M3068929 Mersenne number exponent details

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M3068929

<<<

>>>

is 2 ^3068929 - 1

has 923840 decimal digits

takes 0.261 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	A3D36FF77CFE2D80	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	2⁶⁸	19.4220	67.6471%	3000000	100000000	1.0224	8.0399%	20.4445	70.2482%	2.6011%
PrimeNet	2⁶⁰	0.0500	63.3333%	12000	220000	0.0029	2.5257%	0.0529	64.2594%	0.9261%
GPU72	2⁶⁴	1.1598	65.6250%	14000	220000	0.0031	1.4667%	1.1629	66.1292%	0.5042%
Difference	+4	+18.2622	+2.0221%	+2986000	+99780000	+1.0193	+6.5732%	+19.2816	+4.1190%	+4.1190%

Known prime factors (1 factor, 86.0 bits, 0.00280151% 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
3068929	76106043998011510763018623	26	85.976	12399446842532282559 3 × 13 × 53917 × 154159 × 38251027	2018-01-03	154159	38251027	3,801,686	0.2752	0.4804

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-09-23T02:04:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.668%
2016-10-20T14:39:38	Squeeky_Squirrel	P4_2600	195000	5411250	6	-		-	-	0.059	-	-	3.510%
2017-01-04T22:58:52	Jocelyn Larouche	low 4M	132000	132000		-		-	-	0.016	-	-	1.001%
2018-01-03T13:38:22	Jocelyn Larouche	low 4M	3068929	6137858	6	-		-	-	0.399	-	-	4.584%
2018-01-03T22:44:07	mikr	MSI	3000000	100000000	12		76106043998011510763018623	26	85.976	1.022	0.522	2.045	8.040%
2018-01-15T10:44:34	Jocelyn Larouche	low 4M	3068929	12275716	6	-		-	-	0.441	-	-	5.439%
2018-01-20T19:20:11	Jocelyn Larouche	low 4M	3068929	24551432	6	-		-	-	0.523	-	-	6.298%
2020-11-12T20:32:50	Jocelyn Larouche	Manual testing	306892	3068929	6	-		-	-	0.056	-	-	3.297%
2022-01-06T11:35:12	Jocelyn Larouche	Manual testing	1210338	116447100		-	skipped known factor: 76106043998011510763018623	-	-	0.924	-	-	7.594%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-13T23:36:00	Sturle Sunde	buxtehude.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-10-19T09:52:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.100	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.320	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.640	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.217	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.435	-	-
2017-05-14T00:43:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.870	-	-
2021-04-11T11:38:30	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.74	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.749 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.749 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.749

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-16T23:21:00	Adel El-Atawy	SRVRARC	50000	5000000						3	0.350
2011-06-23T07:47:00	Smurgs	Praca	50000	5000000						3	0.350
2013-11-01T05:14:00	arnaud	Chamot18	50000	5000000						3	0.350
2016-02-26T05:02:06	Sintax	ECM	50000	5000000						3	0.350
2017-09-20T12:59:36	Bruce	desk	50000	5000000						3	0.350

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	7AE952B844047F__	0.261
1999-10-07T00:00:00	foxkid	v4_computers	A3D36FF77CFE2D80	0.261

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-06T20:56:18

Oliver Kruse

GTX-5

76106043998011510763018623

6B48D287A6C00A__

2018-01-06T21:36:24

ATH

ec2-1xf

76106043998011510763018623

6B48D287A6C00A__

2018-01-07T09:05:22

AdolfNor

Manual testing

76106043998011510763018623

6B48D287A6C00A__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1210338, B2 = 116447100 (P-1 stage 2)

B1 = 3068929, B2 = 24551432 (P-1 stage 2)

B1 = 3068929, B2 = 12275716 (P-1 stage 2)

B1 = 3068929, B2 = 6137858 (P-1 stage 2)

B1 = 3068929 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 1210338 (P-1 stage 1)

B1 = 195000, B2 = 5411250 (P-1 stage 2)

B1 = 306892, B2 = 3068929 (P-1 stage 2)

B1 = 306892 (P-1 stage 1)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-06T11:35:12+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