	374110		-		-	-	0.029	-	-	1.543%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411521	411521		-		-	-	0.032	-	-	1.612%
2015-03-08T04:50:00	Jocelyn Larouche	Manual testing	452673	452673		-		-	-	0.036	-	-	1.683%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	497940	497940		-		-	-	0.039	-	-	1.756%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602507	602507		-		-	-	0.047	-	-	1.906%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729032	729032		-		-	-	0.057	-	-	2.064%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	801935	801935		-		-	-	0.063	-	-	2.146%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882128	882128		-		-	-	0.069	-	-	2.229%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	970340	970340		-		-	-	0.076	-	-	2.314%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067374	1067374		-		-	-	0.084	-	-	2.401%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174111	1174111		-		-	-	0.092	-	-	2.490%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1291522	1291522		-		-	-	0.102	-	-	2.581%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	1420674	1420674		-		-	-	0.112	-	-	2.673%
2015-07-27T01:26:00	Jocelyn Larouche	Manual testing	1562741	1562741		-		-	-	0.123	-	-	2.767%
2015-09-15T15:52:00	Jocelyn Larouche	Manual testing	1719015	1719015		-		-	-	0.135	-	-	2.863%
2015-09-18T12:23:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.966%
2018-10-03T11:47:42	Jocelyn Larouche	low 4M	1890916	17319290	12	-		-	-	0.215	-	-	5.351%
2018-10-11T10:50:40	Jocelyn Larouche	low 4M	1890916	173192900	12	-		-	-	0.883	-	-	7.927%
2018-10-17T22:59:53	Jocelyn Larouche	low 4M	1890916	190512190	12	-		-	-	0.957	-	-	8.035%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-23T13:38:00	Architects Cubed	m1_f2	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.177	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.922	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.567	-	-
2015-05-04T20:01:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.134	-	-
2015-05-04T20:01:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.157	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.315	-	-
2018-06-04T13:10:09	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.629	-	-
2019-08-06T10:06:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.468 GHz-days
Estimated T-Level:	24.804

Digits	B1	Curves	Complete	FacMiss
20	11000	269 / 100	2.690	6.697%
25	50000	269 / 280	0.961	38.196%

New Calculation Method

Total ECM effort:	18.468 GHz-days
Estimated T-Level:	24.804

Digits	B1	Complete	FacMiss
20	11000	8.677	0.017%
25	50000	0.784	45.646%
30	250000	0.048	95.285%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		266	18.26
50000	5000000	1253414493813527420471	3	0.206

