M1716667 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	34.7213	69.1176%	3642200	123456789	0.6940	7.9591%	35.4153	71.5756%	2.4580%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7923%	0.0122	64.1866%	1.0287%
GPU72	2⁶¹	0.1789	65.5738%	7000	110000	0.0009	1.3431%	0.1798	66.0362%	0.4624%
Difference	+7	+34.5423	+3.5439%	+3635200	+123346789	+0.6931	+6.6160%	+35.2355	+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
1716667	5842478394291864250537	22	72.307	1701692405775804 2² × 3 × 13 × 269 × 40551244061	2020-04-08	269	40551244061	1,037.6	150.77	281.59

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-09T06:19:00	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	187389	187389		-		-	-	0.013	-	-	1.093%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	281083	281083		-		-	-	0.019	-	-	1.344%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	309191	309191		-		-	-	0.021	-	-	1.408%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	374121	374121		-		-	-	0.026	-	-	1.541%
2015-02-22T09:50:00	Jocelyn Larouche	Manual testing	411533	411533		-		-	-	0.028	-	-	1.610%
2015-03-06T12:09:00	Jocelyn Larouche	Manual testing	452686	452686		-		-	-	0.031	-	-	1.681%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	497954	497954		-		-	-	0.034	-	-	1.753%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602523	602523		-		-	-	0.041	-	-	1.904%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729052	729052		-		-	-	0.050	-	-	2.062%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801957	801957		-		-	-	0.055	-	-	2.143%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882152	882152		-		-	-	0.060	-	-	2.226%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	970367	970367		-		-	-	0.066	-	-	2.312%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067403	1067403		-		-	-	0.073	-	-	2.398%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174143	1174143		-		-	-	0.080	-	-	2.487%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1291557	1291557		-		-	-	0.088	-	-	2.578%
2015-07-13T12:24:00	Jocelyn Larouche	Manual testing	1420712	1420712		-		-	-	0.097	-	-	2.670%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1562783	1562783		-		-	-	0.107	-	-	2.764%
2015-08-08T18:11:00	mikr	MSI	3642200	123456789		-		-	-	0.694	-	-	7.959%
2018-08-21T11:49:45	Jocelyn Larouche	low 4M	1716667	171666700	12	-		-	-	0.749	-	-	7.836%
2018-10-16T21:51:22	Jocelyn Larouche	low 4M	1716667	188833370	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	-	-
2015-05-02T07:36:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.144	-	-
2015-05-02T07:36:00	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		-	-	8.706	-	-
2019-06-17T12:15:06	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.125 GHz-days
Estimated T-Level:	24.839

Digits	B1	Curves	Complete	FacMiss
20	11000	271 / 100	2.710	6.564%
25	50000	271 / 280	0.968	37.924%

New Calculation Method

Total ECM effort:	16.125 GHz-days
Estimated T-Level:	24.839

Digits	B1	Complete	FacMiss
20	11000	8.742	0.016%
25	50000	0.790	45.381%
30	250000	0.049	95.251%
35	1000000	0.002	99.777%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		269	16.01
50000	5000000	5842478394291864250537	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-01T23:58:00	Team_Bundu	bundu4	50000	5000000						3	0.179
2009-06-29T08:54:00	James Hintz	05_060309	50000	5000000						3	0.179
2010-07-22T05:04:00	SubPrime	abd0	50000	5000000						3	0.179
2010-07-22T06:14:00	SubPrime	abd0	50000	5000000						3	0.179
2013-04-25T16:48:00	Donna Noble	opt4820	50000	5000000						3	0.179
2014-01-17T19:51:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-10-20T15:02:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-06-22T17:24:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2015-09-30T19:41:12	mikr	MSI	50000	5000000						12	0.714
2016-09-15T17:33:48	Bruce	DESK3	50000	5000000						3	0.179
2016-11-17T20:58:40	Bruce	DESK3	50000	5000000						3	0.179
2017-01-12T04:16:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2017-04-28T22:26:00	ANONYMOUS	Worker	50000	5000000						3	0.179
2017-11-24T11:34:18	Bruce	DESK3	50000	5000000						3	0.179
2018-01-28T08:47:57	Bruce	DESK3	50000	5000000						3	0.179
2019-07-05T23:52:38	storm5510	7700_Kaby_Lake	50000	5000000						3	0.179
2019-07-17T18:14:20	nordi	nordiputer	50000	5000000						50	2.975
2019-11-15T02:26:37	wazuma	G751	50000	5000000						3	0.179
2019-11-15T10:06:38	mnd9	25836b	50000	5000000						3	0.179
2019-11-15T17:57:59	mnd9	25836b	50000	5000000						3	0.179
2019-11-17T05:42:44	penlu	grizzly	50000	5000000						3	0.179
2020-02-18T06:04:37	EricP	Cannonfodder	50000	5000000						3	0.179
2020-02-25T14:05:56	Keysarecool	HPLaptop	50000	5000000						3	0.179
2020-03-03T13:04:53	mnd9	l2lounge	50000	5000000						3	0.179
2020-03-10T01:16:33	daveward2005	Davy	50000	5000000						3	0.179
2020-03-17T23:34:05	mnd9	25836b	50000	5000000						3	0.179
2020-03-27T19:34:54	EricP	Cannonfodder	50000	5000000						3	0.179
2020-04-08T23:15:11	MarkS	laptop64	50000	5000000	5842478394291864250537	72.307	2	2	5699554646540678	2	0.119
2020-05-04T10:43:21	TJAOI	Manual testing	50000	5000000						132	7.854

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	CD86DCD7280938D5	0.081
2015-06-27T00:56:00	MadPoo	Manual testing	CD86DCD7280938D5	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 = 1716667, B2 = 188833370 (P-1 stage 2)

B1 = 1716667, B2 = 171666700 (P-1 stage 2)

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

B1 = 3642200 (P-1 stage 1)

B1 = 1716667 (P-1 stage 1)

B1 = 1562783 (P-1 stage 1)

B1 = 1420712 (P-1 stage 1)

B1 = 1291557 (P-1 stage 1)

B1 = 1174143 (P-1 stage 1)

B1 = 1067403 (P-1 stage 1)

B1 = 970367 (P-1 stage 1)

B1 = 882152 (P-1 stage 1)

B1 = 801957 (P-1 stage 1)

B1 = 729052 (P-1 stage 1)

B1 = 602523 (P-1 stage 1)

B1 = 497954 (P-1 stage 1)

B1 = 452686 (P-1 stage 1)

B1 = 411533 (P-1 stage 1)

B1 = 374121 (P-1 stage 1)

B1 = 309191 (P-1 stage 1)

B1 = 281083 (P-1 stage 1)

B1 = 187389 (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

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