M7003327 Mersenne number exponent details

Residue

Status

L-L

6B6803E394A6AB22

double-checked

PRP

808756FD959119__

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	2⁷²	136.5542	68.0556%	12000000	500000000	12.2006	8.8845%	148.7548	70.8937%	2.8381%
PrimeNet	2⁶³	0.2279	63.4921%	30000	800000	0.0227	3.3138%	0.2506	64.7019%	1.2098%
GPU72	2⁶⁷	4.2428	65.6716%	45000	900000	0.0290	2.2407%	4.2718	66.4408%	0.7692%
Difference	+5	+132.3114	+2.3839%	+11955000	+499100000	+12.1717	+6.6438%	+144.4830	+4.4528%	+4.4528%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

136.5542

68.0556%

12000000

500000000

12.2006

8.8845%

148.7548

70.8937%

2.8381%

PrimeNet

2⁶³

0.2279

63.4921%

30000

800000

0.0227

3.3138%

0.2506

64.7019%

1.2098%

GPU72

2⁶⁷

4.2428

65.6716%

45000

900000

0.0290

2.2407%

4.2718

66.4408%

0.7692%

Difference

+132.3114

+2.3839%

+11955000

+499100000

+12.1717

+6.6438%

+144.4830

+4.4528%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7003327	4334867297721758720752617959	28	91.808	309486283999144886477 71 × 263 × 1889 × 153059 × 57323999	2021-03-15	153059	57323999	119,298,464	1.0332	1.8443

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

7003327

4334867297721758720752617959

91.808

309486283999144886477
71 × 263 × 1889 × 153059 × 57323999

2021-03-15

153059

57323999

119,298,464

1.0332

1.8443

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-30T00:00:00	ANONYMOUS	v4_computers	35000	481250		-		-	-	0.019	-	-	0.891%
2011-11-28T02:51:00	bcp19	HP-2400	85000	1530000		-		-	-	0.052	-	-	1.574%
2015-06-02T07:34:00	Squeeky_Squirrel	P4_2600	180000	4230000		-		-	-	0.127	-	-	2.367%
2021-03-15T18:17:01	mikr	Nitron	12000000	500000000	12		4334867297721758720752617959	28	91.808	12.20	3.054	24.40	8.884%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2001-09-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-06T08:04:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.280	-	-
2014-02-13T22:32:00	ANONYMOUS	Manual testing	2⁶⁴	2⁶⁵		-	-	0.534	-	-
2015-06-12T10:16:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.067	-	-
2016-04-26T18:24:30	america64	Manual testing	2⁶⁶	2⁶⁷		-	-	2.134	-	-
2016-06-09T11:50:28	kkmrkkblmbrbk	Manual testing	2⁶⁷	2⁶⁸		-	-	4.268	-	-
2016-06-15T12:43:37	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	8.536	-	-
2016-06-15T12:43:37	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	17.07	-	-
2016-06-15T12:43:37	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	34.14	-	-
2020-10-29T16:55:40	mikr	Manual testing	2⁷¹	2⁷²		-	-	68.29	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-28T18:54:00	sebastian	desktop	50000	5000000						3	0.995
2017-05-23T23:18:37	William Wallace		50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	B6C36449EBD91B__	1.527
1999-09-14T00:00:00	ANONYMOUS	v4_computers	6B6803E394A6AB22	1.527
2001-10-20T00:00:00	ANONYMOUS	v4_computers	6B6803E394A6AB22	1.527

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 = 12000000, B2 = 500000000 (P-1 stage 2)

B1 = 12000000 (P-1 stage 1)

B1 = 180000, B2 = 4230000 (P-1 stage 2)

B1 = 180000 (P-1 stage 1)

B1 = 85000, B2 = 1530000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 481250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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