M3480623 Mersenne number exponent details

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M3480623

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>>>

is 2 ^3480623 - 1

has 1047772 decimal digits

takes 0.366 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	5E0F24B8220C2923	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	34.3004	68.1159%	5000000	405000000	4.0803	9.5492%	38.3807	71.1606%	3.0447%
PrimeNet	2⁶⁰	0.0441	63.3333%	15000	300000	0.0046	2.9576%	0.0488	64.4178%	1.0844%
GPU72	2⁶⁴	1.0226	65.6250%	19000	360000	0.0057	1.8868%	1.0283	66.2736%	0.6486%
Difference	+5	+33.2778	+2.4909%	+4981000	+404640000	+4.0746	+7.6623%	+37.3524	+4.8870%	+4.8870%

Known prime factors (1 factor, 92.0 bits, 0.00264239% 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
3480623	4855474138748770981055523113	28	91.972	697500725983361452972 2² × 397 × 30089 × 49409 × 295447519	2022-01-22	49409	295447519	256,100,087	2.4585	4.5785

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T04:46:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.812%
2011-11-13T13:06:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.689%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78440	78440		-		-	-	0.012	-	-	0.653%
2014-09-28T04:17:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.167%
2021-11-15T10:56:22	Aaron Haviland	Manual testing	1500000	30000000	12	-		-	-	0.465	-	-	5.772%
2022-01-22T16:26:12	mikr	MSI	5000000	405000000			4855474138748770981055523113	28	91.972	4.080	0.731	8.161	9.549%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-02-02T14:49:50	riccardo uberti	Colab_noGPU12	5000000	100000000	2	7			-	-	1.930
2022-02-15T16:03:41	riccardo uberti	Colab_noGPU15	5000000	100000000	6	5			-	-	1.930

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:31	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-03-19T18:08:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-20T23:09:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.088	-	-
2012-08-18T15:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.459	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.282	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.564	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.073	-	-
2016-01-05T09:38:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.147	-	-
2017-02-18T19:55:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.294	-	-
2018-11-05T15:44:26	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.588	-	-
2021-01-10T16:07:21	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.793 GHz-days
Estimated T-Level:	2.650

Digits	B1	Curves	Complete	FacMiss
20	11000	53 / 100	0.530	58.704%
25	50000	53 / 280	0.189	82.727%

New Calculation Method

Total ECM effort:	9.793 GHz-days
Estimated T-Level:	2.650

Digits	B1	Complete	FacMiss
20	11000	1.872	15.383%
25	50000	0.169	84.475%
30	250000	0.010	98.960%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	7	0.567
50000	5000000	36	5.301
50000	6750000	7	1.195
50000	14400000	10	2.730

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-18T09:52:00	Gerry Snyder	blu	50000	5000000						3	0.442
2012-02-27T13:54:00	Lukasz Wrobel	i-5	50000	5000000						3	0.442
2015-04-05T13:03:00	Pool Party	St.P.p	50000	5000000						3	0.442
2017-01-12T06:14:31	Sid & Andy	Mrs_Potato_Head	50000	5000000						3	0.442
2019-07-02T09:49:50	IanGlencross	glenx24	50000	5000000						3	0.442
2021-04-09T15:53:48	GAN	N-23	50000	50000						7	0.567
2021-04-15T10:43:18	Zenzoma	AMD3970X	50000	5000000						7	1.031
2021-06-07T07:12:19	kutens	terra	50000	6750000						7	1.195
2021-07-23T03:43:28	Alvin Bunk	BADCAT	50000	5000000						7	1.031
2021-09-16T14:55:38	RIHATEC	i7-3770K	50000	5000000						7	1.031
2022-01-31T23:01:40	riccardo uberti	Colab_noGPU10	50000	14400000						10	2.730

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-01T00:00:00	ANONYMOUS	v4_computers	F3164F11D1FA6A__	0.366

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-01-27T18:04:27

riccardo uberti

Nomad2C

4855474138748770981055523113

5E0F24B8220C2923

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 = 405000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1500000, B2 = 30000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

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

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 78440 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-15T16:03:41+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