M1827197 Mersenne number exponent details

Residue

Status

L-L

8ECF3429C4798056

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	16.2620	68.6567%	500000	15000000	0.1015	5.0676%	16.3635	70.2451%	1.5884%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8783%	0.0117	64.2183%	1.0604%
GPU72	2⁶¹	0.1681	65.5738%	9000	140000	0.0013	1.5941%	0.1694	66.1226%	0.5488%
Difference	+6	+16.0939	+3.0829%	+491000	+14860000	+0.1002	+3.4735%	+16.1941	+4.1225%	+4.1225%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.2620

68.6567%

500000

15000000

0.1015

5.0676%

16.3635

70.2451%

1.5884%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8783%

0.0117

64.2183%

1.0604%

GPU72

2⁶¹

0.1681

65.5738%

9000

140000

0.0013

1.5941%

0.1694

66.1226%

0.5488%

Difference

+16.0939

+3.0829%

+491000

+14860000

+0.1002

+3.4735%

+16.1941

+4.1225%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1827197	630204535715694943	18	59.129	172451174043 3 × 57483724681	-	3	57483724681	0.0819	246.36	460.13
1827197	4466975740388225609	19	61.954	1222357452532 2² × 305589363133	2016-06-15	4	305589363133	0.1984	1,309.7	2,446.1
1827197	164660143631746679516329	24	77.124	45058125541949412 2² × 3 × 19 × 197623357640129	2019-10-22	19	197623357640129	33,111	846,964	1,581,893

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1827197

630204535715694943

59.129

172451174043
3 × 57483724681

57483724681

0.0819

246.36

460.13

1827197

4466975740388225609

61.954

1222357452532
2² × 305589363133

2016-06-15

305589363133

0.1984

1,309.7

2,446.1

1827197

164660143631746679516329

77.124

45058125541949412
2² × 3 × 19 × 197623357640129

2019-10-22

197623357640129

33,111

846,964

1,581,893

exponent	prime factors	composite factor	digits	bits*
1827197	630204535715694943 4466975740388225609	2815108372524634387294470740104395287	37	121.083
1827197	630204535715694943 164660143631746679516329	103769569368324559513276895138893351224247	42	136.252
1827197	4466975740388225609 164660143631746679516329	735532867011853195764458903247414651469361	42	139.078
1827197	630204535715694943 4466975740388225609 164660143631746679516329	46353614895883893605567964591465919656693665963286 4187141423	60	198.206

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:38:59	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.068%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:38:59

alpertron

Manual testing

500000

15000000

0.101

-

-

5.068%

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	-	-
2022-03-08T23:06:28	LordJulius	Manual testing	2⁵⁸	2⁶¹	630204535715694943	59.129	18	0.061	0.202	0.124
2022-03-09T03:44:03	LordJulius	Manual testing	2¹	2⁶¹	630204535715694943	59.129	18	0.082	0.202	0.167
2016-06-15T15:50:06	TJAOI	Manual testing	2⁶¹	2⁶²*	4466975740388225609	61.954	19	0.030	0.202	0.062

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.742 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:	19.742 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.810	0.015%
25	50000	0.798	45.019%
30	250000	0.049	95.183%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.555
50000	5000000	164660143631746679516329	2	0.138
50000	6600000		219	17.05

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-08-27T01:20:28	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-04T19:53:36	ATH	ec2-ECMCF	50000	5000000						3	0.207
2019-10-22T12:15:36	Chang Chia-Tche	exbpc13	50000	5000000	164660143631746679516329	77.124	2	2		2	0.138
2020-05-06T01:44:43	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-06-06T17:51:19	nordi	sweet16	50000	5000000						3	0.207
2020-07-03T22:02:12	LaurV	3tits	50000	5000000						3	0.207
2020-07-31T20:43:23	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-10-09T01:57:35	J.R. Allen	lapacer	50000	5000000						7	0.483
2020-12-04T19:30:23	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2021-03-10T05:49:05	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.483
2021-04-09T16:12:40	TJAOI	Manual testing	50000	6600000						219	17.05

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	8ECF3429C4798056	0.099

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

8ECF3429C4798056

0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T00:56:00

Oliver Kruse

GTX-0

630204535715694943

4466975740388225609

64654349A2E190__

2017-11-06T08:33:46

bayanne

iMac1

630204535715694943

4466975740388225609

64654349A2E190__

2019-10-22T12:24:00

ATH

ec2-PRPCF

630204535715694943

4466975740388225609

164660143631746679516329

74B25FFEA8D34B8A

2019-10-23T09:36:04

kkmrkkblmbrbk

c5.large

630204535715694943

4466975740388225609

164660143631746679516329

74B25FFEA8D34B8A

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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