M1422691 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	2⁶⁸	41.8959	69.1176%	1422691	156496010	0.5465	7.4404%	42.4424	71.4154%	2.2978%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7708%	0.0074	63.5390%	1.0390%
GPU72	2⁶⁰	0.1080	65.0000%	6000	80000	0.0006	1.3022%	0.1085	65.4558%	0.4558%
Difference	+8	+41.7879	+4.1176%	+1416691	+156416010	+0.5459	+6.1382%	+42.3339	+5.9597%	+5.9597%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	15000	232500		-		-	-	0.001	-	-	0.703%
2009-07-30T20:41:00	markr	lounge	200000	5000000		-		-	-	0.026	-	-	3.117%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	245114	245114		-		-	-	0.014	-	-	1.217%
2015-01-15T22:03:00	Jocelyn Larouche	Manual testing	367671	367671		-		-	-	0.020	-	-	1.484%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	404438	404438		-		-	-	0.022	-	-	1.551%
2015-02-20T16:55:00	Jocelyn Larouche	Manual testing	444881	444881		-		-	-	0.025	-	-	1.620%
2015-03-11T16:22:00	alpertron	Manual testing	2000000	60000000		-		-	-	0.286	-	-	6.624%
2016-08-17T05:42:45	Bruno Victal	5820K-factoring	2500000	62500000	12	-		-	-	0.319	-	-	6.795%
2016-08-27T10:53:41	Bruno Victal	Manual testing	2500000	62500000	12	-		-	-	0.319	-	-	6.795%
2018-05-25T20:22:28	Jocelyn Larouche	low 4M	1422691	142269100	12	-		-	-	0.504	-	-	7.338%
2018-10-15T08:20:49	Jocelyn Larouche	low 4M	1422691	156496010	12	-		-	-	0.547	-	-	7.440%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-
2016-02-23T16:28:31	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.081	-	-
2009-02-15T08:34:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.108	-	-
2016-02-23T16:28:31	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.216	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.122	-	-
2016-02-23T16:28:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.690	-	-
2015-03-17T06:25:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.380	-	-
2015-03-17T06:25:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.626	-	-
2015-09-29T08:27:45	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	5.253	-	-
2018-04-30T12:03:48	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	10.51	-	-
2020-04-07T16:27:52	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	21.01	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.343 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	26.343 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.674	18.740%
30	250000	0.144	86.623%
35	1000000	0.010	99.005%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.84
250000	40000000		50	14.50

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-03T05:34:00	Sturle Sunde	minister	50000	5000000						1	0.047
2009-01-02T23:00:00	Carsten Kossendey	durandal	50000	5000000						1	0.047
2009-04-07T10:33:00	Carsten Kossendey	Manual testing	50000	5000000						1	0.047
2009-04-09T01:41:00	James Hintz	4115	50000	5000000						3	0.142
2009-08-28T05:26:00	Ottichris	slowly	50000	5000000						3	0.142
2010-05-06T21:59:00	josibo	surval	50000	5000000						3	0.142
2012-02-18T10:23:00	S36049	Wolle5	50000	5000000						3	0.142
2012-07-07T04:12:00	Oscar Östlin		50000	5000000						5	0.236
2014-04-03T16:57:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2014-12-27T19:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-06-10T05:29:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-11-30T20:28:16	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-02-25T21:13:11	Bruce	DESK3	50000	5000000						3	0.142
2016-04-05T07:11:44	Conductor	Alex1	50000	5000000						3	0.142
2016-05-02T02:45:12	Bruce	DESK3	50000	5000000						3	0.142
2016-06-27T00:01:41	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-09-08T11:45:11	Bruce	test	50000	5000000						3	0.142
2016-10-26T04:33:29	Bruce	DESK3	50000	5000000						3	0.142
2016-12-15T07:11:40	Bruce	DESK3	50000	5000000						3	0.142
2017-01-28T13:00:26	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2017-05-26T08:20:28	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2017-11-21T06:01:10	Bruce	DESK3	50000	5000000						3	0.142
2018-01-16T18:02:36	Lelikoid	QH	50000	5000000						3	0.142
2018-03-04T19:09:21	Lelikoid	QH	50000	5000000						3	0.142
2018-05-14T01:57:24	Lelikoid	QH	50000	5000000						3	0.142
2019-01-18T13:09:03	TJAOI	Manual testing	50000	5000000						180	8.493
2022-03-10T10:37:56	TJAOI	Manual testing	250000	40000000						50	14.50

date	userid	compid	res64	spent (GHz-days)
2015-07-01T17:36:00	MadPoo	Manual testing	466F2F0A9D5FDC88	0.054

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 = 1422691, B2 = 156496010 (P-1 stage 2)

B1 = 1422691, B2 = 142269100 (P-1 stage 2)

B1 = 2500000, B2 = 62500000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 1422691 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 444881 (P-1 stage 1)

B1 = 404438 (P-1 stage 1)

B1 = 367671 (P-1 stage 1)

B1 = 245114 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 15000, B2 = 232500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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