M1977721 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	2⁷¹	241.7319	70.4225%	1977721	247215125	1.4624	6.6140%	243.1943	72.3788%	1.9562%
PrimeNet	2⁵⁸	0.0194	63.7931%	8000	140000	0.0014	2.4735%	0.0209	64.6887%	0.8956%
GPU72	2⁶²	0.3106	66.1290%	8000	100000	0.0012	1.1969%	0.3119	66.5344%	0.4054%
Difference	+9	+241.4213	+4.2935%	+1969721	+247115125	+1.4611	+5.4171%	+242.8824	+5.8444%	+5.8444%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1977721	4715671413430074865209913	25	81.964	1192198346842167036 2² × 3⁴ × 23 × 78593 × 2035597001	2020-04-02	78593	2035597001	317,089	10.580	19.748

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-25T05:26:00	kurly	slice	1000000	30000000		-		-	-	0.246	-	-	4.323%
2018-01-23T13:04:03	Jocelyn Larouche	low 4M	1977721	30000000	12	-		-	-	0.334	-	-	4.646%
2018-02-14T12:53:58	Jocelyn Larouche	low 4M	1977721	60000000	12	-		-	-	0.490	-	-	5.282%
2018-03-06T12:48:08	Jocelyn Larouche	low 4M	1977721	120000000	12	-		-	-	0.802	-	-	5.928%
2018-05-28T10:19:12	Jocelyn Larouche	low 4M	1977721	197772100	12	-		-	-	1.206	-	-	6.401%
2018-11-26T12:53:53	Jocelyn Larouche	Manual testing	1977721	247215125	12	-		-	-	1.462	-	-	6.614%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:01	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.058	-	-
2009-12-23T06:27:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.078	-	-
2016-02-23T16:29:01	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.155	-	-
2011-09-03T15:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.807	-	-
2016-02-23T16:29:01	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.496	-	-
2015-03-17T13:10:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.993	-	-
2015-03-17T13:10:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.889	-	-
2015-09-10T08:47:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.778	-	-
2018-03-08T06:00:50	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	7.557	-	-
2018-03-08T06:00:50	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	15.11	-	-
2018-03-08T06:00:50	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	30.23	-	-
2018-03-08T06:00:50	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	60.46	-	-
2018-06-11T14:43:00	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	120.9	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.024 GHz-days
Estimated T-Level:	4.750

Digits	B1	Curves	Complete	FacMiss
20	11000	95 / 100	0.950	38.490%
25	50000	95 / 280	0.339	71.185%

New Calculation Method

Total ECM effort:	8.024 GHz-days
Estimated T-Level:	4.750

Digits	B1	Complete	FacMiss
20	11000	3.065	4.668%
25	50000	0.277	75.808%
30	250000	0.017	98.309%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	7.856
50000	5000000	4715671413430074865209913	2	0.169

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-24T13:05:00	dachshund	Ann	50000	5000000						3	0.253
2009-08-26T12:03:00	SubPrime	mysql0	50000	5000000						3	0.253
2011-01-28T19:56:00	BlackburnCode	SpecOpUs2	50000	5000000						3	0.253
2012-12-11T08:27:00	OS1	L3	50000	5000000						3	0.253
2014-02-02T20:44:00	arnaud	srv-630	50000	5000000						3	0.253
2015-06-25T18:35:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.253
2016-02-14T22:53:37	Jason U	Server7	50000	5000000						3	0.253
2016-04-05T13:58:48	StarionHost	Bluto	50000	5000000						3	0.253
2016-07-07T22:48:03	Bruce	test	50000	5000000						3	0.253
2016-11-06T21:46:38	Bruce	Desk6	50000	5000000						3	0.253
2017-06-11T22:15:42	Bruce	Desk6	50000	5000000						3	0.253
2017-10-17T09:52:10	Clark B. Wierda	CF-27	50000	5000000						3	0.253
2018-02-04T22:32:36	Bruce	Desk6	50000	5000000						3	0.253
2018-07-10T09:31:47	Bruce	Desk6	50000	5000000						3	0.253
2019-06-25T09:36:35	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.253
2019-12-17T04:21:52	S04803	lfmcal	50000	5000000						3	0.253
2019-12-21T02:48:00	mnd9	50871b	50000	5000000						3	0.253
2019-12-22T17:29:05	Brett Walker	brain	50000	5000000						3	0.253
2019-12-28T11:04:35	George Woltman	colab	50000	5000000						3	0.253
2020-01-02T09:36:32	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.253
2020-01-16T11:06:37	mnd9	kitchen	50000	5000000						3	0.253
2020-01-21T20:17:04	Keysarecool	HPLaptop	50000	5000000						3	0.253
2020-01-23T04:04:19	mnd9	75201b	50000	5000000						3	0.253
2020-01-28T23:47:43	David_McCann	i5	50000	5000000						3	0.253
2020-02-07T07:27:49	mnd9	25836b	50000	5000000						3	0.253
2020-02-14T17:55:33	mnd9	75201b	50000	5000000						3	0.253
2020-02-22T07:51:53	Sergey Nosov	TS140-02	50000	5000000						3	0.253
2020-02-28T18:21:04	mnd9	27016b	50000	5000000						3	0.253
2020-03-06T10:59:44	mnd9	75201b	50000	5000000						3	0.253
2020-03-13T04:39:50	Nesowa	6700T	50000	5000000						3	0.253
2020-03-20T22:38:41	mnd9	office2	50000	5000000						3	0.253
2020-04-02T08:01:53	MarkS	desktop-i7	50000	5000000	4715671413430074865209913	81.964	2	2	1454142880495500	2	0.169

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	8BD5C0A72A24D085	0.130
2015-07-12T18:10:00	MadPoo	Manual testing	8BD5C0A72A24D085	0.130

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 = 1977721, B2 = 247215125 (P-1 stage 2)

B1 = 1977721, B2 = 197772100 (P-1 stage 2)

B1 = 1977721, B2 = 120000000 (P-1 stage 2)

B1 = 1977721, B2 = 60000000 (P-1 stage 2)

B1 = 1977721, B2 = 30000000 (P-1 stage 2)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1977721 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10³

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10⁷

10³

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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