M3688189 Mersenne number exponent details

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M3688189

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>>>

is 2 ^3688189 - 1

has 1110256 decimal digits

takes 0.387 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	A13DE3D33C925B7E	double-checked
PRP	D59C879918F2B091	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷⁰	64.7881	68.5714%	30000000	600000000	9.2981	10.3834%	74.0862	71.8348%	3.2633%
PrimeNet	2⁶⁰	0.0416	63.3333%	16000	320000	0.0050	3.0819%	0.0466	64.4634%	1.1300%
GPU72	2⁶⁴	0.9651	65.6250%	22000	450000	0.0069	2.1044%	0.9720	66.3484%	0.7234%
Difference	+6	+63.8230	+2.9464%	+29978000	+599550000	+9.2912	+8.2789%	+73.1142	+5.4864%	+5.4864%

Known prime factors (1 factor, 75.1 bits, 0.00203514% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3688189	39377257760788649363633	23	75.060	5338291741663544 2³ × 67 × 71 × 140274641099	2021-11-29	71	140274641099	3,064.5	1,163.9	2,173.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-13T10:16:00	Carsten Kossendey	durandal	20000	260000		-		-	-	0.005	-	-	0.723%
2012-02-18T05:36:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	1.880%
2016-07-09T02:37:05	Jocelyn Larouche	Manual testing	90000	3285000	6	-		-	-	0.040	-	-	2.216%
2016-12-26T21:22:48	Jocelyn Larouche	low 4M	108000	108000		-		-	-	0.016	-	-	0.696%
2016-12-29T20:13:42	Jocelyn Larouche	low 4M	129600	129600		-		-	-	0.020	-	-	0.776%
2017-01-30T01:31:02	Jocelyn Larouche	low 4M	167520	167520		-		-	-	0.026	-	-	0.899%
2017-02-08T21:16:25	Jocelyn Larouche	low 4M	201024	2010240	6	-		-	-	0.046	-	-	2.302%
2017-02-13T00:36:32	Jocelyn Larouche	low 4M	241228	2412280	6	-		-	-	0.055	-	-	2.481%
2020-11-17T11:50:42	axn	Manual testing	30000000	600000000	12	-		-	-	9.298	-	-	10.383%
2022-03-04T04:18:42	Jocelyn Larouche	Manual testing	90000	90000		-		-	-	0.014	-	-	0.622%
2022-03-22T11:10:16	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.664%
2022-05-25T14:13:23	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	4.369%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-07T07:42:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-05-18T18:47:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.083	-	-
2012-06-05T02:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.433	-	-
2016-02-23T16:29:36	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.266	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.532	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.013	-	-
2015-10-20T08:54:41	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.026	-	-
2017-01-05T14:31:28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.052	-	-
2018-08-06T14:04:57	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.105	-	-
2020-10-28T01:27:29	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.21	-	-
2020-10-28T01:27:29	axn	Manual testing	2⁶⁹	2⁷⁰		-	-	32.42	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.315 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	4.315 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.919	39.900%
25	50000	0.083	92.026%
30	250000	0.005	99.489%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.830
50000	5000000	39377257760788649363633	2	0.298
50000	6500000		7	1.187

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-27T12:16:00	Chang Chia-Tche	euler06	50000	5000000						3	0.447
2012-07-07T07:50:00	Smurgs	Praca	50000	5000000						3	0.447
2015-10-28T04:51:05	WileECoyote	Beaker	50000	5000000						3	0.447
2015-10-28T06:04:05	WileECoyote	Beaker	50000	5000000						3	0.447
2021-07-15T11:58:48	lycorn	colab_D_2	50000	6500000						7	1.187
2021-09-09T04:14:52	daveward2005	d12436	50000	5000000						7	1.043
2021-11-29T17:20:57	MarkS	laptop64	50000	5000000	39377257760788649363633	75.060	2	2	5767480159489301	2	0.298

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-14T00:00:00	ANONYMOUS	v4_computers	A13DE3D33C925B7E	0.387
1999-08-16T00:00:00	ANONYMOUS	v4_computers	A13DE3D33C925B7E	0.387

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-12-06T10:08:27

LaurV

trabi

39377257760788649363633

D59C879918F2B091

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 = 30000000, B2 = 600000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 241228, B2 = 2412280 (P-1 stage 2)

B1 = 201024, B2 = 2010240 (P-1 stage 2)

B1 = 90000, B2 = 3285000 (P-1 stage 2)

B1 = 241228 (P-1 stage 1)

B1 = 201024 (P-1 stage 1)

B1 = 90000, B2 = 1642500 (P-1 stage 2)

B1 = 167520 (P-1 stage 1)

B1 = 129600 (P-1 stage 1)

B1 = 108000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-05-25T14:13:23+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