M3006439 Mersenne number exponent details

≡

M3006439

<<<

>>>

is 2 ^3006439 - 1

has 905029 decimal digits

takes 0.256 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	4A668647BF3029C2	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	2⁷¹	159.0181	69.0141%	32773938	1868114466	16.3851	11.1319%	175.4032	72.4634%	3.4493%
PrimeNet	2⁶⁰	0.0511	63.3333%	12000	220000	0.0029	2.5161%	0.0540	64.2559%	0.9226%
GPU72	2⁶⁴	1.1839	65.6250%	13000	200000	0.0029	1.3875%	1.1868	66.1020%	0.4770%
Difference	+7	+157.8342	+3.3891%	+32760938	+1867914466	+16.3822	+9.7444%	+174.2165	+6.3614%	+6.3614%

Known prime factors (1 factor, 74.7 bits, 0.00248445% 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
3006439	30545590353890093573863	23	74.693	5080028291591829 3 × 53 × 31949863469131	2021-09-29	53	31949863469131	1,622.1	214,824	401,231

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.081%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.129%
2009-07-08T04:45:00	BigBrother	Miniluv	1000000	100000000		-		-	-	0.789	-	-	5.570%
2016-08-14T22:30:26	trebor		1650000	120000000	12	-		-	-	0.999	-	-	6.079%
2016-10-05T04:15:00	trebor		1650000	300000000	12	-		-	-	2.210	-	-	6.957%
2019-01-06T07:40:51	oodaira	com5	32773938	1868114466	12	-		-	-	16.39	-	-	11.132%
2022-01-22T13:05:18	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	5.728%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-30T00:00:00	Ignacio_Larrosa	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
2000-11-15T00:00:00	Alex Kruppa	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2016-02-23T16:29:25	Mark Rose	Manual testing	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-04-08T13:58:00	Richard B. Woods	Puttputt	2⁶¹	2⁶²		-	-	0.102	-	-
2010-05-18T22:34:00	Richard B. Woods	Manual testing	2⁶²	2⁶³		-	-	0.327	-	-
2010-05-18T22:34:00	Richard B. Woods	Manual testing	2⁶³	2⁶⁴		-	-	0.653	-	-
2010-08-25T19:46:00	Richard B. Woods	Puttputt	2⁶⁴	2⁶⁵		-	-	1.243	-	-
2012-02-25T08:24:00	Richard B. Woods	Puttputt	2⁶⁵	2⁶⁶		-	-	2.486	-	-
2014-04-02T14:51:00	ramgeis	Manual testing	2⁶⁶	2⁶⁷		-	-	4.971	-	-
2022-01-15T12:00:50	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.94	-	-
2014-04-02T14:51:00	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.94	-	-
2022-01-15T12:00:50	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.88	-	-
2014-04-02T14:51:00	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	19.88	-	-
2014-04-02T14:51:00	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	39.77	-	-
2016-01-05T09:39:00	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	79.54	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.973 GHz-days
Estimated T-Level:	4.200

Digits	B1	Curves	Complete	FacMiss
20	11000	84 / 100	0.840	42.989%
25	50000	84 / 280	0.300	74.042%

New Calculation Method

Total ECM effort:	9.973 GHz-days
Estimated T-Level:	4.200

Digits	B1	Complete	FacMiss
20	11000	2.741	6.452%
25	50000	0.248	78.038%
30	250000	0.015	98.483%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		67	7.784
50000	5000000	30545590353890093573863	3	0.349
50000	6350000		7	0.910
50000	6650000		7	0.931

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-10T22:10:00	Helgen	newone	50000	5000000						3	0.349
2010-12-30T20:08:00	Oscar Östlin		50000	5000000						3	0.349
2013-09-02T21:56:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-17T13:21:26	Bruce	Desk7	50000	5000000						3	0.349
2016-11-28T09:43:32	trebor		50000	5000000						20	2.324
2020-12-11T01:58:52	daveward2005	Davy	50000	5000000						7	0.813
2021-01-12T03:06:35	RIHATEC	i7-3770K	50000	5000000						7	0.813
2021-02-11T15:46:42	daveward2005	Dave2	50000	5000000						7	0.813
2021-03-12T02:01:55	gLauss	laptop-arbeit	50000	5000000						7	0.813
2021-04-20T18:10:47	GAN	KL-SCH07	50000	5000000						7	0.813
2021-06-10T03:12:13	Dylan Delgado	colab	50000	6350000						7	0.910
2021-07-25T10:51:58	kutens	pbs1	50000	6650000						7	0.931
2021-09-29T23:54:16	MarkS	desktop-i7	50000	5000000	30545590353890093573863	74.693	3	2	3456086301692531	3	0.349

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	4A668647BF3029C2	0.256
2001-06-30T00:00:00	Ignacio_Larrosa	v4_computers	4A668647BF3029C2	0.256
2012-09-02T05:21:00	kdgehman	i5-2500k	4A668647BF3029C2	0.256

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-05T23:37:46

Yuji HASEGAWA

vj20a

30545590353890093573863

659E1DCDC43871__

2021-10-06T11:31:49

LaurV

Zero818

30545590353890093573863

659E1DCDC43871B6

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 = 32773938, B2 = 1868114466 (P-1 stage 2)

B1 = 32773938 (P-1 stage 1)

B1 = 1650000, B2 = 300000000 (P-1 stage 2)

B1 = 1650000, B2 = 120000000 (P-1 stage 2)

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 1000000, B2 = 100000000 (P-1 stage 2)

B1 = 1650000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-22T13:05:18+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