M1749887 Mersenne number exponent details

Residue

Status

L-L

2A788FBAF71F9FA9

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	16.9805	68.6567%	500000	15000000	0.1015	5.0413%	17.0820	70.2368%	1.5801%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8024%	0.0122	64.1904%	1.0325%
GPU72	2⁶¹	0.1755	65.5738%	8000	110000	0.0011	1.4126%	0.1766	66.0601%	0.4863%
Difference	+6	+16.8049	+3.0829%	+492000	+14890000	+0.1004	+3.6287%	+16.9053	+4.1767%	+4.1767%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9805

68.6567%

500000

15000000

0.1015

5.0413%

17.0820

70.2368%

1.5801%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8024%

0.0122

64.1904%

1.0325%

GPU72

2⁶¹

0.1755

65.5738%

8000

110000

0.0011

1.4126%

0.1766

66.0601%

0.4863%

Difference

+16.8049

+3.0829%

+492000

+14890000

+0.1004

+3.6287%

+16.9053

+4.1767%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1749887	83657343617096895497	20	66.181	23903641668604 2² × 5233 × 1141966447	2014-12-23	5233	1141966447	9.4453	4.8946	9.1410

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1749887

83657343617096895497

66.181

23903641668604
2² × 5233 × 1141966447

2014-12-23

5233

1141966447

9.4453

4.8946

9.1410

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:45:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.402%
2014-04-08T23:00:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.887%
2014-05-06T10:53:00	Jocelyn Larouche	Manual testing	136679	136679		-		-	-	0.011	-	-	1.059%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	173358	173358		-		-	-	0.014	-	-	1.202%
2016-03-16T12:35:33	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.041%

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	-	-
2010-04-24T12:42:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.088	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.912	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.663 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	17.663 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.290	0.025%
25	50000	0.749	47.271%
30	250000	0.046	95.491%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		255	17.53
50000	5000000	83657343617096895497	2	0.137

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-24T03:32:00	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-06-24T11:37:00	Lupo	yorick	50000	5000000						3	0.206
2010-08-22T12:07:00	Kamil_Górski	thefault	50000	5000000						3	0.206
2012-01-02T08:27:00	S36049	Wolle5	50000	5000000						3	0.206
2013-05-19T07:31:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-16T20:10:00	Sara	Sara	50000	5000000						3	0.206
2014-12-23T01:02:00	Chang Chia-Tche	exbpc13	50000	5000000	83657343617096895497	66.181	2	2		2	0.137
2020-05-09T14:53:42	Greg Hogan	azure	50000	5000000						3	0.206
2020-06-18T20:07:19	nordi	sweet16	50000	5000000						3	0.206
2020-07-15T21:01:48	kracker	O0	50000	5000000						3	0.206
2020-08-14T09:31:12	TJAOI	Manual testing	50000	5000000						228	15.67

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2A788FBAF71F9FA9	0.095

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

2A788FBAF71F9FA9

0.095

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 = 1543750 (P-1 stage 2)

B1 = 173358 (P-1 stage 1)

B1 = 136679 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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