M3000409 Mersenne number exponent details

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M3000409

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is 2 ^3000409 - 1

has 903214 decimal digits

takes 0.255 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	6840848BF73A5ECC	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	2⁶⁹	39.7902	68.1159%	20000000	116564442540	786.0872	18.0496%	825.8773	73.8709%	5.7550%
PrimeNet	2⁶⁰	0.0512	63.3333%	12000	220000	0.0029	2.5152%	0.0541	64.2556%	0.9222%
GPU72	2⁶⁴	1.1863	65.6250%	13000	200000	0.0029	1.3870%	1.1891	66.1018%	0.4768%
Difference	+5	+38.6039	+2.4909%	+19987000	+116564242540	+786.0843	+16.6627%	+824.6882	+7.7691%	+7.7691%

Known prime factors (2 factors, 159.6 bits, 0.00531782% 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
3000409	29433411722853840161	20	64.674	4904899919120 2⁴ × 5 × 107 × 573002327	2013-12-12	107	573002327	1.3857	3.8528	7.1958
3000409	36506847546234971967385191137	29	94.882	6083645187411944832752 2⁴ × 2081 × 10321 × 39371 × 449648957	2021-09-28	39371	449648957	2.249e+9	3.0279	5.6468

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3000409	29433411722853840161 36506847546234971967385191137	1074521074531790373457656409909448966263431853057	49	159.556

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.200%
2009-05-08T18:54:00	Rob_Dee	twopc	35000	551250		-		-	-	0.008	-	-	1.213%
2010-04-16T13:40:00	Rob_Dee	twopc	100000	200000		-		-	-	0.013	-	-	1.056%
2010-04-17T16:23:00	Rob_Dee	twopc	200000	300000		-		-	-	0.025	-	-	1.329%
2010-04-18T19:54:00	Rob_Dee	twopc	300000	400000		-		-	-	0.038	-	-	1.531%
2010-04-19T15:33:00	Rob_Dee	twopc	400000	500000		-		-	-	0.050	-	-	1.697%
2010-04-20T15:16:00	Rob_Dee	twopc	500000	600000		-		-	-	0.062	-	-	1.838%
2010-04-21T14:13:00	Rob_Dee	twopc	600000	700000		-		-	-	0.075	-	-	1.962%
2010-04-22T15:36:00	Rob_Dee	twopc	700000	800000		-		-	-	0.087	-	-	2.073%
2010-04-23T15:33:00	Rob_Dee	twopc	800000	900000		-		-	-	0.099	-	-	2.174%
2010-04-24T20:41:00	Rob_Dee	twopc	900000	1000000		-		-	-	0.112	-	-	2.267%
2010-04-25T12:32:00	Rob_Dee	twopc	1000000	1100000		-		-	-	0.124	-	-	2.352%
2020-09-10T19:23:57	Jocelyn Larouche	Manual testing	350035	6000818		-		-	-	0.081	-	-	3.508%
2021-01-13T11:21:19	Jocelyn Larouche	Manual testing	350035	30004090	12	-		-	-	0.243	-	-	4.774%
2021-01-14T22:58:07	Jocelyn Larouche	Manual testing	3000409	3000409		-		-	-	0.370	-	-	3.353%
2021-09-16T18:54:14	Jocelyn Larouche	Manual testing	3000409	3000409		-		-	-	0.370	-	-	3.353%
2021-09-18T11:40:55	Jocelyn Larouche	Manual testing	3000409	30004090	12	-		-	-	0.552	-	-	5.987%
2021-12-11T09:24:59	Luminescence	Main	20000000	116564442540		-	skipped known factors(?)	-	-	786.1	-	-	18.050%
2021-12-21T11:44:45	Jocelyn Larouche	Manual testing	3000409	138761700		-		-	-	1.283	-	-	7.779%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-28T20:47:56	mikr	Nitron	15000000	1530000000	197	11	36506847546234971967385191137	P-1	29	94.882	12.80

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	?	2⁶⁰		-	-	0.026	-	-
2009-01-23T05:59:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-08-18T01:42:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.102	-	-
2013-01-07T13:52:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.327	-	-
2013-12-04T00:20:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.654	-	-
2013-12-12T21:14:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵	29433411722853840161	64.674	20	0.199	0.518	0.405
2021-01-15T03:12:21	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.491	-	-
2021-02-21T11:36:43	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.981	-	-
2021-03-02T21:51:13	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.96	-	-
2021-12-30T12:54:15	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.92	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.045 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.045 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.045

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T23:20:00	James Hintz	16_060209	50000	5000000						3	0.348
2011-05-26T06:24:00	Pool Party	desk_2	50000	5000000						3	0.348
2013-08-23T00:52:00	Bruce	fx6840-21	50000	5000000						3	0.348

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-15T00:00:00	ANONYMOUS	v4_computers	6840848BF73A5ECC	0.255
2000-01-19T00:00:00	ANONYMOUS	v4_computers	6840848BF73A5ECC	0.255

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-27T04:44:44

Oliver Kruse

GTX-3

29433411722853840161

E5278F56E350BE__

2017-12-10T07:25:39

kkmrkkblmbrbk

c4.xlarge

29433411722853840161

E5278F56E350BE__

2021-09-29T11:03:29

SRJ2877

LTOS

29433411722853840161

36506847546234971967385191137

E5278F56E350BE51

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 = 20000000, B2 = 116564442540 (P-1 stage 2)

B1 = 15000000, B2 = 1530000000 (P-1 stage 2)

B1 = 20000000 (P-1 stage 1)

B1 = 15000000 (P-1 stage 1)

B1 = 3000409, B2 = 138761700 (P-1 stage 2)

B1 = 3000409, B2 = 30004090 (P-1 stage 2)

B1 = 3000409 (P-1 stage 1)

B1 = 350035, B2 = 30004090 (P-1 stage 2)

B1 = 1000000, B2 = 1100000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000, B2 = 1000000 (P-1 stage 2)

B1 = 900000 (P-1 stage 1)

B1 = 800000, B2 = 900000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 700000, B2 = 800000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 350035, B2 = 6000818 (P-1 stage 2)

B1 = 600000, B2 = 700000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 500000, B2 = 600000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 400000, B2 = 500000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 350035 (P-1 stage 1)

B1 = 300000, B2 = 400000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 35000, B2 = 551250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

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TF factor-bounds graph:

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2¹⁰⁰

Last modified: 2021-12-30T12:54:15+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