M1842497 Mersenne number exponent details

Residue

Status

L-L

5981BE0331206F43

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	16.1270	68.6567%	1000000	188329050	0.8815	8.2207%	17.0085	71.2334%	2.5766%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8828%	0.0117	64.2200%	1.0621%
GPU72	2⁶¹	0.1667	65.5738%	9000	140000	0.0013	1.5968%	0.1680	66.1235%	0.5497%
Difference	+6	+15.9603	+3.0829%	+991000	+188189050	+0.8802	+6.6239%	+16.8405	+5.1099%	+5.1099%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1270

68.6567%

1000000

188329050

0.8815

8.2207%

17.0085

71.2334%

2.5766%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8828%

0.0117

64.2200%

1.0621%

GPU72

2⁶¹

0.1667

65.5738%

9000

140000

0.0013

1.5968%

0.1680

66.1235%

0.5497%

Difference

+15.9603

+3.0829%

+991000

+188189050

+0.8802

+6.6239%

+16.8405

+5.1099%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1842497	86356783625647324146871	23	76.193	23434714853171355 3 × 5 × 283 × 5231 × 6007 × 175687	2011-02-07	6007	175687	8,656.7	0.0012	0.0014
1842497	18626020385970676257084409	26	83.946	5054559216642055932 2² × 3 × 7 × 60173324007643523	2021-03-01	7	60173324007643523	1,604,458	257,887,823	481,662,637

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1842497

86356783625647324146871

76.193

23434714853171355
3 × 5 × 283 × 5231 × 6007 × 175687

2011-02-07

6007

175687

8,656.7

0.0012

0.0014

1842497

18626020385970676257084409

83.946

5054559216642055932
2² × 3 × 7 × 60173324007643523

2021-03-01

60173324007643523

1,604,458

257,887,823

481,662,637

exponent	prime factors	composite factor	digits	bits*
1842497	86356783625647324146871 18626020385970676257084409	1608483212278165747883913503519342725525760234239	49	160.138

exponent

prime factors

composite factor

digits

bits*

1842497

86356783625647324146871
18626020385970676257084409

1608483212278165747883913503519342725525760234239

160.138

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:35:00	Carsten Kossendey	leela					86356783625647324146871	23	76.193	-	0.200	-	0.000%
2022-04-03T12:49:06	Jocelyn Larouche	Manual testing	1000000	188329050		-	skipped known factor: 86356783625647324146871	-	-	0.882	-	-	8.221%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-09T12:50:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.083	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.866	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.813 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:	19.813 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.821	0.015%
25	50000	0.799	44.960%
30	250000	0.049	95.175%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.005
50000	5000000	18626020385970676257084409	5	0.346
50000	6600000		217	16.91
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-11T09:41:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-18T15:01:00	James Hintz	02_071509	50000	5000000						3	0.207
2010-11-20T02:20:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2020-06-28T18:06:43	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-07-25T18:07:42	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-10-05T03:56:13	nordi	sweet16	50000	5000000						7	0.484
2020-11-30T09:13:33	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-03-01T01:18:59	Chang Chia-Tche	exbpc13	50000	5000000	18626020385970676257084409	83.946	5	2	669251818861516	5	0.346
2021-05-28T13:25:51	happy5214	Focus	50000	6750000						7	0.551
2021-06-26T09:34:22	TJAOI	Manual testing	50000	6600000						217	16.91

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	5981BE0331206F43	0.100

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

5981BE0331206F43

0.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T04:29:19

Oliver Kruse

GTX-1

86356783625647324146871

7B3AE4EC68F587__

2017-11-06T15:23:31

kkmrkkblmbrbk

c4.xlarge

86356783625647324146871

7B3AE4EC68F587__

2021-03-02T23:15:26

-Anonymous-

86356783625647324146871

18626020385970676257084409

18059E0D91FD20__

2021-03-15T12:42:21

Anton Repko

DeskMini

86356783625647324146871

18626020385970676257084409

18059E0D91FD20BF

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 = 1000000, B2 = 188329050 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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