M1784053 Mersenne number exponent details

Residue

Status

L-L

151D481B7A769C2F

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	16.6553	68.6567%	2475400	2475400	0.1947	3.5983%	16.8500	69.7845%	1.1278%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8127%	0.0120	64.1942%	1.0363%
GPU72	2⁶¹	0.1722	65.5738%	8000	130000	0.0012	1.4924%	0.1733	66.0875%	0.5138%
Difference	+6	+16.4831	+3.0829%	+2467400	+2345400	+0.1936	+2.1059%	+16.6767	+3.6970%	+3.6970%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6553

68.6567%

2475400

0.1947

3.5983%

16.8500

69.7845%

1.1278%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8127%

0.0120

64.1942%

1.0363%

GPU72

2⁶¹

0.1722

65.5738%

8000

130000

0.0012

1.4924%

0.1733

66.0875%

0.5138%

Difference

+16.4831

+3.0829%

+2467400

+2345400

+0.1936

+2.1059%

+16.6767

+3.6970%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1784053	106776688743693830655970275217	30	96.431	29925312965392236288936 2³ × 3 × 13² × 2927 × 30269 × 161783 × 514739	2015-06-02	161783	514739	1.222e+10	0.0142	0.0259

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1784053

106776688743693830655970275217

96.431

29925312965392236288936
2³ × 3 × 13² × 2927 × 30269 × 161783 × 514739

2015-06-02

161783

514739

1.222e+10

0.0142

0.0259

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:33:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.436%
2014-04-10T20:52:00	ANONYMOUS	Manual testing	100000	100000		-		-	-	0.008	-	-	0.891%
2014-05-09T20:32:00	Jocelyn Larouche	Manual testing	135977	135977		-		-	-	0.011	-	-	1.060%
2014-09-19T20:39:00	Jocelyn Larouche	Manual testing	171954	171954		-		-	-	0.014	-	-	1.201%
2015-06-02T12:35:00	mikr	MSI	2475400	2475400			106776688743693830655970275217	30	96.431	0.195	0.194	0.389	3.598%

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		-	-	0.022	-	-
2010-04-21T13:12:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.086	-	-
2010-10-16T22:17:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.895	-	-
2015-05-14T21:29:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.100	-	-
2015-05-14T21:29:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.094	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.770 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.770 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		258	17.77

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26T23:21:00	Scott Kurowski	UW4	50000	5000000						3	0.207
2009-07-08T00:16:00	SubPrime	stor	50000	5000000						3	0.207
2010-12-22T10:41:00	James Hintz	ryan	50000	5000000						3	0.207
2012-02-23T07:45:00	OS1	L3	50000	5000000						3	0.207
2013-06-18T14:50:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-02-19T08:53:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2015-02-13T19:56:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-07-22T09:04:22	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-09-23T20:34:05	Chang Chia-Tche	exbpc13	50000	5000000						7	0.482
2020-10-30T10:29:33	TJAOI	Manual testing	50000	5000000						227	15.63

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	151D481B7A769C2F	0.097

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

151D481B7A769C2F

0.097

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 = 2475400 (P-1 stage 1)

B1 = 95000, B2 = 1615000 (P-1 stage 2)

B1 = 171954 (P-1 stage 1)

B1 = 135977 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

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