M3580669 Mersenne number exponent details

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M3580669

<<<

>>>

is 2 ^3580669 - 1

has 1077889 decimal digits

takes 0.376 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	9EEF96A4110E9B48	double-checked
PRP	381282FB32045A4F	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	2⁷²	267.0824	69.4444%	3580669	3598822500	30.3757	9.6580%	297.4581	72.3955%	2.9511%
PrimeNet	2⁶⁰	0.0429	63.3333%	15000	300000	0.0046	2.9723%	0.0475	64.4232%	1.0898%
GPU72	2⁶⁴	0.9940	65.6250%	20000	400000	0.0062	1.9785%	1.0002	66.3051%	0.6801%
Difference	+8	+266.0884	+3.8194%	+3560669	+3598422500	+30.3695	+7.6795%	+296.4579	+6.0904%	+6.0904%

Known prime factors (1 factor, 74.8 bits, 0.00208810% 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
3580669	32167069585215254252441	23	74.768	4491768100488380 2² × 5 × 584719 × 384096301	2021-06-29	584719	384096301	2,016.7	3.2711	5.9523

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T19:18:00	Carsten Kossendey	leela	20000	245000		-		-	-	0.005	-	-	0.516%
2011-12-26T08:57:00	Squeeky_Squirrel	P4_2600	85000	1593750		-		-	-	0.025	-	-	1.423%
2016-05-07T11:39:02	Squeeky_Squirrel	P4_2600	225000	6581250	12	-		-	-	0.087	-	-	2.473%
2022-03-01T15:51:53	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.015	-	-	0.493%
2022-05-25T14:13:21	Jocelyn Larouche	Manual testing	100000	130364850		-		-	-	1.096	-	-	3.491%
2022-08-13T14:06:56	Jocelyn Larouche	Manual testing	3580669	3598822500		-	skipped known factor: 32167069585215254252441	-	-	30.38	-	-	9.658%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11T00:00:00	netconx	v4_computers	2¹	2⁶⁰		-	-	0.043	-	-
2009-03-15T08:10:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.043	-	-
2011-06-26T19:26:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.086	-	-
2012-07-02T04:04:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.446	-	-
2016-02-23T16:29:34	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.274	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.548	-	-
2015-01-30T19:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.043	-	-
2016-02-25T15:27:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.087	-	-
2017-01-20T05:22:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.174	-	-
2018-10-15T12:54:50	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.348	-	-
2020-12-19T09:45:59	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	16.70	-	-
2021-03-18T17:14:31	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	33.39	-	-
2021-03-18T17:14:31	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	66.78	-	-
2021-03-20T11:11:42	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	133.6	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.157 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	3.157 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.814	44.304%
25	50000	0.075	92.746%
30	250000	0.005	99.526%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		19	2.813
50000	6750000	32167069585215254252441	2	0.344

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-08-05T23:57:00	Marzbug	Xeon	50000	5000000						3	0.444
2012-04-20T15:53:00	Adel El-Atawy	MyGD	50000	5000000						3	0.444
2015-07-13T11:05:00	Bruce	agent86	50000	5000000						3	0.444
2017-04-01T05:39:44	jafarism	jafarism-r07	50000	5000000						3	0.444
2021-05-22T18:41:41	daveward2005	d12436	50000	5000000						7	1.036
2021-06-29T16:54:33	kutens	terra	50000	6750000	32167069585215254252441	74.768	2	2	3669549781865729	2	0.344

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-01T00:00:00	netconx	v4_computers	9EEF96A4110E9B48	0.376
1999-08-16T00:00:00	ANONYMOUS	v4_computers	9EEF96A4110E9B48	0.376

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-06-30T20:58:16

kutens

sol

32167069585215254252441

381282FB32045A4F

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 = 3580669, B2 = 3598822500 (P-1 stage 2)

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

B1 = 3580669 (P-1 stage 1)

B1 = 225000, B2 = 6581250 (P-1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 85000, B2 = 1593750 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 20000, B2 = 245000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-13T14:06:56+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