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-12T03:07:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-09-30T12:36:00	SubPrime	abd0	50000	5000000						3	0.206
2010-08-04T18:59:00	Kamil_Górski	thefault	50000	5000000						3	0.206
2011-12-15T01:17:00	S36049	Wolle5	50000	5000000						3	0.206
2013-05-06T21:41:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-03T18:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-17T09:34:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-15T18:36:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-16T09:02:11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-09T11:44:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-04-23T03:05:42	Bruce	DESK3	50000	5000000						3	0.206
2016-07-10T21:51:30	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-09-24T20:46:13	Bruce	DESK3	50000	5000000						3	0.206
2016-11-25T12:25:30	Bruce	DESK3	50000	5000000						3	0.206
2017-01-18T18:19:49	Bruce	DESK3	50000	5000000						3	0.206
2017-05-27T00:34:40	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-08T04:20:18	Bruce	DESK3	50000	5000000						3	0.206
2018-02-06T09:02:36	Bruce	DESK3	50000	5000000						3	0.206
2019-11-16T14:03:32	MichaelE	Zwoelfer	50000	5000000						3	0.206
2019-11-17T11:52:05	IanGlencross	glenx24	50000	5000000						3	0.206
2019-11-19T06:06:43	Nesowa	entropy_generator_2	50000	5000000						3	0.206
2019-11-19T16:01:01	mnd9	50869	50000	5000000						3	0.206
2019-11-21T06:35:12	DevilDawg93	Old_gaming_comp	50000	5000000						3	0.206
2019-11-26T23:53:31	Alvin Bunk	i7-Core	50000	5000000						3	0.206
2019-11-28T21:52:12	Alvin Bunk	i7-Core	50000	5000000						3	0.206
2019-11-29T02:24:53	S04803	lfmcal	50000	5000000						3	0.206
2019-12-02T17:33:28	J.R. Allen	lapdell	50000	5000000						3	0.206
2019-12-06T10:48:49	mnd9	consult	50000	5000000						3	0.206
2019-12-10T17:24:51	IanGlencross	glenx24	50000	5000000						3	0.206
2019-12-15T17:45:50	Alvin Bunk	BADCAT	50000	5000000						3	0.206
2019-12-22T15:32:01	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.206
2019-12-27T12:50:10	daveward2005	Davy	50000	5000000						3	0.206
2020-01-01T01:51:09	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.206
2020-01-06T10:49:03	IanGlencross	glenx24	50000	5000000						3	0.206
2020-01-14T18:22:31	cappy95833	HomePC	50000	5000000						3	0.206
2020-01-21T04:43:40	Brett Walker	brain	50000	5000000						3	0.206
2020-01-27T07:39:25	mnd9	25836b	50000	5000000						3	0.206
2020-02-05T06:32:21	David_McCann	i5	50000	5000000						3	0.206
2020-02-13T00:28:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.206
2020-02-20T22:31:34	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.206
2020-02-26T18:33:36	EricP	Cannonfodder	50000	5000000						3	0.206
2020-03-04T21:01:51	mnd9	office2	50000	5000000						3	0.206
2020-03-11T15:53:11	mnd9	75211backdoorb	50000	5000000						3	0.206
2020-03-19T07:00:52	mnd9	libproj	50000	5000000						3	0.206
2020-03-30T13:11:05	MarkS	laptop64	50000	5000000						3	0.206
2020-04-12T01:15:47	Keysarecool	Boat_Anchor	50000	5000000						3	0.206
2020-04-24T00:39:20	mnd9	25836b	50000	5000000						3	0.206
2020-05-01T07:11:13	nordi	sweet16	50000	5000000						3	0.206
2020-05-13T03:12:28	mnd9	75203b	50000	5000000	1253414493813527420471	70.086	3	2	8278326884381011	3	0.206
2020-06-01T14:16:55	TJAOI	Manual testing	50000	5000000						122	8.376

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	3D9D403C86BD26CD	0.094
2015-07-18T19:04:00	MadPoo	Manual testing	3D9D403C86BD26CD	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 = 1890916, B2 = 190512190 (P-1 stage 2)

B1 = 1890916, B2 = 173192900 (P-1 stage 2)

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

B1 = 3642200 (P-1 stage 1)

B1 = 1890916, B2 = 17319290 (P-1 stage 2)

B1 = 1890916 (P-1 stage 1)

B1 = 1719015 (P-1 stage 1)

B1 = 1562741 (P-1 stage 1)

B1 = 1420674 (P-1 stage 1)

B1 = 1291522 (P-1 stage 1)

B1 = 1174111 (P-1 stage 1)

B1 = 1067374 (P-1 stage 1)

B1 = 970340 (P-1 stage 1)

B1 = 882128 (P-1 stage 1)

B1 = 801935 (P-1 stage 1)

B1 = 729032 (P-1 stage 1)

B1 = 602507 (P-1 stage 1)

B1 = 497940 (P-1 stage 1)

B1 = 452673 (P-1 stage 1)

B1 = 411521 (P-1 stage 1)

B1 = 374110 (P-1 stage 1)

B1 = 340100 (P-1 stage 1)

B1 = 281075 (P-1 stage 1)

B1 = 255523 (P-1 stage 1)

B1 = 211177 (P-1 stage 1)

B1 = 174118 (P-1 stage 1)

B1 = 95000, B2 = 1543750 (P-1 stage 2)

B1 = 137059 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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