M1745561 Mersenne number exponent details

Residue

Status

L-L

BE0E3FF46C3CD455

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	17.0226	68.6567%	2475400	15000000	0.2484	5.7792%	17.2710	70.4681%	1.8114%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8011%	0.0122	64.1899%	1.0320%
GPU72	2⁶¹	0.1760	65.5738%	8000	110000	0.0011	1.4119%	0.1770	66.0598%	0.4861%
Difference	+6	+16.8466	+3.0829%	+2467400	+14890000	+0.2473	+4.3673%	+17.0939	+4.4083%	+4.4083%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.0226

68.6567%

2475400

15000000

0.2484

5.7792%

17.2710

70.4681%

1.8114%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8011%

0.0122

64.1899%

1.0320%

GPU72

2⁶¹

0.1760

65.5738%

8000

110000

0.0011

1.4119%

0.1770

66.0598%

0.4861%

Difference

+16.8466

+3.0829%

+2467400

+14890000

+0.2473

+4.3673%

+17.0939

+4.4083%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1745561	55986650684781102086262125500903063	35	115.431	16036864562390286585877584771 3 × 17 × 31 × 241 × 2719 × 15671 × 18181 × 25339 × 2144161	2015-04-19	25339	2144161	1.074e+11	0.0111	0.0172

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1745561

55986650684781102086262125500903063

115.431

16036864562390286585877584771
3 × 17 × 31 × 241 × 2719 × 15671 × 18181 × 25339 × 2144161

2015-04-19

25339

2144161

1.074e+11

0.0111

0.0172

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:49:00	Carsten Kossendey	leela	95000	1543750		-		-	-	0.014	-	-	2.401%
2014-04-05T13:21:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.887%
2014-05-06T10:53:00	Jocelyn Larouche	Manual testing	136770	136770		-		-	-	0.011	-	-	1.059%
2014-09-15T22:12:00	ANONYMOUS	Manual testing	173540	173540		-		-	-	0.014	-	-	1.203%
2015-04-19T08:37:00	mikr	MSI	2475400	15000000			55986650684781102086262125500903063	35	115.431	0.195	0.189	0.389	5.779%
2016-03-16T12:34:56	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 55986650684781102086262125500903063	-	-	0.101	-	-	5.040%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2022-03-08T23:06:25	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.066	-	-
2022-03-09T03:01:43	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.088	-	-
2010-04-24T12:42:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.088	-	-
2010-11-18T02:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.914	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.453 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	17.453 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		254	17.45

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-21T23:11:00	James Heinrich	Q6600	50000	5000000						3	0.206
2009-06-23T09:59:00	Lupo	yorick	50000	5000000						3	0.206
2010-08-20T07:22:00	Kamil_Górski	thefault	50000	5000000						3	0.206
2011-12-25T19:11:00	Wojciech Florek	gafel	50000	5000000						3	0.206
2013-05-15T18:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-02-13T02:37:00	Bruce	snowflake	50000	5000000						3	0.206
2014-12-16T15:33:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-05-14T09:02:59	Oliver Kruse	IOS-2	50000	5000000						3	0.206
2020-06-20T22:15:29	kracker	O0	50000	5000000						3	0.206
2020-06-29T11:37:08	TJAOI	Manual testing	50000	5000000						227	15.60

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	BE0E3FF46C3CD455	0.095

date

userid

compid

res64

spent (GHz-days)

1999-01-10T00:00:00

ANONYMOUS

v4_computers

BE0E3FF46C3CD455

0.095

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T09:47:22

Oliver Kruse

Doppelherz

55986650684781102086262125500903063

7D4F623ADB0CF8__

2017-11-03T17:18:00

kkmrkkblmbrbk

c4.xlarge

55986650684781102086262125500903063

7D4F623ADB0CF8__

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, B2 = 15000000 (P-1 stage 2)

B1 = 2475400 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 95000, B2 = 1543750 (P-1 stage 2)

B1 = 173540 (P-1 stage 1)

B1 = 136770 (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

10⁸

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