M2020661 Mersenne number exponent details

is 2 ^2020661 - 1

has 608280 decimal digits

takes 0.133 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	29.4977	69.1176%	4000000	200000000	1.3994	8.7489%	30.8971	71.8195%	2.7019%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6121%	0.0206	64.7389%	0.9458%
GPU72	2⁶²	0.3040	66.1290%	8000	120000	0.0013	1.2734%	0.3054	66.5603%	0.4313%
Difference	+6	+29.1937	+2.9886%	+3992000	+199880000	+1.3981	+7.4755%	+30.5918	+5.2592%	+5.2592%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2020661	1132338949833807693397259503	28	89.871	280190232264048173691 3 × 13 × 409 × 17565684425054741	2020-02-29	409	17565684425054741	123,163,214	91,240,556	170,411,950

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.017%
2002-12-31T00:00:00	ANONYMOUS	v4_computers	25000	412500		-		-	-	0.004	-	-	1.078%
2010-12-08T22:41:00	Jocelyn Larouche	Manual testing	202066	202066		-		-	-	0.019	-	-	1.170%
2013-10-18T06:05:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	4.745%
2019-02-25T12:57:37	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.749%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-02T10:33:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-04T16:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.152	-	-
2013-02-11T20:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.486	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.972	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.849	-	-
2015-10-28T09:42:37	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.698	-	-
2016-07-02T13:21:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.396	-	-
2019-03-18T03:51:00	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.79	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.521 GHz-days
Estimated T-Level:	3.850

Digits	B1	Curves	Complete	FacMiss
20	11000	77 / 100	0.770	46.122%
25	50000	77 / 280	0.275	75.920%

New Calculation Method

Total ECM effort:	6.521 GHz-days
Estimated T-Level:	3.850

Digits	B1	Complete	FacMiss
20	11000	2.484	8.342%
25	50000	0.224	79.892%
30	250000	0.014	98.627%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	6.352
50000	5000000	1132338949833807693397259503	2	0.169

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-03T00:10:00	mognuts	hallowes	50000	5000000						3	0.254
2009-09-09T20:07:00	James Hintz	08_071509	50000	5000000						3	0.254
2011-02-12T20:32:00	Richard Kint	Desktop	50000	5000000						3	0.254
2013-02-08T19:05:00	S00030	op9020-usff	50000	5000000						3	0.254
2014-03-18T09:52:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-02T14:13:00	guru	w1	50000	5000000						3	0.254
2015-10-06T11:44:50	mikr	MSI	50000	5000000						12	1.016
2017-05-09T00:03:04	Bruce	Desk6	50000	5000000						3	0.254
2017-11-08T18:56:23	Bruce	Desk6	50000	5000000						3	0.254
2018-03-13T10:50:08	Bruce	Desk6	50000	5000000						3	0.254
2018-08-14T10:02:09	-Anonymous-	Kitchen	50000	5000000						3	0.254
2019-11-02T09:35:04	monsted	rootweiler	50000	5000000						3	0.254
2019-12-23T11:56:38	Sergey Nosov	TS140-02	50000	5000000						3	0.254
2020-01-02T22:43:18	J.R. Allen	lapacer	50000	5000000						3	0.254
2020-01-08T22:44:20	EricP	Cannonfodder	50000	5000000						3	0.254
2020-01-12T11:40:07	mnd9	office2	50000	5000000						3	0.254
2020-01-17T12:56:21	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-01-22T18:40:21	mnd9	221Lb	50000	5000000						3	0.254
2020-01-30T03:02:28	David_McCann	i5	50000	5000000						3	0.254
2020-02-08T06:18:44	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-02-15T22:10:36	mnd9	office2	50000	5000000						3	0.254
2020-02-23T04:51:55	Keysarecool	Boat_Anchor	50000	5000000						3	0.254
2020-02-29T19:02:54	Keysarecool	HPLaptop	50000	5000000	1132338949833807693397259503	89.871	2	2	5451787440860108	2	0.169

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	977603765C5A01F6	0.133
2016-07-15T13:25:59	Mark Rose	michelangelo	977603765C5A01F6	0.133

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-03-01T12:25:18

Christoph Zenger

Manual testing

1132338949833807693397259503

2CB145E40B6A8506

2020-03-03T19:02:53

Bommer

2600X

1132338949833807693397259503

2CB145E40B6A8506

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 580000, B2 = 15080000 (P-1 stage 2)

B1 = 580000 (P-1 stage 1)

B1 = 202066 (P-1 stage 1)

B1 = 25000, B2 = 412500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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10¹⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-03-03T19:02:53+00:00

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