M1716529 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	34.7241	69.1176%	3642200	123456789	0.6940	7.9591%	35.4181	71.5756%	2.4580%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7922%	0.0122	64.1866%	1.0287%
GPU72	2⁶¹	0.1790	65.5738%	7000	110000	0.0009	1.3431%	0.1798	66.0361%	0.4624%
Difference	+7	+34.5451	+3.5439%	+3635200	+123346789	+0.6931	+6.6160%	+35.2383	+5.5395%	+5.5395%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1716529	4387354074997998369044737	25	81.860	1277972604889867392 2⁷ × 3 × 11 × 302550332597033	2020-03-17	128	302550332597033	497,245	1,124,863	2,100,931

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-11T06:19:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	2.085%
2014-04-01T22:36:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.767%
2014-05-03T14:50:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	0.969%
2014-10-05T22:25:00	Jocelyn Larouche	Manual testing	187392	187392		-		-	-	0.013	-	-	1.093%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	281088	281088		-		-	-	0.019	-	-	1.344%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	309196	309196		-		-	-	0.021	-	-	1.408%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	340115	340115		-		-	-	0.023	-	-	1.474%
2015-02-20T16:56:00	Jocelyn Larouche	Manual testing	374126	374126		-		-	-	0.026	-	-	1.541%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411538	411538		-		-	-	0.028	-	-	1.610%
2015-03-06T12:09:00	Jocelyn Larouche	Manual testing	452691	452691		-		-	-	0.031	-	-	1.681%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	497960	497960		-		-	-	0.034	-	-	1.753%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602531	602531		-		-	-	0.041	-	-	1.904%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729062	729062		-		-	-	0.050	-	-	2.062%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801968	801968		-		-	-	0.055	-	-	2.143%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882164	882164		-		-	-	0.060	-	-	2.226%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	970380	970380		-		-	-	0.066	-	-	2.312%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067418	1067418		-		-	-	0.073	-	-	2.398%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174159	1174159		-		-	-	0.080	-	-	2.487%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1291574	1291574		-		-	-	0.088	-	-	2.577%
2015-07-13T12:24:00	Jocelyn Larouche	Manual testing	1420731	1420731		-		-	-	0.097	-	-	2.670%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1562804	1562804		-		-	-	0.107	-	-	2.764%
2015-08-08T10:54:00	mikr	MSI	3642200	123456789		-		-	-	0.694	-	-	7.959%
2018-08-21T11:49:45	Jocelyn Larouche	low 4M	1716529	171652900	12	-		-	-	0.749	-	-	7.836%
2018-10-16T21:51:22	Jocelyn Larouche	low 4M	1716529	188818190	12	-		-	-	0.813	-	-	7.943%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-22T12:45:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.179	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.930	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.572	-	-
2015-05-02T03:49:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.144	-	-
2015-05-02T03:49:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.177	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.353	-	-
2018-05-28T14:40:35	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.707	-	-
2019-06-17T12:15:06	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.363 GHz-days
Estimated T-Level:	24.911

Digits	B1	Curves	Complete	FacMiss
20	11000	275 / 100	2.750	6.305%
25	50000	275 / 280	0.982	37.385%

New Calculation Method

Total ECM effort:	16.363 GHz-days
Estimated T-Level:	24.911

Digits	B1	Complete	FacMiss
20	11000	8.871	0.014%
25	50000	0.802	44.854%
30	250000	0.049	95.183%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		272	16.18
50000	5000000	4387354074997998369044737	3	0.179

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-02T11:40:00	paulie	iMac3.4	50000	5000000						3	0.179
2009-06-27T08:31:00	James Hintz	05_060309	50000	5000000						3	0.179
2010-07-19T15:34:00	ANONYMOUS		50000	5000000						3	0.179
2011-12-02T06:18:00	S36049	Wolle5	50000	5000000						3	0.179
2013-04-25T07:04:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-01-17T17:22:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-10-20T07:03:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-06-22T08:54:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-09-30T09:12:10	mikr	MSI	50000	5000000						12	0.714
2016-09-15T14:56:49	Bruce	DESK3	50000	5000000						3	0.179
2016-11-17T19:12:47	Bruce	DESK3	50000	5000000						3	0.179
2017-01-12T03:26:05	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2017-04-28T21:19:50	ANONYMOUS	Worker	50000	5000000						3	0.179
2017-11-24T08:59:51	Bruce	DESK3	50000	5000000						3	0.179
2018-01-28T06:11:27	Bruce	DESK3	50000	5000000						3	0.179
2019-05-30T22:27:41	nordi	nordiputer	50000	5000000						50	2.975
2020-01-12T09:14:31	Alvin Bunk	BADCAT	50000	5000000						3	0.179
2020-01-20T02:21:51	mnd9	kitchen	50000	5000000						3	0.179
2020-01-25T07:19:47	daveward2005	Davy	50000	5000000						3	0.179
2020-02-03T04:48:10	Sergey Nosov	TS140-02	50000	5000000						3	0.179
2020-02-18T17:15:18	mnd9	libproj	50000	5000000						3	0.179
2020-02-25T10:59:35	EricP	Cannonfodder	50000	5000000						3	0.179
2020-03-03T14:46:07	daveward2005	Davy	50000	5000000						3	0.179
2020-03-10T07:01:56	kracker	O0	50000	5000000						3	0.179
2020-03-17T17:32:41	mnd9	75201b	50000	5000000	4387354074997998369044737	81.860	3	2	102715332735110	3	0.179
2020-04-20T10:38:51	TJAOI	Manual testing	50000	5000000						144	8.568

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	E505729E3E7E02D2	0.081
2015-07-19T18:02:00	MadPoo	Manual testing	E505729E3E7E02D2	0.081

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 = 1716529, B2 = 188818190 (P-1 stage 2)

B1 = 1716529, B2 = 171652900 (P-1 stage 2)

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

B1 = 3642200 (P-1 stage 1)

B1 = 1716529 (P-1 stage 1)

B1 = 1562804 (P-1 stage 1)

B1 = 1420731 (P-1 stage 1)

B1 = 1291574 (P-1 stage 1)

B1 = 1174159 (P-1 stage 1)

B1 = 1067418 (P-1 stage 1)

B1 = 970380 (P-1 stage 1)

B1 = 882164 (P-1 stage 1)

B1 = 801968 (P-1 stage 1)

B1 = 729062 (P-1 stage 1)

B1 = 602531 (P-1 stage 1)

B1 = 497960 (P-1 stage 1)

B1 = 452691 (P-1 stage 1)

B1 = 411538 (P-1 stage 1)

B1 = 374126 (P-1 stage 1)

B1 = 340115 (P-1 stage 1)

B1 = 309196 (P-1 stage 1)

B1 = 281088 (P-1 stage 1)

B1 = 187392 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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