M1028411 Mersenne number exponent details

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M1028411

<<<

>>>

is 2 ^1028411 - 1

has 309583 decimal digits

takes 0.030 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	8497EEC4C86592BE	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	2⁶⁷	28.8930	70.1493%	10000000	1000000000	2.7478	11.6403%	31.6409	73.6240%	3.4747%
PrimeNet	2⁵⁶	0.0093	64.2857%	4500	60000	0.0003	1.9503%	0.0097	64.9823%	0.6965%
GPU72	2⁶⁰	0.1493	66.6667%	4500	17000	0.0002	0.5982%	0.1496	66.8661%	0.1994%
Difference	+7	+28.7437	+3.4826%	+9995500	+999983000	+2.7476	+11.0421%	+31.4913	+6.7579%	+6.7579%

Known prime factors (1 factor, 68.7 bits, 0.00667880% 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
1028411	474691217131666808593	21	68.686	230788671616536 2³ × 3 × 11 × 19 × 46010500721	2009-07-29	19	46010500721	96.158	107.73	201.21

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22T00:00:00	Jocelyn Larouche	v4_computers	10000	100000		-		-	-	0.001	-	-	0.491%
2002-11-09T00:00:00	Jocelyn Larouche	v4_computers	11000	11000		-		-	-	0.000	-	-	0.148%
2002-11-09T00:00:00	Jocelyn Larouche	v4_computers	15000	15000		-		-	-	0.001	-	-	0.198%
2002-11-16T00:00:00	Jocelyn Larouche	v4_computers	10284	1028411		-		-	-	0.003	-	-	0.979%
2002-11-16T00:00:00	Jocelyn Larouche	v4_computers	20000	20000		-		-	-	0.001	-	-	0.255%
2016-03-17T18:59:19	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.079%
2021-07-14T12:57:32	ViliamF	3	10000000	1000000000		-		-	-	2.748	-	-	11.640%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.019	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.037	-	-
2022-03-07T17:30:26	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.112	-	-
2009-02-16T21:44:00	Sturle Sunde	gerle.ifi	2⁶⁰	2⁶¹		-	-	0.149	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.409 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.409 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		474691217131666808593	1	0.00000e+0
50000	5000000		279	9.73
250000	25000000		44	7.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-21T11:52:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-04-22T17:21:00	arnaud	ATTAX04	50000	5000000						3	0.105
2008-11-29T04:15:00	Sturle Sunde	v21	50000	5000000						3	0.105
2009-03-20T01:21:00	Sturle Sunde	v21	50000	5000000						3	0.105
2009-07-29T01:45:00	JimBa	SAserv			474691217131666808593	68.686		1		1	-
2017-02-24T21:19:28	TJAOI	Manual testing	50000	5000000						88	3.070
2017-04-28T21:37:28	TJAOI	Manual testing	50000	5000000						90	3.140
2018-01-19T13:24:19	TJAOI	Manual testing	50000	5000000						91	3.175
2020-04-27T10:13:56	TJAOI	Manual testing	250000	25000000						44	7.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-02-03T00:00:00	ANONYMOUS	v4_computers	8497EEC4C86592BE	0.030

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T18:17:39

Oliver Kruse

GTX-0

474691217131666808593

25CC7D6B6C4951__

2017-10-15T19:10:16

Oliver Kruse

Threadripper

474691217131666808593

25CC7D6B6C4951__

2017-12-27T12:50:00

ATH

ec2-1xf

474691217131666808593

25CC7D6B6C4951__

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 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 10284, B2 = 1028411 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 10000, B2 = 100000 (P-1 stage 2)

B1 = 11000 (P-1 stage 1)

B1 = 10284 (P-1 stage 1)

B1 = 10000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T17:30:26+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