M3204581 Mersenne number exponent details

Residue

Status

L-L

55F43AFD08C5F564

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	18.5999	67.6471%	1061374	116447100	0.9068	7.5244%	19.5067	70.0814%	2.4344%
PrimeNet	2⁶⁰	0.0479	63.3333%	13000	240000	0.0031	2.6581%	0.0511	64.3080%	0.9746%
GPU72	2⁶⁴	1.1107	65.6250%	16000	260000	0.0036	1.6162%	1.1143	66.1806%	0.5556%
Difference	+4	+17.4892	+2.0221%	+1045374	+116187100	+0.9032	+5.9082%	+18.3924	+3.9009%	+3.9009%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.5999

67.6471%

1061374

116447100

0.9068

7.5244%

19.5067

70.0814%

2.4344%

PrimeNet

2⁶⁰

0.0479

63.3333%

13000

240000

0.0031

2.6581%

0.0511

64.3080%

0.9746%

GPU72

2⁶⁴

1.1107

65.6250%

16000

260000

0.0036

1.6162%

1.1143

66.1806%

0.5556%

Difference

+17.4892

+2.0221%

+1045374

+116187100

+0.9032

+5.9082%

+18.3924

+3.9009%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3204581	390185678964564427601	21	68.403	60879359729800 2³ × 5² × 229283 × 1327603	2009-05-11	229283	1327603	34.752	0.0357	0.0576
3204581	33989616272291881340177	23	74.848	5303285557814248 2³ × 12073 × 79601 × 689797	2020-12-29	79601	689797	1,433.7	0.0139	0.0200

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3204581

390185678964564427601

68.403

60879359729800
2³ × 5² × 229283 × 1327603

2009-05-11

229283

1327603

34.752

0.0357

0.0576

3204581

33989616272291881340177

74.848

5303285557814248
2³ × 12073 × 79601 × 689797

2020-12-29

79601

689797

1,433.7

0.0139

0.0200

exponent	prime factors	composite factor	digits	bits*
3204581	390185678964564427601 33989616272291881340177	13262261502949215098673365266293240769025377	44	143.250

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-29T03:27:51	Jocelyn Larouche	Manual testing	320458	3204581	6		33989616272291881340177	23	74.848	0.059	0.545	0.118	3.368%
2022-01-07T11:58:22	Jocelyn Larouche	Manual testing	1061374	116447100		-	skipped known factor: 390185678964564427601 skipped known factor: 33989616272291881340177	-	-	0.907	-	-	7.524%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-08T17:56:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2022-04-03T00:03:42	LordJulius	Manual testing	2⁶¹	2⁶³		-	-	0.402	-	-
2022-04-03T00:03:42	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.613	-	-
2022-04-03T00:03:42	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.166	-	-
2022-04-03T00:03:42	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.332	-	-
2022-04-03T00:03:42	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.664	-	-
2021-09-28T10:32:40	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.328	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.352 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.352 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		390185678964564427601	1	0.00000e+0
50000	5000000		3	0.352

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-11T04:18:00	Aca Arsov	backo6400			390185678964564427601	68.403		1		1	-
2019-10-09T00:35:16	ATH	ec2-ECMCF	50000	5000000						3	0.352

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-01T16:07:09

Oliver Kruse

GTX-2

390185678964564427601

410124AAA17164__

2017-12-13T06:06:20

kkmrkkblmbrbk

c4.xlarge

390185678964564427601

410124AAA17164__

2020-12-29T10:23:54

firejuggler

Maison

390185678964564427601

33989616272291881340177

410124AAA17164E6

2020-12-30T03:03:43

Yuji HASEGAWA

vj20a

390185678964564427601

33989616272291881340177

410124AAA17164E6

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 = 1061374, B2 = 116447100 (P-1 stage 2)

B1 = 1061374 (P-1 stage 1)

B1 = 320458, B2 = 3204581 (P-1 stage 2)

B1 = 320458 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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