M1649783 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	18.0108	68.6567%	2000000	20000000	0.2034	6.0137%	18.2142	70.5416%	1.8849%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5634%	0.0125	64.1023%	0.9444%
GPU72	2⁶¹	0.1862	65.5738%	6500	80000	0.0007	1.1721%	0.1869	65.9773%	0.4035%
Difference	+6	+17.8246	+3.0829%	+1993500	+19920000	+0.2027	+4.8417%	+18.0273	+4.5644%	+4.5644%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1649783	8423430207674977145687	22	72.835	2552890352147821 7 × 364698621735403	2017-12-17	7	364698621735403	617.45	1,355,927	2,532,493

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:08:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.878%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.281%
2012-02-29T18:08:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.562%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.782%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.964%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.120%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.258%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.381%
2012-02-29T21:09:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.492%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.594%
2012-03-01T06:08:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.723%
2012-03-01T07:08:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.688%
2017-12-17T12:26:34	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.203	-	-	6.014%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2010-05-01T20:30:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.093	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.186	-	-
2010-08-03T22:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.967	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.595	-	-
2015-05-07T00:03:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.190	-	-
2015-05-07T16:26:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.265	-	-
2015-10-11T16:52:49	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.530	-	-
2017-10-20T14:50:28	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.059	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.873 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:	14.873 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	14.75
50000	5000000	8423430207674977145687	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-17T08:24:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-08T04:55:00	James Hintz	08_060209	50000	5000000						3	0.178
2010-05-10T06:17:00	StKl	Workstation	50000	5000000						3	0.178
2011-09-25T19:39:00	Bud	annan	50000	5000000						3	0.178
2013-03-13T05:14:00	Donna Noble	opt4820	50000	5000000						3	0.178
2013-11-27T08:51:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-07-21T09:04:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-14T14:54:00	mikr	MSI	50000	5000000						12	0.711
2016-05-15T06:53:33	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-08-08T17:52:35	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-10-11T14:22:30	Bruce	DESK3	50000	5000000						3	0.178
2016-12-08T07:06:37	Bruce	DESK3	50000	5000000						3	0.178
2017-01-30T01:46:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-08-14T16:55:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-12-17T06:22:06	Bruce	DESK3	50000	5000000	8423430207674977145687	72.835	2	2		2	0.119
2019-12-23T11:26:00	TJAOI	Manual testing	50000	5000000						198	11.73

date	userid	compid	res64	spent (GHz-days)
1998-11-14T00:00:00	ANONYMOUS	v4_computers	990A445251F0FAB1	0.078
2015-07-01T17:36:00	MadPoo	Manual testing	990A445251F0FAB1	0.078

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 = 2000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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