M2039651 Mersenne number exponent details

is 2 ^2039651 - 1

has 613997 decimal digits

takes 0.134 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	29.2231	69.1176%	4000000	200000000	1.3994	8.7566%	30.6225	71.8219%	2.7043%
PrimeNet	2⁵⁸	0.0188	63.7931%	9000	160000	0.0016	2.6631%	0.0205	64.7573%	0.9642%
GPU72	2⁶²	0.3012	66.1290%	9000	120000	0.0014	1.3289%	0.3026	66.5791%	0.4501%
Difference	+6	+28.9219	+2.9886%	+3991000	+199880000	+1.3980	+7.4277%	+30.3199	+5.2428%	+5.2428%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2039651	232096989155324736161985479	27	87.585	56896250671150293889 359 × 19891 × 7967692821581	2020-08-03	19891	7967692821581	16,727,212	41,386	77,298

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.221%
2009-02-10T22:35:00	markr	Manual testing	100000	3000000		-		-	-	0.025	-	-	2.578%
2014-07-18T01:19:00	Jocelyn Larouche	Manual testing	131468	131468		-		-	-	0.013	-	-	0.928%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	162936	162936		-		-	-	0.016	-	-	1.045%
2015-10-05T16:36:02	Bruno Victal	4790K-windows	500000	15000000	12	-		-	-	0.123	-	-	4.661%
2019-06-21T15:05:43	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.757%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	twmoss	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-02T12:27:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-02-11T14:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.151	-	-
2013-08-30T08:22:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.481	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.963	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.832	-	-
2015-11-01T21:50:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.664	-	-
2016-07-30T17:09:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.327	-	-
2019-03-21T06:49:56	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.344 GHz-days
Estimated T-Level:	22.179

Digits	B1	Curves	Complete	FacMiss
20	11000	122 / 100	1.220	29.342%
25	50000	122 / 280	0.436	64.630%

New Calculation Method

Total ECM effort:	10.344 GHz-days
Estimated T-Level:	22.179

Digits	B1	Complete	FacMiss
20	11000	3.935	1.954%
25	50000	0.356	70.069%
30	250000	0.022	97.834%
35	1000000	0.001	99.900%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		120	10.17
50000	5000000	232096989155324736161985479	2	0.170

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-10T16:43:00	Architects Cubed	m1_01	50000	5000000						3	0.254
2009-10-15T11:08:00	SubPrime	abd0	50000	5000000						3	0.254
2011-03-02T19:03:00	James Hintz	ryan	50000	5000000						3	0.254
2013-02-26T11:02:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.254
2014-03-21T08:03:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-08T20:05:00	nranks	wlaptop	50000	5000000						3	0.254
2016-02-19T07:02:11	Sintax	cloud	50000	5000000						3	0.254
2016-04-29T07:47:34	Jason U	Server7	50000	5000000						3	0.254
2016-07-15T02:55:07	Bruce	test	50000	5000000						3	0.254
2016-11-22T11:30:33	NBCC		50000	5000000						3	0.254
2017-06-18T23:10:25	Bruce	Desk6	50000	5000000						3	0.254
2017-11-22T02:33:04	Bruce	Desk6	50000	5000000						3	0.254
2018-03-29T01:08:31	Bruce	Desk6	50000	5000000						3	0.254
2018-09-13T18:37:36	Bruce	Desk6	50000	5000000						3	0.254
2019-12-22T20:54:01	daveward2005	Davy	50000	5000000						3	0.254
2019-12-28T19:15:06	TheJudger	myECM	50000	5000000						3	0.254
2020-01-02T17:45:37	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-01-09T03:33:08	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-01-16T15:59:48	EricP	Cannonfodder	50000	5000000						3	0.254
2020-01-22T08:10:14	Keysarecool	Boat_Anchor	50000	5000000						3	0.254
2020-01-29T00:39:48	IanGlencross	glenx24	50000	5000000						3	0.254
2020-02-08T08:46:05	ANONYMOUS		50000	5000000						3	0.254
2020-02-15T01:45:10	mat10243x	B2	50000	5000000						3	0.254
2020-02-22T21:33:07	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-02-29T23:40:41	MarkS	desktop-i7	50000	5000000						3	0.254
2020-03-06T20:10:52	mnd9	75211backdoorb	50000	5000000						3	0.254
2020-03-13T23:39:37	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.254
2020-03-22T00:06:40	mnd9	libproj	50000	5000000						3	0.254
2020-04-02T20:11:07	EricP	Cannonfodder	50000	5000000						3	0.254
2020-04-16T18:01:41	EricP	Cannonfodder	50000	5000000						3	0.254
2020-04-26T01:57:39	mnd9	office2	50000	5000000						3	0.254
2020-05-04T22:00:03	mnd9	colab	50000	5000000						3	0.254
2020-05-16T16:20:17	mnd9	50871b	50000	5000000						3	0.254
2020-06-04T17:32:30	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.254
2020-06-21T18:51:10	Dylan Delgado	colab	50000	5000000						3	0.254
2020-07-03T13:30:56	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.254
2020-07-08T06:39:12	GAN	PG-HP	50000	5000000						3	0.254
2020-07-14T08:17:17	GAN	LMS-02	50000	5000000						3	0.254
2020-07-20T07:30:24	Summy	CHB	50000	5000000						3	0.254
2020-07-26T20:54:32	GAN	LMS-07	50000	5000000						3	0.254
2020-08-03T04:53:38	MarkS	desktop-i7	50000	5000000	232096989155324736161985479	87.585	2	2	50254725682046	2	0.170

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	FFBBD71DA26537BC	0.134
2016-07-15T19:16:45	Mark Rose	raphael	FFBBD71DA26537BC	0.134

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-03T08:36:45

CrypticClue

cruncher

232096989155324736161985479

D2945FB528252CA4

2020-08-06T01:25:05

kutens

spica

232096989155324736161985479

D2945FB528252CA4

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 100000, B2 = 3000000 (P-1 stage 2)

B1 = 162936 (P-1 stage 1)

B1 = 131468 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-06T01:25:05+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