M3446789 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

2B556A2F99E76E__

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	34.6371	68.1159%	500000	10000000	0.1550	4.1618%	34.7921	69.4429%	1.3270%
PrimeNet	2⁶⁰	0.0446	63.3333%	15000	280000	0.0045	2.9009%	0.0490	64.3970%	1.0637%
GPU72	2⁶⁴	1.0327	65.6250%	19000	340000	0.0056	1.8544%	1.0382	66.2625%	0.6375%
Difference	+5	+33.6045	+2.4909%	+481000	+9660000	+0.1494	+2.3074%	+33.7539	+3.1804%	+3.1804%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.6371

68.1159%

500000

10000000

0.1550

4.1618%

34.7921

69.4429%

1.3270%

PrimeNet

2⁶⁰

0.0446

63.3333%

15000

280000

0.0045

2.9009%

0.0490

64.3970%

1.0637%

GPU72

2⁶⁴

1.0327

65.6250%

19000

340000

0.0056

1.8544%

1.0382

66.2625%

0.6375%

Difference

+33.6045

+2.4909%

+481000

+9660000

+0.1494

+2.3074%

+33.7539

+3.1804%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3446789	1496504320252172969993	22	70.342	217086732064564 2² × 6577 × 8251738333	2021-05-15	6577	8251738333	127.95	68.467	127.88

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3446789

1496504320252172969993

70.342

217086732064564
2² × 6577 × 8251738333

2021-05-15

6577

8251738333

127.95

68.467

127.88

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T21:07:00	Carsten Kossendey	durandal	15000	210000		-		-	-	0.004	-	-	0.699%
2011-11-04T10:24:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.665%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78621	78621		-		-	-	0.012	-	-	0.653%
2014-09-19T09:52:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.162%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-22T09:55:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-04T20:50:00	markr	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2012-08-18T15:34:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.463	-	-
2016-02-23T16:29:30	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.285	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.570	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.084	-	-
2015-04-16T08:55:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.168	-	-
2017-02-09T04:36:20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.336	-	-
2022-01-19T07:45:01	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.672	-	-
2018-07-23T16:23:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.672	-	-
2021-01-04T04:39:06	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.34	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.883 GHz-days
Estimated T-Level:	0.950

Digits	B1	Curves	Complete	FacMiss
20	11000	19 / 100	0.190	82.617%
25	50000	19 / 280	0.068	93.428%

New Calculation Method

Total ECM effort:	2.883 GHz-days
Estimated T-Level:	0.950

Digits	B1	Complete	FacMiss
20	11000	0.744	47.540%
25	50000	0.069	93.355%
30	250000	0.004	99.566%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.205
50000	6700000	1496504320252172969993	4	0.678

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-02T00:11:00	Marzbug	Xeon	50000	5000000						3	0.441
2012-02-01T02:55:00	Piepen	Acer_Aspire_1522	50000	5000000						3	0.441
2015-02-02T13:49:00	codest	aliyun	50000	5000000						3	0.441
2016-12-20T14:01:41	Sid & Andy	Mrs_Potato_Head	50000	5000000						3	0.441
2019-06-01T23:26:39	furkell	furkell1	50000	5000000						3	0.441
2021-05-15T14:34:12	kutens	terra	50000	6700000	1496504320252172969993	70.342	4	2	9043381615564440	4	0.678

date	userid	compid	res64	spent (GHz-days)
1999-10-21T00:00:00	ANONYMOUS	v4_computers	126B3FCF69B8C2__	0.362

date

userid

compid

res64

spent (GHz-days)

1999-10-21T00:00:00

ANONYMOUS

v4_computers

126B3FCF69B8C2__

0.362

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

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78621 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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