M1647689 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	18.0337	68.6567%	2000000	20000000	0.1930	6.0129%	18.2267	70.5414%	1.8846%
PrimeNet	2⁵⁷	0.0117	63.1579%	7000	120000	0.0009	2.5627%	0.0125	64.1021%	0.9442%
GPU72	2⁶¹	0.1864	65.5738%	6500	80000	0.0007	1.1717%	0.1871	65.9772%	0.4034%
Difference	+6	+17.8473	+3.0829%	+1993500	+19920000	+0.1924	+4.8412%	+18.0396	+4.5642%	+4.5642%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1647689	343910857014521343965809	24	78.186	104361580678914936 2³ × 3² × 13 × 17 × 6491 × 1010425433	2017-12-15	6491	1010425433	69,288	3.5659	6.6593

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:07:00	Axon	Manual testing	100000	100000		-		-	-	0.006	-	-	0.878%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.013	-	-	1.281%
2012-02-29T18:07:00	Axon	Manual testing	300000	300000		-		-	-	0.019	-	-	1.562%
2012-02-29T18:11:00	Axon	Manual testing	400000	400000		-		-	-	0.026	-	-	1.782%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.032	-	-	1.964%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.039	-	-	2.120%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.045	-	-	2.257%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.052	-	-	2.380%
2012-02-29T21:09:00	Axon	Manual testing	900000	900000		-		-	-	0.058	-	-	2.492%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.065	-	-	2.594%
2012-03-01T06:07:00	Axon	Manual testing	1000000	8000000		-		-	-	0.089	-	-	4.722%
2012-03-01T07:08:00	Axon	Manual testing	1000000	20000000		-		-	-	0.132	-	-	5.687%
2017-08-27T00:26:41	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.193	-	-	6.013%

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	-	-
2003-05-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2010-04-30T05:20:00	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		-	-	0.969	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.596	-	-
2015-05-06T17:29:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.192	-	-
2015-05-07T09:32:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.268	-	-
2015-10-11T16:52:49	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.535	-	-
2017-10-27T12:33:03	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.071	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.114 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:	14.114 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	14.00
50000	5000000	343910857014521343965809	2	0.112

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-19T19:30:00	Matt	HP	50000	5000000						3	0.169
2009-06-07T09:13:00	KAMCOBILL	PC18	50000	5000000						3	0.169
2010-05-09T17:10:00	Lupo	yorick	50000	5000000						3	0.169
2011-09-24T07:13:00	S36049	Wolle5	50000	5000000						3	0.169
2013-03-12T08:45:00	Donna Noble	opt4820	50000	5000000						3	0.169
2013-11-25T21:37:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2014-07-19T15:52:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2014-09-09T15:19:00	mikr	MSI	50000	5000000						12	0.675
2016-05-14T14:30:22	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2016-08-07T13:30:31	Bruce	DESK3	50000	5000000						3	0.169
2016-10-10T17:29:54	Bruce	DESK3	50000	5000000						3	0.169
2016-12-07T02:52:00	Bruce	DESK3	50000	5000000						3	0.169
2017-01-28T08:38:59	Bruce	DESK3	50000	5000000						3	0.169
2017-08-06T16:03:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.169
2017-12-15T11:06:13	Bruce	DESK3	50000	5000000	343910857014521343965809	78.186	2	2		2	0.112
2019-11-18T17:51:32	TJAOI	Manual testing	50000	5000000						198	11.13

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	BC66F96FD748C300	0.074
2015-07-19T18:02:00	MadPoo	Manual testing	BC66F96FD748C300	0.074

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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