M3440893 Mersenne number exponent details

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M3440893

<<<

>>>

is 2 ^3440893 - 1

has 1035813 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	1E9E881F58469131	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	34.6965	68.1159%	5000000	200000000	2.3794	8.6464%	37.0759	70.8728%	2.7568%
PrimeNet	2⁶⁰	0.0446	63.3333%	15000	280000	0.0045	2.9000%	0.0491	64.3967%	1.0633%
GPU72	2⁶⁴	1.0344	65.6250%	19000	340000	0.0056	1.8539%	1.0400	66.2623%	0.6373%
Difference	+5	+33.6620	+2.4909%	+4981000	+199660000	+2.3738	+6.7926%	+36.0359	+4.6105%	+4.6105%

Known prime factors (1 factor, 87.2 bits, 0.00253320% 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
3440893	173455091566748111001595783	27	87.165	25204952837351831487 3 × 47 × 263 × 679690231031789	2021-08-05	263	679690231031789	10,818,364	5,639,522	10,533,057

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2010-09-28T05:03:00	Rob_Dee	twopc	10000	20000		-		-	-	0.002	-	-	0.216%
2010-09-29T05:06:00	Rob_Dee	twopc	30000	40000		-		-	-	0.005	-	-	0.407%
2010-09-29T20:32:00	Rob_Dee	twopc	40000	50000		-		-	-	0.006	-	-	0.480%
2010-09-30T04:44:00	Rob_Dee	twopc	50000	60000		-		-	-	0.008	-	-	0.545%
2010-10-01T04:58:00	Rob_Dee	twopc	60000	70000		-		-	-	0.009	-	-	0.604%
2010-10-02T05:02:00	Rob_Dee	twopc	70000	80000		-		-	-	0.011	-	-	0.659%
2010-10-03T05:00:00	Rob_Dee	twopc	80000	90000		-		-	-	0.012	-	-	0.709%
2010-10-04T04:40:00	Rob_Dee	twopc	90000	100000		-		-	-	0.014	-	-	0.756%
2010-10-04T23:40:00	Rob_Dee	twopc	100000	200000		-		-	-	0.016	-	-	1.081%
2010-10-05T04:55:00	Rob_Dee	twopc	100000	300000		-		-	-	0.017	-	-	1.277%
2010-10-05T22:28:00	Rob_Dee	twopc	100000	400000		-		-	-	0.018	-	-	1.419%
2010-10-06T04:22:00	Rob_Dee	twopc	100000	500000		-		-	-	0.019	-	-	1.530%
2010-10-06T23:02:00	Rob_Dee	twopc	100000	600000		-		-	-	0.019	-	-	1.622%
2010-10-07T04:26:00	Rob_Dee	twopc	100000	700000		-		-	-	0.020	-	-	1.701%
2010-10-07T21:08:00	Rob_Dee	twopc	100000	800000		-		-	-	0.021	-	-	1.770%
2010-10-08T04:54:00	Rob_Dee	twopc	100000	900000		-		-	-	0.022	-	-	1.831%
2010-10-08T20:46:00	Rob_Dee	twopc	100000	1000000		-		-	-	0.023	-	-	1.886%
2014-09-18T01:53:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.161%
2021-06-08T06:40:09	mognuts	Manual testing	1000000	30000000		-		-	-	0.393	-	-	5.545%
2021-06-14T19:29:09	mikr	MSI	5000000	200000000	12	-		-	-	2.379	-	-	8.646%
2022-02-12T19:37:10	Jocelyn Larouche	Manual testing	1000000	114656850		-		-	-	1.095	-	-	6.891%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-23T09:16:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-11T20:38:00	markr	Manual testing	2¹	2⁶²		-	-	0.179	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.464	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.285	-	-
2015-02-24T22:14:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.571	-	-
2015-02-24T22:14:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.086	-	-
2015-04-15T14:57:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.172	-	-
2017-02-05T22:59:59	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.343	-	-
2022-01-22T13:05:29	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.687	-	-
2018-08-13T14:25:19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.687	-	-
2021-01-03T02:54:25	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.37	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.171 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	6.171 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.355	25.799%
25	50000	0.122	88.475%
30	250000	0.008	99.249%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.289
50000	5000000	173455091566748111001595783	6	0.882

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-23T09:26:00	S00030	op9020-usff	50000	5000000						3	0.441
2012-01-22T18:24:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.441
2015-02-02T07:14:00	S36049	Wolle6	50000	5000000						3	0.441
2016-12-14T06:52:26	Dennis Schreiber	z400	50000	5000000						3	0.441
2019-05-27T04:25:42	furkell	furkell1	50000	5000000						3	0.441
2021-03-25T22:17:02	MarkS	laptop64	50000	5000000						21	3.085
2021-08-05T01:15:01	daveward2005	d12436	50000	5000000	173455091566748111001595783	87.165	6	2	4257578957162454	6	0.882

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-15T00:00:00	Mark Blanke	v4_computers	2E65DED928B548__	0.361

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-08-05T05:18:53

SRJ2877

LTOS

173455091566748111001595783

1E9E881F58469131

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 1000000, B2 = 114656850 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (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 = 100000, B2 = 1000000 (P-1 stage 2)

B1 = 100000, B2 = 900000 (P-1 stage 2)

B1 = 100000, B2 = 800000 (P-1 stage 2)

B1 = 100000, B2 = 700000 (P-1 stage 2)

B1 = 100000, B2 = 600000 (P-1 stage 2)

B1 = 100000, B2 = 500000 (P-1 stage 2)

B1 = 100000, B2 = 400000 (P-1 stage 2)

B1 = 100000, B2 = 300000 (P-1 stage 2)

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

B1 = 100000 (P-1 stage 1)

B1 = 90000, B2 = 100000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 80000, B2 = 90000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 70000, B2 = 80000 (P-1 stage 2)

B1 = 70000 (P-1 stage 1)

B1 = 60000, B2 = 70000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 50000, B2 = 60000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 40000, B2 = 50000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

B1 = 30000, B2 = 40000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 10000, B2 = 20000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

10¹

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TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

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2¹⁰⁰

Last modified: 2022-02-12T19:37:10+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