M1719857 Mersenne number exponent details

Residue

Status

L-L

AEC1C83AF7FF21C2

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	17.2770	68.6567%	500000	15000000	0.0880	5.0308%	17.3650	70.2335%	1.5768%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7933%	0.0122	64.1870%	1.0291%
GPU72	2⁶¹	0.1786	65.5738%	7000	110000	0.0009	1.3436%	0.1795	66.0363%	0.4626%
Difference	+6	+17.0984	+3.0829%	+493000	+14890000	+0.0872	+3.6871%	+17.1855	+4.1972%	+4.1972%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.2770

68.6567%

500000

15000000

0.0880

5.0308%

17.3650

70.2335%

1.5768%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

140000

0.0010

2.7933%

0.0122

64.1870%

1.0291%

GPU72

2⁶¹

0.1786

65.5738%

7000

110000

0.0009

1.3436%

0.1795

66.0363%

0.4626%

Difference

+17.0984

+3.0829%

+493000

+14890000

+0.0872

+3.6871%

+17.1855

+4.1972%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1719857	125664720949900007424100319	27	86.700	36533479513093241887 13 × 47 × 2609339 × 22914971503	2014-10-25	2609339	22914971503	13,622,754	85.365	159.12
1719857	1864167629521559028113997383	28	90.591	541954252452837366163 7 × 16927 × 58031 × 157561 × 500237	2015-06-06	157561	500237	209,633,019	0.0120	0.0219

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1719857

125664720949900007424100319

86.700

36533479513093241887
13 × 47 × 2609339 × 22914971503

2014-10-25

2609339

22914971503

13,622,754

85.365

159.12

1719857

1864167629521559028113997383

90.591

541954252452837366163
7 × 16927 × 58031 × 157561 × 500237

2015-06-06

157561

500237

209,633,019

0.0120

0.0219

exponent	prime factors	composite factor	digits	bits*
1719857	125664720949900007424100319 1864167629521559028113997383	23426010496766329435371402302139407211015793949546 5177	54	177.290

exponent

prime factors

composite factor

digits

bits*

1719857

125664720949900007424100319
1864167629521559028113997383

23426010496766329435371402302139407211015793949546
5177

177.290

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	90000	1507500		-		-	-	0.011	-	-	2.356%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.885%
2014-05-03T14:50:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.010	-	-	1.110%
2014-10-06T21:12:00	Jocelyn Larouche	Manual testing	187319	187319		-		-	-	0.013	-	-	1.248%
2015-06-06T12:14:00	alpertron	Manual testing	500000	15000000	12		1864167629521559028113997383	28	90.591	0.088	0.162	0.176	5.031%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2010-04-24T12:42:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.089	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.928	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.295 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:	15.295 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	15.18
50000	5000000	125664720949900007424100319	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-19T21:59:00	Scott Kurowski	UW2	50000	5000000						3	0.179
2009-09-24T06:15:00	SubPrime	abd0	50000	5000000						3	0.179
2010-07-23T11:05:00	James Classen	towerofart	50000	5000000						3	0.179
2011-12-03T12:16:00	Bud	annan	50000	5000000						3	0.179
2013-04-26T16:36:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-01-21T04:08:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2014-10-25T21:21:00	Chang Chia-Tche	exbpc13	50000	5000000	125664720949900007424100319	86.700	2	2		2	0.119
2020-03-23T08:12:08	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-04-30T17:32:21	Greg	azure2	50000	5000000						3	0.179
2020-05-04T10:43:43	TJAOI	Manual testing	50000	5000000						231	13.75

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	Phantomas	v4_computers	AEC1C83AF7FF21C2	0.081

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

Phantomas

v4_computers

AEC1C83AF7FF21C2

0.081

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:36

alpertron

Manual testing

125664720949900007424100319

1864167629521559028113997383

7CF7F1272E39C3__

2017-10-19T02:23:29

Oliver Kruse

Threadripper

125664720949900007424100319

1864167629521559028113997383

7CF7F1272E39C3__

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 = 187319 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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