M2138629 Mersenne number exponent details

is 2 ^2138629 - 1

has 643792 decimal digits

takes 0.141 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	27.8706	67.6471%	2500000	125000000	0.8746	7.9127%	28.7452	70.2071%	2.5600%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7310%	0.0196	63.1049%	1.0359%
GPU72	2⁶²	0.2873	64.5161%	10000	150000	0.0017	1.4873%	0.2889	65.0439%	0.5278%
Difference	+6	+27.5833	+3.1309%	+2490000	+124850000	+0.8730	+6.4254%	+28.4563	+5.1632%	+5.1632%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2138629	2439444139337221008155447	25	81.013	570328967608973087 21649 × 26344356210863	2020-04-12	21649	26344356210863	391,917	136,839	255,577

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2010-10-26T06:40:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.669%
2010-11-27T10:40:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.103%
2013-12-03T16:49:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.330%
2017-10-19T20:43:04	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.913%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:06	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T22:58:00	Sturle Sunde	figaro.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-16T06:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.459	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.918	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.747	-	-
2015-12-27T16:49:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.494	-	-
2016-10-29T15:24:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.988	-	-
2019-04-22T13:11:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.98	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.056 GHz-days
Estimated T-Level:	3.550

Digits	B1	Curves	Complete	FacMiss
20	11000	71 / 100	0.710	48.989%
25	50000	71 / 280	0.254	77.567%

New Calculation Method

Total ECM effort:	6.056 GHz-days
Estimated T-Level:	3.550

Digits	B1	Complete	FacMiss
20	11000	2.290	10.123%
25	50000	0.207	81.302%
30	250000	0.013	98.733%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	5.885
50000	5000000	2439444139337221008155447	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-02T14:25:00	dragon325	x-liberty	50000	5000000						3	0.256
2009-11-23T04:22:00	SubPrime	mysql0	50000	5000000						3	0.256
2011-07-30T13:01:00	Andrew B	dell_xps_8100_i7_x86	50000	5000000						3	0.256
2013-04-21T08:26:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2014-12-19T06:12:00	OS1	L3	50000	5000000						3	0.256
2015-08-13T21:12:00	guru	w6	50000	5000000						3	0.256
2016-03-14T07:20:03	Dave Matthews	VMW7-001	50000	5000000						3	0.256
2016-06-15T00:27:58	Bruce	test	50000	5000000						3	0.256
2016-09-15T18:07:48	Bruce	Desk6	50000	5000000						3	0.256
2017-03-11T02:57:04	Bruce	Desk6	50000	5000000						3	0.256
2017-09-25T02:35:14	Bruce	Desk6	50000	5000000						3	0.256
2018-02-06T19:41:37	Bruce	Desk6	50000	5000000						3	0.256
2018-07-20T22:05:38	Bruce	Desk6	50000	5000000						3	0.256
2019-10-04T04:33:46	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-21T11:59:02	David_McCann	i5	50000	5000000						3	0.256
2020-01-27T13:25:02	mnd9	75204b	50000	5000000						3	0.256
2020-02-05T19:52:08	cappy95833	HomePC	50000	5000000						3	0.256
2020-02-13T00:16:13	IanGlencross	glenx24	50000	5000000						3	0.256
2020-02-20T18:38:25	mnd9	colab	50000	5000000						3	0.256
2020-02-27T03:13:06	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-03-05T07:46:34	kracker	O0	50000	5000000						3	0.256
2020-03-11T21:50:53	mnd9	75201b	50000	5000000						3	0.256
2020-03-19T03:15:09	EricP	Cannonfodder	50000	5000000						3	0.256
2020-04-12T21:22:21	mnd9	eileen	50000	5000000	2439444139337221008155447	81.013	2	2	6258004143673607	2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	A2BD463D0C88C10B	0.141
2018-04-07T05:59:02	kkmrkkblmbrbk	old	A2BD463D0C88C10B	0.141

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-04-13T01:42:03

CrypticClue

cruncher

2439444139337221008155447

3EF1A6DEF6165F57

2020-04-13T04:35:04

Igvan28

MineOld

2439444139337221008155447

3EF1A6DEF6165F57

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 80000, B2 = 1500000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 75011 (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

10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-13T04:35:04+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