M1657729 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	17.9245	68.6567%	1000000	20000000	0.1389	5.6908%	18.0634	70.4404%	1.7837%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5658%	0.0125	64.1032%	0.9453%
GPU72	2⁶¹	0.1853	65.5738%	7000	70000	0.0007	1.1523%	0.1860	65.9705%	0.3967%
Difference	+6	+17.7392	+3.0829%	+993000	+19930000	+0.1382	+4.5385%	+17.8773	+4.4699%	+4.4699%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1657729	90798090778825316764942252553	29	96.197	27386288946753455107844 2² × 7 × 13 × 75237057546025975571	2017-09-12	13	75237057546025975571	1.015e+10	2.797e+11	5.225e+11

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	-	-	0.879%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.282%
2012-02-29T18:09:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.564%
2012-02-29T18:12:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.783%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.966%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.122%
2012-02-29T20:09:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.259%
2012-02-29T20:12:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.382%
2012-02-29T21:10:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.494%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.596%
2012-03-01T06:08:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.725%
2012-03-01T07:09:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.691%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:28:44	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.093	-	-
2010-04-28T14:50:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.093	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.185	-	-
2010-08-13T02:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.963	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.592	-	-
2015-05-08T21:33:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.184	-	-
2015-05-09T21:50:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.254	-	-
2015-10-11T16:53:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.508	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.881 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:	14.881 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		250	14.82
50000	5000000	90798090778825316764942252553	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-23T13:54:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-09T23:56:00	James Hintz	11_060902	50000	5000000						3	0.178
2010-05-15T00:14:00	James Classen	towerofart	50000	5000000						3	0.178
2011-10-03T19:52:00	Bud	annan	50000	5000000						3	0.178
2013-03-16T03:09:00	Donna Noble	opt4820	50000	5000000						3	0.178
2013-12-03T17:19:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-07-27T05:54:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-30T19:21:00	mikr	MSI	50000	5000000						12	0.711
2016-05-19T02:16:29	Bruce	DESK3	50000	5000000						3	0.178
2016-08-12T02:34:20	Bruce	DESK3	50000	5000000						3	0.178
2016-10-14T05:04:17	Bruce	DESK3	50000	5000000						3	0.178
2016-12-12T06:09:21	Bruce	DESK3	50000	5000000						3	0.178
2017-02-12T01:36:20	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-09-12T02:58:51	Chang Chia-Tche	exbpc13	50000	5000000	90798090778825316764942252553	96.197	1	2		1	0.059
2019-12-02T14:38:08	TJAOI	Manual testing	50000	5000000						202	11.98

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	FF7C00B4108E8C43	0.078
2015-07-10T01:00:00	MadPoo	Manual testing	FF7C00B4108E8C43	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 = 1000000, B2 = 20000000 (P-1 stage 2)

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

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10⁰

10¹

10²

10³

10⁴

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10⁶

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10⁸

10⁹

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10¹³

10¹⁴

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10²⁰

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