M3486097 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

621579DBAB0C225B

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	34.2465	68.1159%	1000000	126668850	1.1950	7.0024%	35.4415	70.3486%	2.2327%
PrimeNet	2⁶⁰	0.0441	63.3333%	15000	300000	0.0046	2.9584%	0.0487	64.4181%	1.0847%
GPU72	2⁶⁴	1.0210	65.6250%	19000	360000	0.0057	1.8874%	1.0267	66.2738%	0.6488%
Difference	+5	+33.2255	+2.4909%	+981000	+126308850	+1.1893	+5.1151%	+34.4148	+4.0748%	+4.0748%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.2465

68.1159%

1000000

126668850

1.1950

7.0024%

35.4415

70.3486%

2.2327%

PrimeNet

2⁶⁰

0.0441

63.3333%

15000

300000

0.0046

2.9584%

0.0487

64.4181%

1.0847%

GPU72

2⁶⁴

1.0210

65.6250%

19000

360000

0.0057

1.8874%

1.0267

66.2738%

0.6488%

Difference

+33.2255

+2.4909%

+981000

+126308850

+1.1893

+5.1151%

+34.4148

+4.0748%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3486097	4378972447595021129133431	25	81.857	628062335556787595 5 × 751 × 2143667 × 78025307	2021-04-12	2143667	78025307	161,615	0.9561	1.2091

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3486097

4378972447595021129133431

81.857

628062335556787595
5 × 751 × 2143667 × 78025307

2021-04-12

2143667

78025307

161,615

0.9561

1.2091

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-07T17:48:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.813%
2011-11-15T05:10:00	harlee	P4_2600	60000	990000		-		-	-	0.017	-	-	1.689%
2014-08-21T21:46:00	Jocelyn Larouche	Manual testing	78411	78411		-		-	-	0.012	-	-	0.653%
2014-09-29T17:40:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.168%
2022-04-10T23:56:44	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	7.002%

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	-	-
2009-03-19T18:07:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-15T12:06:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.088	-	-
2012-08-18T15:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.458	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.282	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.563	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.072	-	-
2016-01-06T22:34:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.144	-	-
2017-02-18T19:55:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.287	-	-
2018-10-01T11:53:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.574	-	-
2021-01-11T17:48:16	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.15	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.504 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	2.504 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.548	57.788%
25	50000	0.050	95.165%
30	250000	0.003	99.695%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.209
50000	5000000	4378972447595021129133431	2	0.295

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-16T12:39:00	James Hintz	4115	50000	5000000						3	0.442
2012-02-29T15:15:00	oodaira	Linux01	50000	5000000						3	0.442
2015-04-06T12:09:00	Bruce	S2600KP	50000	5000000						3	0.442
2017-01-17T02:17:08	Alexandr	zrhenjq123	50000	5000000						3	0.442
2019-07-07T12:59:19	furkell	furkell1	50000	5000000						3	0.442
2021-04-12T23:03:37	daveward2005	Davy	50000	5000000	4378972447595021129133431	81.857	2	2	7991306525844647	2	0.295

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	AEC80CAF7C8558__	0.366

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

AEC80CAF7C8558__

0.366

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 = 1000000, B2 = 126668850 (P-1 stage 2)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

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

B1 = 78411 (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

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