M1713403 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	17.3420	68.6567%	1713403	188474330	0.8113	8.6188%	18.1533	71.3581%	2.7014%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7913%	0.0122	64.1863%	1.0284%
GPU72	2⁶¹	0.1793	65.5738%	7000	110000	0.0009	1.3426%	0.1801	66.0360%	0.4622%
Difference	+6	+17.1628	+3.0829%	+1706403	+188364330	+0.8104	+7.2762%	+17.9732	+5.3222%	+5.3222%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1713403	533082896563008226748839	24	78.819	155562613279832073 3 × 7 × 165931 × 44643517423	2019-04-28	165931	44643517423	70,319	165.99	310.01

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:42:00	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	2.355%
2014-04-01T22:35:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.884%
2014-05-03T00:50:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	1.110%
2014-10-05T22:25:00	Jocelyn Larouche	Manual testing	187460	187460		-		-	-	0.013	-	-	1.248%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	281190	281190		-		-	-	0.019	-	-	1.525%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	309309	309309		-		-	-	0.021	-	-	1.595%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	340239	340239		-		-	-	0.023	-	-	1.666%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	374262	374262		-		-	-	0.026	-	-	1.740%
2015-03-01T03:15:00	Jocelyn Larouche	Manual testing	411688	411688		-		-	-	0.028	-	-	1.816%
2015-03-05T14:27:00	Jocelyn Larouche	Manual testing	452856	452856		-		-	-	0.031	-	-	1.893%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	498141	498141		-		-	-	0.034	-	-	1.972%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602750	602750		-		-	-	0.041	-	-	2.136%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729327	729327		-		-	-	0.050	-	-	2.308%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	802259	802259		-		-	-	0.055	-	-	2.396%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882484	882484		-		-	-	0.060	-	-	2.487%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	970732	970732		-		-	-	0.066	-	-	2.579%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067805	1067805		-		-	-	0.073	-	-	2.673%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174585	1174585		-		-	-	0.080	-	-	2.769%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1292043	1292043		-		-	-	0.088	-	-	2.866%
2015-07-13T12:24:00	Jocelyn Larouche	Manual testing	1421247	1421247		-		-	-	0.097	-	-	2.966%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1563371	1563371		-		-	-	0.107	-	-	3.067%
2015-08-01T05:33:00	mikr	MSI	3642200	123456789		-		-	-	0.694	-	-	8.618%
2018-08-21T11:49:44	Jocelyn Larouche	low 4M	1713403	171340300	12	-		-	-	0.748	-	-	8.505%
2018-10-16T21:51:21	Jocelyn Larouche	low 4M	1713403	188474330	12	-		-	-	0.811	-	-	8.619%

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	-	-
2010-04-23T13:38:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.179	-	-
2010-10-16T22:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.931	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.573	-	-
2015-04-28T21:21:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.146	-	-
2015-04-28T21:21:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.181	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.361	-	-
2018-06-11T13:42:37	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.723	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.932 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:	14.932 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		232	13.80
50000	5000000	533082896563008226748839	19	1.130

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-03T09:50:00	Scott Kurowski	UW1	50000	5000000						3	0.178
2009-06-25T18:55:00	James Hintz	02_060209	50000	5000000						3	0.178
2010-07-15T07:21:00	firejuggler		50000	5000000						3	0.178
2011-11-29T04:00:00	S36049	Wolle5	50000	5000000						3	0.178
2013-04-24T15:44:00	Donna Noble	opt4820	50000	5000000						3	0.178
2014-01-15T06:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-10-19T05:45:00	LordJulius	Ranory	50000	5000000						3	0.178
2015-06-16T15:15:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-09-18T21:09:00	mikr	MSI	50000	5000000						12	0.714
2016-09-13T09:18:24	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-11-16T03:52:22	Bruce	DESK3	50000	5000000						3	0.178
2017-01-10T09:05:49	Bruce	DESK3	50000	5000000						3	0.178
2017-04-27T14:47:12	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-11-21T06:43:36	Bruce	DESK3	50000	5000000						3	0.178
2018-01-26T03:45:59	Bruce	DESK3	50000	5000000						3	0.178
2019-04-28T20:36:43	nordi	nordiputer	50000	5000000	533082896563008226748839	78.819	19	2		19	1.130
2020-04-13T10:22:19	TJAOI	Manual testing	50000	5000000						178	10.59

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	670739961CF431B5	0.081
2015-06-28T05:06:00	MadPoo	Manual testing	670739961CF431B5	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 = 1713403, B2 = 188474330 (P-1 stage 2)

B1 = 1713403, B2 = 171340300 (P-1 stage 2)

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

B1 = 3642200 (P-1 stage 1)

B1 = 1713403 (P-1 stage 1)

B1 = 1563371 (P-1 stage 1)

B1 = 1421247 (P-1 stage 1)

B1 = 1292043 (P-1 stage 1)

B1 = 1174585 (P-1 stage 1)

B1 = 1067805 (P-1 stage 1)

B1 = 970732 (P-1 stage 1)

B1 = 882484 (P-1 stage 1)

B1 = 802259 (P-1 stage 1)

B1 = 729327 (P-1 stage 1)

B1 = 602750 (P-1 stage 1)

B1 = 498141 (P-1 stage 1)

B1 = 452856 (P-1 stage 1)

B1 = 411688 (P-1 stage 1)

B1 = 374262 (P-1 stage 1)

B1 = 340239 (P-1 stage 1)

B1 = 309309 (P-1 stage 1)

B1 = 281190 (P-1 stage 1)

B1 = 187460 (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)

10³

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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