M3411671 Mersenne number exponent details

Residue

Status

L-L

2A8630631552A6C7

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	17.4709	67.6471%	3411671	111907950	1.4198	8.3422%	18.8907	70.3460%	2.6989%
PrimeNet	2⁶⁰	0.0450	63.3333%	14000	280000	0.0043	2.8489%	0.0494	64.3779%	1.0446%
GPU72	2⁶⁴	1.0433	65.6250%	19000	320000	0.0054	1.8203%	1.0487	66.2507%	0.6257%
Difference	+4	+16.4276	+2.0221%	+3392671	+111587950	+1.4144	+6.5218%	+17.8420	+4.0953%	+4.0953%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.4709

67.6471%

3411671

111907950

1.4198

8.3422%

18.8907

70.3460%

2.6989%

PrimeNet

2⁶⁰

0.0450

63.3333%

14000

280000

0.0043

2.8489%

0.0494

64.3779%

1.0446%

GPU72

2⁶⁴

1.0433

65.6250%

19000

320000

0.0054

1.8203%

1.0487

66.2507%

0.6257%

Difference

+16.4276

+2.0221%

+3392671

+111587950

+1.4144

+6.5218%

+17.8420

+4.0953%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3411671	407037540729853046809	21	68.464	59653691802324 2² × 3² × 19 × 1871 × 46613041	2016-12-01	1871	46613041	29.168	0.3870	0.7224
3411671	16240547539522509968032049	26	83.748	2380145614791477544 2³ × 11 × 1019 × 353867 × 75007831	2021-12-20	353867	75007831	1,044,472	0.6733	1.1624

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3411671

407037540729853046809

68.464

59653691802324
2² × 3² × 19 × 1871 × 46613041

2016-12-01

1871

46613041

29.168

0.3870

0.7224

3411671

16240547539522509968032049

83.748

2380145614791477544
2³ × 11 × 1019 × 353867 × 75007831

2021-12-20

353867

75007831

1,044,472

0.6733

1.1624

exponent	prime factors	composite factor	digits	bits*
3411671	407037540729853046809 16240547539522509968032049	6610512530593508335580156111326724152409181641	46	152.212

exponent

prime factors

composite factor

digits

bits*

3411671

407037540729853046809
16240547539522509968032049

6610512530593508335580156111326724152409181641

152.212

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04T06:49:00	Carsten Kossendey	leela	15000	210000		-		-	-	0.004	-	-	0.817%
2011-10-31T19:13:00	markr	tiny	215000	4783750		-		-	-	0.071	-	-	3.522%
2021-03-16T01:10:03	Jocelyn Larouche	Manual testing	341167	3752838	6	-		-	-	0.080	-	-	3.551%
2021-06-09T12:35:17	Jocelyn Larouche	Manual testing	3411671	3411671		-		-	-	0.520	-	-	3.910%
2021-12-20T20:11:19	Jocelyn Larouche	Manual testing	3411671	111907950			16240547539522509968032049	26	83.748	1.420	0.717	2.840	8.342%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:28	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-24T06:24:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2¹	2⁶²		-	-	0.180	-	-
2011-07-25T11:39:00	Carsten Kossendey	Manual testing	2⁶¹	2⁶³		-	-	0.378	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.288	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.575	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.575	-	-
2015-01-30T19:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.095	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.095	-	-
2015-04-08T08:56:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.190	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.190	-	-
2022-04-25T04:20:03	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.381	-	-
2021-06-09T12:35:19	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.761	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.320 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.320 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
		407037540729853046809	1	0.00000e+0
50000	5000000		9	1.320

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-21T19:39:00	Piepen	C589696BF	50000	5000000						3	0.440
2012-01-03T23:37:00	CuBr	H0E2035EE	50000	5000000						3	0.440
2014-12-14T10:25:00	Pool Party	St.P.p	50000	5000000						3	0.440
2016-12-01T05:17:24	f0rteOC	Fortissimo			407037540729853046809	68.464		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2A8630631552A6C7	0.358

date

userid

compid

res64

spent (GHz-days)

1999-07-27T00:00:00

ANONYMOUS

v4_computers

2A8630631552A6C7

0.358

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T04:15:10

alpertron

407037540729853046809

40BAAE7FA6AD59__

2017-11-21T08:23:42

Oliver Kruse

Threadripper

407037540729853046809

40BAAE7FA6AD59__

2021-12-27T13:56:50

GAN

LMS-09

407037540729853046809

16240547539522509968032049

40BAAE7FA6AD5916

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 = 3411671, B2 = 111907950 (P-1 stage 2)

B1 = 3411671 (P-1 stage 1)

B1 = 341167, B2 = 3752838 (P-1 stage 2)

B1 = 215000, B2 = 4783750 (P-1 stage 2)

B1 = 341167 (P-1 stage 1)

B1 = 215000 (P-1 stage 1)

B1 = 15000, B2 = 210000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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