M3072947 Mersenne number exponent details

Residue

Status

L-L

4A3953FAB099EA17

double-checked

PRP

63DD998CBB82E722

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	19.3966	67.6471%	3000000	100000000	1.0224	8.0409%	20.4191	70.2485%	2.6015%
PrimeNet	2⁶⁰	0.0500	63.3333%	12000	220000	0.0029	2.5263%	0.0529	64.2596%	0.9263%
GPU72	2⁶⁴	1.1583	65.6250%	14000	220000	0.0031	1.4671%	1.1614	66.1293%	0.5043%
Difference	+4	+18.2384	+2.0221%	+2986000	+99780000	+1.0193	+6.5738%	+19.2577	+4.1192%	+4.1192%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.3966

67.6471%

3000000

100000000

1.0224

8.0409%

20.4191

70.2485%

2.6015%

PrimeNet

2⁶⁰

0.0500

63.3333%

12000

220000

0.0029

2.5263%

0.0529

64.2596%

0.9263%

GPU72

2⁶⁴

1.1583

65.6250%

14000

220000

0.0031

1.4671%

1.1614

66.1293%

0.5043%

Difference

+18.2384

+2.0221%

+2986000

+99780000

+1.0193

+6.5738%

+19.2577

+4.1192%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3072947	14834950851273211847017	23	73.651	2413798684336764 2² × 3⁴ × 37 × 201351241603	2020-11-18	81	201351241603	1,207.8	1,353.8	2,528.6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3072947

14834950851273211847017

73.651

2413798684336764
2² × 3⁴ × 37 × 201351241603

2020-11-18

201351241603

1,207.8

1,353.8

2,528.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-09-21T07:05:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.668%
2016-10-23T05:57:15	Squeeky_Squirrel	P4_2600	195000	5460000	12	-		-	-	0.059	-	-	3.517%
2017-01-04T22:58:53	Jocelyn Larouche	low 4M	132000	132000		-		-	-	0.016	-	-	1.001%
2018-01-30T07:10:49	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.041%
2022-02-04T00:38:13	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	7.475%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
2001-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-13T16:54:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-10-27T16:50:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.100	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.319	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.639	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.216	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.432	-	-
2017-05-14T00:43:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.864	-	-
2018-08-05T23:31:44	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.73	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.265 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	3.265 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.903	40.526%
25	50000	0.082	92.161%
30	250000	0.005	99.499%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	2.566
50000	5000000	14834950851273211847017	6	0.700

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-21T10:43:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.350
2011-07-02T12:56:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.350
2013-11-07T12:44:00	arnaud	Chamot18	50000	5000000						3	0.350
2016-03-20T02:34:12	Sintax	ECM	50000	5000000						3	0.350
2017-09-27T10:53:23	bayanne	iMac	50000	5000000						3	0.350
2020-10-16T12:06:39	mnd9	75204	50000	5000000						7	0.816
2020-11-18T09:03:50	daveward2005	Dave2	50000	5000000	14834950851273211847017	73.651	6	2	7706109011571203	6	0.700

date	userid	compid	res64	spent (GHz-days)
1998-02-01T00:00:00	ANONYMOUS	v4_computers	4A3953FAB099EA17	0.262
1999-08-31T00:00:00	ANONYMOUS	v4_computers	4A3953FAB099EA17	0.262

date

userid

compid

res64

spent (GHz-days)

1998-02-01T00:00:00

ANONYMOUS

v4_computers

4A3953FAB099EA17

0.262

1999-08-31T00:00:00

ANONYMOUS

v4_computers

4A3953FAB099EA17

0.262

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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