M1598873 Mersenne number exponent details

Residue

Status

L-L

1A8290DA9FB31D8D

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	18.5843	68.6567%	500000	15000000	0.0835	4.9867%	18.6678	70.2197%	1.5630%
PrimeNet	2⁵⁷	0.0120	63.1579%	7000	120000	0.0009	2.5478%	0.0129	64.0965%	0.9386%
GPU72	2⁶¹	0.1921	65.5738%	6500	60000	0.0006	1.0562%	0.1927	65.9374%	0.3636%
Difference	+6	+18.3922	+3.0829%	+493500	+14940000	+0.0829	+3.9305%	+18.4751	+4.2823%	+4.2823%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.5843

68.6567%

500000

15000000

0.0835

4.9867%

18.6678

70.2197%

1.5630%

PrimeNet

2⁵⁷

0.0120

63.1579%

7000

120000

0.0009

2.5478%

0.0129

64.0965%

0.9386%

GPU72

2⁶¹

0.1921

65.5738%

6500

60000

0.0006

1.0562%

0.1927

65.9374%

0.3636%

Difference

+18.3922

+3.0829%

+493500

+14940000

+0.0829

+3.9305%

+18.4751

+4.2823%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1598873	116404650699089657351	21	66.658	36402094068475 5² × 1456083762739	2010-03-28	25	1456083762739	12.626	5,138.0	9,596.4

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1598873

116404650699089657351

66.658

36402094068475
5² × 1456083762739

2010-03-28

1456083762739

12.626

5,138.0

9,596.4

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:29:00	alpertron	Manual testing	500000	15000000	12	-		-	-	0.084	-	-	4.987%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-06T00:00:00	chris lueders	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.015 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	14.015 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	9.615	0.007%
25	50000	0.890	41.079%
30	250000	0.056	94.543%
35	1000000	0.003	99.738%

ECM Summary

B1	B2	factor	curves	GHz-days
		116404650699089657351	1	0.00000e+0
50000	5000000		250	14.02

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-03-28T15:09:00	Steve Scott	Celeron	50000	5000000						3	0.168
2009-05-27T19:46:00	ksims	ZhViZCJBj2sims	50000	5000000						3	0.168
2010-03-28T05:08:00	SubPrime	abd0			116404650699089657351	66.658		1		1	-
2019-09-30T12:54:41	TJAOI	Manual testing	50000	5000000						244	13.68

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	1A8290DA9FB31D8D	0.071

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

ANONYMOUS

v4_computers

1A8290DA9FB31D8D

0.071

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T03:11:40

Oliver Kruse

GTX-1

116404650699089657351

DBE7D4AFE7995E__

2017-10-31T23:18:12

kkmrkkblmbrbk

c4.xlarge

116404650699089657351

DBE7D4AFE7995E__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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