M1732271 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	2⁶⁷	17.1532	68.6567%	3642200	123456789	0.8000	8.6271%	17.9532	71.3607%	2.7040%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7971%	0.0123	64.1884%	1.0305%
GPU72	2⁶¹	0.1773	65.5738%	7000	110000	0.0010	1.3457%	0.1783	66.0370%	0.4633%
Difference	+6	+16.9758	+3.0829%	+3635200	+123346789	+0.7990	+7.2814%	+17.7748	+5.3237%	+5.3237%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1732271	321541579228769352067289	24	78.089	92809259991297364 2² × 37 × 627089594535793	2018-02-06	37	627089594535793	61,071	2,687,549	5,019,594

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:40:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.398%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.886%
2014-05-06T10:52:00	Jocelyn Larouche	Manual testing	137052	137052		-		-	-	0.011	-	-	1.059%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	174104	174104		-		-	-	0.014	-	-	1.203%
2014-12-02T21:55:00	Jocelyn Larouche	Manual testing	211156	211156		-		-	-	0.017	-	-	1.328%
2015-01-27T21:58:00	Jocelyn Larouche	Manual testing	255498	255498		-		-	-	0.020	-	-	1.459%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	281047	281047		-		-	-	0.022	-	-	1.527%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	374093	374093		-		-	-	0.029	-	-	1.743%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411502	411502		-		-	-	0.032	-	-	1.818%
2015-03-08T04:50:00	Jocelyn Larouche	Manual testing	452652	452652		-		-	-	0.036	-	-	1.896%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	497917	497917		-		-	-	0.039	-	-	1.975%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602478	602478		-		-	-	0.047	-	-	2.139%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728997	728997		-		-	-	0.057	-	-	2.311%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	801896	801896		-		-	-	0.063	-	-	2.400%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882085	882085		-		-	-	0.069	-	-	2.490%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	970293	970293		-		-	-	0.076	-	-	2.582%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067322	1067322		-		-	-	0.084	-	-	2.676%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174054	1174054		-		-	-	0.092	-	-	2.772%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1291459	1291459		-		-	-	0.102	-	-	2.870%
2015-07-21T01:20:00	Jocelyn Larouche	Manual testing	1420604	1420604		-		-	-	0.112	-	-	2.970%
2015-07-27T01:26:00	Jocelyn Larouche	Manual testing	1562664	1562664		-		-	-	0.123	-	-	3.071%
2015-09-15T15:52:00	Jocelyn Larouche	Manual testing	1718930	1718930		-		-	-	0.135	-	-	3.174%
2015-09-19T15:11:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	8.627%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
1999-02-21T00:00:00	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		-	-	0.066	-	-
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		-	-	0.921	-	-
2016-02-23T16:28:49	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.567	-	-
2015-05-04T21:05:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.133	-	-
2015-05-04T21:05:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.157	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.314	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.232 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.232 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	17.10
50000	5000000	321541579228769352067289	2	0.137

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-12T07:34:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-09-29T06:05:00	JimBa	E5400	50000	5000000						3	0.206
2010-08-05T03:47:00	Lupo	yorick	50000	5000000						3	0.206
2011-12-19T09:34:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.206
2013-05-07T03:38:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-05T19:14:00	Sara	Sara	50000	5000000						3	0.206
2014-11-18T00:02:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-16T04:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-16T16:22:12	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2016-03-09T11:49:24	Bruce	DESK3	50000	5000000						3	0.206
2016-04-23T07:10:35	Bruce	DESK3	50000	5000000						3	0.206
2016-07-11T01:58:25	Bruce	DESK3	50000	5000000						3	0.206
2016-09-25T01:17:29	Bruce	DESK3	50000	5000000						3	0.206
2016-11-25T16:54:56	Bruce	DESK3	50000	5000000						3	0.206
2017-01-18T20:46:14	Bruce	DESK3	50000	5000000						3	0.206
2017-06-22T07:28:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-08T11:45:11	Bruce	DESK3	50000	5000000						3	0.206
2018-02-06T13:31:35	Bruce	DESK3	50000	5000000	321541579228769352067289	78.089	2	2		2	0.137
2020-05-25T09:38:33	TJAOI	Manual testing	50000	5000000						198	13.59

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	48F4C102779CB83B	0.094
1999-02-07T00:00:00	ANONYMOUS	v4_computers	48F4C102779CB83B	0.094
1999-02-21T00:00:00	ANONYMOUS	v4_computers	48F4C102779CB83B	0.094
2015-07-10T01:00:00	MadPoo	Manual testing	48F4C102779CB83B	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 = 1718930 (P-1 stage 1)

B1 = 1562664 (P-1 stage 1)

B1 = 1420604 (P-1 stage 1)

B1 = 1291459 (P-1 stage 1)

B1 = 1174054 (P-1 stage 1)

B1 = 1067322 (P-1 stage 1)

B1 = 970293 (P-1 stage 1)

B1 = 882085 (P-1 stage 1)

B1 = 801896 (P-1 stage 1)

B1 = 728997 (P-1 stage 1)

B1 = 602478 (P-1 stage 1)

B1 = 497917 (P-1 stage 1)

B1 = 452652 (P-1 stage 1)

B1 = 411502 (P-1 stage 1)

B1 = 374093 (P-1 stage 1)

B1 = 281047 (P-1 stage 1)

B1 = 255498 (P-1 stage 1)

B1 = 211156 (P-1 stage 1)

B1 = 174104 (P-1 stage 1)

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

B1 = 137052 (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