M1775927 Mersenne number exponent details

Residue

Status

L-L

94340CC0C434BA1C

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	16.7315	68.6567%	500000	15000000	0.1015	5.0503%	16.8330	70.2396%	1.5829%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8103%	0.0120	64.1933%	1.0354%
GPU72	2⁶¹	0.1730	65.5738%	8000	120000	0.0011	1.4554%	0.1741	66.0748%	0.5010%
Difference	+6	+16.5585	+3.0829%	+492000	+14880000	+0.1004	+3.5949%	+16.6589	+4.1648%	+4.1648%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.7315

68.6567%

500000

15000000

0.1015

5.0503%

16.8330

70.2396%

1.5829%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8103%

0.0120

64.1933%

1.0354%

GPU72

2⁶¹

0.1730

65.5738%

8000

120000

0.0011

1.4554%

0.1741

66.0748%

0.5010%

Difference

+16.5585

+3.0829%

+492000

+14880000

+0.1004

+3.5949%

+16.6589

+4.1648%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1775927	12695048371194338305600111	26	83.392	3574203323445822465 3⁴ × 5 × 23 × 223 × 233 × 7384746829	2013-06-09	233	7384746829	1,400,299	31.649	59.112

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1775927

12695048371194338305600111

83.392

3574203323445822465
3⁴ × 5 × 23 × 223 × 233 × 7384746829

2013-06-09

233

7384746829

1,400,299

31.649

59.112

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08T15:58:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.434%
2016-03-16T12:31:54	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.050%

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	-	-
2010-04-19T13:16:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.086	-	-
2010-12-13T03:32:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.899	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.623 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:	17.623 GHz-days
Estimated T-Level:	24.571

Digits	B1	Complete	FacMiss
20	11000	8.258	0.026%
25	50000	0.746	47.409%
30	250000	0.046	95.508%
35	1000000	0.002	99.790%

ECM Summary

B1	B2	factor	curves	GHz-days
		12695048371194338305600111	1	0.00000e+0
50000	5000000		256	17.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-15T20:09:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-07-09T08:05:00	Lukasz Wrobel	cm-1	50000	5000000						3	0.207
2010-12-21T05:55:00	Lupo	yorick	50000	5000000						3	0.207
2012-02-13T08:33:00	OS1	L3	50000	5000000						3	0.207
2013-06-09T16:36:00	Chang Chia-Tche	exbpc13			12695048371194338305600111	83.392		1		1	-
2020-05-02T18:30:11	Oliver Kruse	IOS-1	50000	5000000						3	0.207
2020-05-30T15:52:22	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-28T15:15:56	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-07-25T17:01:03	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-10-04T20:51:31	nordi	sweet16	50000	5000000						7	0.482
2020-10-09T08:35:31	TJAOI	Manual testing	50000	5000000						225	15.49

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	94340CC0C434BA1C	0.096

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

94340CC0C434BA1C

0.096

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

B1 = 95000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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