M1714891 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	17.3270	68.6567%	3642200	123456789	0.6940	8.6188%	18.0210	71.3581%	2.7014%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7917%	0.0122	64.1864%	1.0285%
GPU72	2⁶¹	0.1791	65.5738%	7000	110000	0.0009	1.3428%	0.1800	66.0361%	0.4623%
Difference	+6	+17.1479	+3.0829%	+3635200	+123346789	+0.6931	+7.2760%	+17.8410	+5.3221%	+5.3221%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1714891	158978357229206488048279	24	77.073	46352321293075329 3 × 7 × 2207253394908349	2019-05-09	7	2207253394908349	20,201	8,206,430	15,327,326

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-29T18:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.572%
2011-02-10T06:35:00	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	187428	187428		-		-	-	0.013	-	-	1.248%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	281142	281142		-		-	-	0.019	-	-	1.525%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	309256	309256		-		-	-	0.021	-	-	1.595%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	340181	340181		-		-	-	0.023	-	-	1.666%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	374199	374199		-		-	-	0.026	-	-	1.740%
2015-03-01T03:15:00	Jocelyn Larouche	Manual testing	411618	411618		-		-	-	0.028	-	-	1.816%
2015-03-05T14:27:00	Jocelyn Larouche	Manual testing	452779	452779		-		-	-	0.031	-	-	1.893%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	498056	498056		-		-	-	0.034	-	-	1.972%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	602647	602647		-		-	-	0.041	-	-	2.136%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	729202	729202		-		-	-	0.050	-	-	2.308%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	802122	802122		-		-	-	0.055	-	-	2.396%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	882334	882334		-		-	-	0.060	-	-	2.487%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	970567	970567		-		-	-	0.066	-	-	2.579%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1067623	1067623		-		-	-	0.073	-	-	2.673%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1174385	1174385		-		-	-	0.080	-	-	2.769%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1291823	1291823		-		-	-	0.088	-	-	2.866%
2015-07-13T12:24:00	Jocelyn Larouche	Manual testing	1421005	1421005		-		-	-	0.097	-	-	2.966%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1563105	1563105		-		-	-	0.107	-	-	3.067%
2015-08-04T15:21:00	mikr	MSI	3642200	123456789		-		-	-	0.694	-	-	8.619%
2018-04-01T08:25:35	Jocelyn Larouche	low 4M	1719415	171941500	12	-		-	-	0.750	-	-	8.513%

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	-	-
2010-04-24T12:42:00	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		-	-	0.572	-	-
2015-04-29T06:30:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.145	-	-
2015-04-29T06:30:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.179	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.358	-	-
2018-06-04T13:10:09	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.715	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.933 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:	14.933 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		244	14.52
50000	5000000	158978357229206488048279	7	0.416

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-01T05:14:00	Team_Bundu	bundu4	50000	5000000						3	0.178
2009-06-26T05:14:00	James Hintz	04_060209	50000	5000000						3	0.178
2010-07-22T07:33:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.178
2011-12-01T14:41:00	OS1	L3	50000	5000000						3	0.178
2013-04-25T03:50:00	Donna Noble	opt4820	50000	5000000						3	0.178
2014-01-16T15:15:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-10-17T13:47:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-06-19T09:17:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-09-24T18:01:23	mikr	MSI	50000	5000000						12	0.714
2016-09-14T08:45:42	Bruce	DESK3	50000	5000000						3	0.178
2016-11-16T22:02:35	Bruce	DESK3	50000	5000000						3	0.178
2017-01-11T03:33:30	Bruce	DESK3	50000	5000000						3	0.178
2017-04-28T04:22:41	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-11-22T18:40:17	Bruce	DESK3	50000	5000000						3	0.178
2018-01-27T06:38:20	Bruce	DESK3	50000	5000000						3	0.178
2019-05-09T18:19:49	nordi	nordiputer	50000	5000000	158978357229206488048279	77.073	7	2		7	0.416
2020-04-20T10:38:38	TJAOI	Manual testing	50000	5000000						190	11.30

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	DE074ED317134D88	0.081
2015-07-10T01:00:00	MadPoo	Manual testing	DE074ED317134D88	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 = 1719415, B2 = 171941500 (P-1 stage 2)

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

B1 = 3642200 (P-1 stage 1)

B1 = 1719415 (P-1 stage 1)

B1 = 1563105 (P-1 stage 1)

B1 = 1421005 (P-1 stage 1)

B1 = 1291823 (P-1 stage 1)

B1 = 1174385 (P-1 stage 1)

B1 = 1067623 (P-1 stage 1)

B1 = 970567 (P-1 stage 1)

B1 = 882334 (P-1 stage 1)

B1 = 802122 (P-1 stage 1)

B1 = 729202 (P-1 stage 1)

B1 = 602647 (P-1 stage 1)

B1 = 498056 (P-1 stage 1)

B1 = 452779 (P-1 stage 1)

B1 = 411618 (P-1 stage 1)

B1 = 374199 (P-1 stage 1)

B1 = 340181 (P-1 stage 1)

B1 = 309256 (P-1 stage 1)

B1 = 281142 (P-1 stage 1)

B1 = 187428 (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)

B1 = 50000 (P-1 stage 1)

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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