M3050029 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

6037A342D70A3283

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	19.5424	67.6471%	3000000	100000000	1.0224	8.0350%	20.5648	70.2466%	2.5996%
PrimeNet	2⁶⁰	0.0504	63.3333%	12000	220000	0.0029	2.5228%	0.0532	64.2584%	0.9250%
GPU72	2⁶⁴	1.1670	65.6250%	14000	220000	0.0031	1.4649%	1.1701	66.1286%	0.5036%
Difference	+4	+18.3754	+2.0221%	+2986000	+99780000	+1.0193	+6.5701%	+19.3947	+4.1180%	+4.1180%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.5424

67.6471%

3000000

100000000

1.0224

8.0350%

20.5648

70.2466%

2.5996%

PrimeNet

2⁶⁰

0.0504

63.3333%

12000

220000

0.0029

2.5228%

0.0532

64.2584%

0.9250%

GPU72

2⁶⁴

1.1670

65.6250%

14000

220000

0.0031

1.4649%

1.1701

66.1286%

0.5036%

Difference

+18.3754

+2.0221%

+2986000

+99780000

+1.0193

+6.5701%

+19.3947

+4.1180%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3050029	275018000125340375341577	24	77.864	45084489381140372 2² × 23 × 83 × 5904202380977	2020-10-14	83	5904202380977	13,233	39,699	74,146

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3050029

275018000125340375341577

77.864

45084489381140372
2² × 23 × 83 × 5904202380977

2020-10-14

5904202380977

13,233

39,699

74,146

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-10-04T09:16:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.665%
2016-03-15T11:43:54	Squeeky_Squirrel	P4_2600	205000	5688750	12	-		-	-	0.062	-	-	3.572%
2017-09-23T18:26:21	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.035%
2021-01-14T13:16:35	Jocelyn Larouche	Manual testing	305002	305002		-		-	-	0.038	-	-	1.534%
2021-01-16T21:12:24	Jocelyn Larouche	Manual testing	305002	3050029	6	-		-	-	0.056	-	-	3.287%
2022-01-23T08:35:01	Jocelyn Larouche	Manual testing	1055002	119912100		-		-	-	0.929	-	-	7.512%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-12T06:04:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-03-17T13:03:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.644	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.225	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.450	-	-
2017-05-07T02:13:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.900	-	-
2018-07-25T22:30:18	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.80	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.980 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:	1.980 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	1.747
50000	5000000	275018000125340375341577	2	0.233

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-28T15:10:00	Mitical	Mitical_1	50000	5000000						3	0.349
2010-08-09T01:49:00	Mitical	Manual testing	50000	5000000						3	0.349
2013-10-12T06:18:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-30T21:29:49	Bruce	Desk7	50000	5000000						3	0.349
2017-09-04T02:16:55	Bruce	desk	50000	5000000						3	0.349
2020-10-14T19:39:31	daveward2005	Davy	50000	5000000	275018000125340375341577	77.864	2	2	5926739090844722	2	0.233

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	5EBEC3E36B1BE9__	0.260

date

userid

compid

res64

spent (GHz-days)

1999-05-23T00:00:00

ANONYMOUS

v4_computers

5EBEC3E36B1BE9__

0.260

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 = 1055002, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1055002 (P-1 stage 1)

B1 = 205000, B2 = 5688750 (P-1 stage 2)

B1 = 305002, B2 = 3050029 (P-1 stage 2)

B1 = 305002 (P-1 stage 1)

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

B1 = 205000 (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

10¹³

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