M3271111 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

680DE216347608AA

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	2⁶⁸	18.2216	67.6471%	4000000	150000000	1.8206	8.7791%	20.0422	70.4874%	2.8403%
PrimeNet	2⁶⁰	0.0470	63.3333%	14000	260000	0.0042	2.7741%	0.0511	64.3505%	1.0172%
GPU72	2⁶⁴	1.0881	65.6250%	17000	280000	0.0048	1.6864%	1.0929	66.2047%	0.5797%
Difference	+4	+17.1335	+2.0221%	+3983000	+149720000	+1.8158	+7.0927%	+18.9493	+4.2827%	+4.2827%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.2216

67.6471%

4000000

150000000

1.8206

8.7791%

20.0422

70.4874%

2.8403%

PrimeNet

2⁶⁰

0.0470

63.3333%

14000

260000

0.0042

2.7741%

0.0511

64.3505%

1.0172%

GPU72

2⁶⁴

1.0881

65.6250%

17000

280000

0.0048

1.6864%

1.0929

66.2047%

0.5797%

Difference

+17.1335

+2.0221%

+3983000

+149720000

+1.8158

+7.0927%

+18.9493

+4.2827%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3271111	25024567957613614854024048663223	32	104.303	3825086944101501730455501 3 × 19 × 10781 × 130787 × 1821487 × 26128637	2020-12-10	1821487	26128637	4.188e+10	0.4791	0.5645

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3271111

25024567957613614854024048663223

104.303

3825086944101501730455501
3 × 19 × 10781 × 130787 × 1821487 × 26128637

2020-12-10

1821487

26128637

4.188e+10

0.4791

0.5645

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08T12:41:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.786%
2011-09-18T18:16:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.938%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	79622	79622		-		-	-	0.012	-	-	0.754%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99244	99244		-		-	-	0.015	-	-	0.861%
2016-01-16T00:42:31	Jocelyn Larouche	Manual testing	383400	3834000	6	-		-	-	0.087	-	-	3.598%
2020-12-10T04:53:02	mikr	MSI	4000000	150000000	12		25024567957613614854024048663223	32	104.303	1.821	0.687	3.641	8.779%
2021-01-18T13:43:04	Jocelyn Larouche	Manual testing	403400	3271111	6	-		-	-	0.085	-	-	3.483%
2022-01-06T11:34:10	Jocelyn Larouche	Manual testing	1567775	116447100		-		-	-	1.192	-	-	7.842%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-02T04:52:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-12-14T05:49:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.094	-	-
2012-12-30T00:06:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.300	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.600	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.142	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.284	-	-
2021-02-21T11:36:43	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.284	-	-
2021-02-22T09:03:46	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.569	-	-
2017-04-04T13:00:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.569	-	-
2018-12-10T15:07:55	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.138	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.183 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.183 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.183

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-23T14:02:00	TeamResslerTUB	1062315	50000	5000000						3	0.437
2011-12-19T05:51:00	Huaiyu Wu	eight	50000	5000000						3	0.437
2014-07-03T12:48:00	fireredd	ont111	50000	5000000						3	0.437
2016-09-05T20:48:36	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-01-20T03:58:28	Claude Portenier	Petit-Idiot	50000	5000000						3	0.437

date	userid	compid	res64	spent (GHz-days)
1999-08-07T00:00:00	ANONYMOUS	v4_computers	5602A3354D4AB8__	0.344

date

userid

compid

res64

spent (GHz-days)

1999-08-07T00:00:00

ANONYMOUS

v4_computers

5602A3354D4AB8__

0.344

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1567775, B2 = 116447100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1567775 (P-1 stage 1)

B1 = 383400, B2 = 3834000 (P-1 stage 2)

B1 = 403400, B2 = 3271111 (P-1 stage 2)

B1 = 403400 (P-1 stage 1)

B1 = 383400 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 99244 (P-1 stage 1)

B1 = 79622 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (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