M1537801 Mersenne number exponent details

Residue

Status

L-L

FFBDA0DC18026921

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	19.3223	68.6567%	500000	15000000	0.0835	4.9633%	19.4059	70.2124%	1.5557%
PrimeNet	2⁵⁷	0.0125	63.1579%	6500	110000	0.0008	2.4167%	0.0133	64.0483%	0.8904%
GPU72	2⁶¹	0.1998	65.5738%	6500	55000	0.0006	1.0153%	0.2003	65.9233%	0.3495%
Difference	+6	+19.1226	+3.0829%	+493500	+14945000	+0.0830	+3.9480%	+19.2055	+4.2891%	+4.2891%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.3223

68.6567%

500000

15000000

0.0835

4.9633%

19.4059

70.2124%

1.5557%

PrimeNet

2⁵⁷

0.0125

63.1579%

6500

110000

0.0008

2.4167%

0.0133

64.0483%

0.8904%

GPU72

2⁶¹

0.1998

65.5738%

6500

55000

0.0006

1.0153%

0.2003

65.9233%

0.3495%

Difference

+19.1226

+3.0829%

+493500

+14945000

+0.0830

+3.9480%

+19.2055

+4.2891%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1537801	97258964246602302049	20	66.398	31622740603824 2⁴ × 3 × 658807095913	2013-09-06	16	658807095913	13.945	2,324.7	4,341.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1537801

97258964246602302049

66.398

31622740603824
2⁴ × 3 × 658807095913

2013-09-06

658807095913

13.945

2,324.7

4,341.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	290000		-		-	-	0.002	-	-	0.992%
2011-02-01T22:44:00	James Heinrich	WHS	80000	1340000		-		-	-	0.010	-	-	2.195%
2016-03-17T19:16:04	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.963%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.025	-	-
2010-04-27T04:50:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.100	-	-
2010-05-04T02:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.038	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	30.029 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	299 / 100	2.990	4.954%
25	50000	299 / 280	1.068	34.309%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	30.029 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.199	0.001%
25	50000	1.351	25.899%
30	250000	0.113	89.347%
35	1000000	0.008	99.238%

ECM Summary

B1	B2	factor	curves	GHz-days
		97258964246602302049	1	0.00000e+0
50000	5000000		249	13.91
250000	35000000		50	16.12

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-02-27T19:00:00	Steve Scott	Sue	50000	5000000						3	0.168
2010-02-14T10:10:00	ANONYMOUS	mac_pianoro	50000	5000000						3	0.168
2010-04-19T12:15:00	James Hintz	ryan	50000	5000000						3	0.168
2011-05-01T05:26:00	Lupo	yorick	50000	5000000						3	0.168
2012-11-15T02:06:00	Donna Noble	PH2x6	50000	5000000						3	0.168
2013-09-06T12:52:00	Chang Chia-Tche	exbpc13			97258964246602302049	66.398		1		1	-
2019-07-05T10:25:49	TJAOI	Manual testing	50000	5000000						234	13.07
2022-05-26T10:12:47	TJAOI	Manual testing	250000	35000000						50	16.12

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	FFBDA0DC18026921	0.069

date

userid

compid

res64

spent (GHz-days)

1998-11-28T00:00:00

ANONYMOUS

v4_computers

FFBDA0DC18026921

0.069

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 = 80000, B2 = 1340000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 20000, B2 = 290000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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