M3435881 Mersenne number exponent details

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M3435881

<<<

>>>

is 2 ^3435881 - 1

has 1034304 decimal digits

takes 0.361 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	-unknown-	-unknown-
PRP	68BEB1DB8F522C52	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	2⁶⁹	34.7471	68.1159%	14000000	700000000	7.8239	10.9084%	42.5710	71.5940%	3.4781%
PrimeNet	2⁶⁰	0.0447	63.3333%	15000	280000	0.0045	2.8993%	0.0492	64.3964%	1.0631%
GPU72	2⁶⁴	1.0359	65.6250%	19000	340000	0.0056	1.8534%	1.0415	66.2621%	0.6371%
Difference	+5	+33.7111	+2.4909%	+13981000	+699660000	+7.8184	+9.0551%	+41.5295	+5.3319%	+5.3319%

Known prime factors (1 factor, 76.1 bits, 0.00221532% 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
3435881	81870135678579887591441	23	76.116	11913994646290120 2³ × 5 × 297849866157253	2021-08-08	8	297849866157253	5,418.3	2,471,318	4,615,734

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:56:00	Carsten Kossendey	leela	15000	210000		-		-	-	0.004	-	-	0.699%
2011-11-02T06:42:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.664%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78681	78681		-		-	-	0.012	-	-	0.653%
2014-09-16T13:22:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.160%
2021-05-07T01:40:39	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.908%
2022-04-10T23:56:38	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.992%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:29	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-22T20:32:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-05T10:03:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.089	-	-
2012-08-18T15:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.465	-	-
2016-02-23T16:29:29	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.286	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.571	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.087	-	-
2015-04-13T14:45:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.175	-	-
2017-02-05T22:59:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.350	-	-
2018-09-10T13:18:22	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.700	-	-
2021-01-01T17:29:49	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.248 GHz-days
Estimated T-Level:	2.000

Digits	B1	Curves	Complete	FacMiss
20	11000	40 / 100	0.400	66.897%
25	50000	40 / 280	0.143	86.666%

New Calculation Method

Total ECM effort:	6.248 GHz-days
Estimated T-Level:	2.000

Digits	B1	Complete	FacMiss
20	11000	1.322	26.652%
25	50000	0.119	88.745%
30	250000	0.007	99.266%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.231
50000	6300000		7	1.149
50000	6700000		7	1.186
50000	6750000	81870135678579887591441	4	0.681

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-26T07:14:00	James Hintz	4115	50000	5000000						3	0.441
2012-02-19T10:54:00	Vladimir Tshegolevatykh	aldan	50000	5000000						3	0.441
2015-01-19T16:12:00	driveByUpgrades	Build_4	50000	5000000						3	0.441
2016-12-11T10:12:26	bdani	X58_TUF	50000	5000000						3	0.441
2019-05-22T09:21:41	furkell	furkell1	50000	5000000						3	0.441
2021-03-23T00:01:15	mnd9	kitchen	50000	5000000						7	1.028
2021-05-17T01:48:59	kutens	terra	50000	6700000						7	1.186
2021-06-22T11:34:18	kutens	capella	50000	6300000						7	1.149
2021-08-08T13:25:20	nordi	sweet16	50000	6750000	81870135678579887591441	76.116	4	2	7424944190671718	4	0.681

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	Martijn Otto	v4_computers	F4D15E482E6BF2__	0.361

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-08T18:54:41

SRJ2877

LTOS

81870135678579887591441

68BEB1DB8F522C52

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 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78681 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 210000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

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2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T23:56:38+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