M1805963 Mersenne number exponent details

Residue

Status

L-L

4300D7BF07637621

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	16.4532	68.6567%	500000	15000000	0.1015	5.0605%	16.5547	70.2428%	1.5861%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8719%	0.0119	64.2160%	1.0581%
GPU72	2⁶¹	0.1701	65.5738%	9000	130000	0.0012	1.5554%	0.1713	66.1092%	0.5355%
Difference	+6	+16.2831	+3.0829%	+491000	+14870000	+0.1002	+3.5051%	+16.3834	+4.1336%	+4.1336%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.4532

68.6567%

500000

15000000

0.1015

5.0605%

16.5547

70.2428%

1.5861%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8719%

0.0119

64.2160%

1.0581%

GPU72

2⁶¹

0.1701

65.5738%

9000

130000

0.0012

1.5554%

0.1713

66.1092%

0.5355%

Difference

+16.2831

+3.0829%

+491000

+14870000

+0.1002

+3.5051%

+16.3834

+4.1336%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1805963	7627645597497165454103	22	72.692	2111794537733377 7 × 320741 × 940587371	2013-07-14	320741	940587371	939.61	4.0550	7.5290

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1805963

7627645597497165454103

72.692

2111794537733377
7 × 320741 × 940587371

2013-07-14

320741

940587371

939.61

4.0550

7.5290

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	25000	387500		-		-	-	0.004	-	-	1.199%
2011-02-10T11:16:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.477%
2016-03-16T12:36:24	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.061%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-11T14:32:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.085	-	-
2010-12-13T03:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.884	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.438 GHz-days
Estimated T-Level:	24.571

Digits	B1	Curves	Complete	FacMiss
20	11000	256 / 100	2.560	7.631%
25	50000	256 / 280	0.914	40.015%

New Calculation Method

Total ECM effort:	19.438 GHz-days
Estimated T-Level:	24.571

Digits	B1	Complete	FacMiss
20	11000	8.741	0.016%
25	50000	0.792	45.302%
30	250000	0.049	95.220%
35	1000000	0.002	99.775%

ECM Summary

B1	B2	factor	curves	GHz-days
		7627645597497165454103	1	0.00000e+0
50000	5000000		39	2.690
50000	6500000		217	16.75

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-16T18:01:00	Scott Kurowski	UW2	50000	5000000						3	0.207
2009-07-16T12:43:00	SubPrime	mysql0	50000	5000000						3	0.207
2010-10-16T06:15:00	unconnected	X3220--xp	50000	5000000						3	0.207
2012-04-03T12:35:00	OS1	L3	50000	5000000						3	0.207
2013-07-14T04:43:00	Chang Chia-Tche	exbpc13			7627645597497165454103	72.692		1		1	-
2020-06-22T05:12:00	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-07-19T03:43:16	-Anonymous-	aws	50000	5000000						3	0.207
2020-09-15T17:23:14	Chang Chia-Tche	exbpc13	50000	5000000						7	0.483
2020-11-22T11:15:54	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-02-16T17:13:39	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2021-02-19T17:12:12	TJAOI	Manual testing	50000	6500000						217	16.75

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	4300D7BF07637621	0.098
2000-01-19T00:00:00	ANONYMOUS	v4_computers	4300D7BF07637621	0.098

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

4300D7BF07637621

0.098

2000-01-19T00:00:00

ANONYMOUS

v4_computers

4300D7BF07637621

0.098

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 100000, B2 = 1650000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 25000, B2 = 387500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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