M3667249 Mersenne number exponent details

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M3667249

<<<

>>>

is 2 ^3667249 - 1

has 1103952 decimal digits

takes 0.385 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 L-L tests remaining

	Residue	Status
L-L	1945115FECC47FDE	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	16.2533	67.6471%	30000000	600000000	9.2981	11.8512%	25.5514	71.4813%	8.1479%
PrimeNet	2⁶⁰	0.0419	63.3333%	16000	320000	0.0050	3.0789%	0.0468	64.4623%	1.1289%
GPU72	2⁶⁴	0.9706	65.6250%	22000	400000	0.0065	2.0379%	0.9771	66.3255%	0.7005%
Difference	+4	+15.2827	+2.0221%	+29978000	+599600000	+9.2916	+9.8133%	+24.5743	+5.1557%	+5.1557%

Known prime factors (1 factor, 138.0 bits, 0.00376247% 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
3667249	343439538302947378252521531857403032501081	42	137.979	46825227616524999836733411319684460 2² × 5 × 85643 × 231631 × 13569559 × 20526673 × 423718133	2020-10-10	20526673	423718133	4.781e+10	6.4714	6.5663

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-11T19:28:00	Carsten Kossendey	durandal	20000	260000		-		-	-	0.005	-	-	0.980%
2012-02-06T15:34:00	Squeeky_Squirrel	P4_2600	90000	1642500		-		-	-	0.027	-	-	2.398%
2016-06-22T11:31:19	Jocelyn Larouche	Manual testing	90000	3285000	6	-		-	-	0.040	-	-	2.811%
2016-10-03T01:22:54	Jocelyn Larouche low 4M	Manual testing	90000	3942000		-		-	-	0.046	-	-	2.922%
2016-12-24T20:28:42	Jocelyn Larouche low 4M	Manual testing	108000	108000		-		-	-	0.016	-	-	0.923%
2016-12-30T22:58:49	Jocelyn Larouche low 4M	Manual testing	129600	129600		-		-	-	0.020	-	-	1.023%
2017-01-30T01:30:57	Jocelyn Larouche low 4M	Manual testing	167520	167520		-		-	-	0.026	-	-	1.175%
2017-02-13T00:36:33	Jocelyn Larouche low 4M	Manual testing	241228	2412280	6	-		-	-	0.055	-	-	3.091%
2020-10-10T02:42:23	axn	Manual testing	30000000	600000000	12		343439538302947378252521531857403032501081	42	137.979	9.298	0.770	18.60	11.851%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:36	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.042	-	-
2009-03-09T06:32:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.042	-	-
2011-06-08T23:36:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.084	-	-
2012-06-05T02:31:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.435	-	-
2016-02-23T16:29:36	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.268	-	-
2015-01-23T13:18:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.535	-	-
2015-01-23T13:18:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.019	-	-
2015-10-19T08:19:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.038	-	-
2017-01-03T07:36:03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.075	-	-
2018-11-26T14:19:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.151	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.785 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.785 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.785

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-20T09:38:00	Smurgs	Praca	50000	5000000						3	0.446
2012-06-21T14:26:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.446
2015-10-12T09:06:12	driveByUpgrades	Build_4	50000	5000000						3	0.446
2017-07-08T15:12:55	f0rteOC	Fortissimo	50000	5000000						3	0.446

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-22T00:00:00	ANONYMOUS	v4_computers	1945115FECC47FDE	0.385

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-10T19:45:00

tottenhoff

3-of-4-Ryzen-5-3600

343439538302947378252521531857403032501081

E07E900B3AD087FE

2020-10-11T17:01:05

kutens

spica-b

343439538302947378252521531857403032501081

E07E900B3AD087FE

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

B1 = 90000, B2 = 3942000 (P-1 stage 2)

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

B1 = 241228 (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 = 90000 (P-1 stage 1)

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

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

Last modified: 2020-10-11T17:01:05+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