M1878733 Mersenne number exponent details

Residue

Status

L-L

018D54D34B475A2C

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	15.8159	68.6567%	500000	15000000	0.1015	5.0846%	15.9174	70.2504%	1.5937%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0317%	0.0116	64.2748%	1.1169%
GPU72	2⁶¹	0.1635	65.5738%	10000	150000	0.0014	1.6912%	0.1649	66.1560%	0.5822%
Difference	+6	+15.6524	+3.0829%	+490000	+14850000	+0.1001	+3.3934%	+15.7525	+4.0944%	+4.0944%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.8159

68.6567%

500000

15000000

0.1015

5.0846%

15.9174

70.2504%

1.5937%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0317%

0.0116

64.2748%

1.1169%

GPU72

2⁶¹

0.1635

65.5738%

10000

150000

0.0014

1.6912%

0.1649

66.1560%

0.5822%

Difference

+15.6524

+3.0829%

+490000

+14850000

+0.1001

+3.3934%

+15.7525

+4.0944%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1878733	188426878504223591	18	57.387	50147327615 5 × 7 × 11 × 3583 × 36353	2003-01-09	3583	36353	0.0196	0.0004	0.0006
1878733	792382272147931700993	21	69.425	210882087062912 2⁷ × 52709 × 31256831	2020-12-14	52709	31256831	78.864	0.1379	0.2502
1878733	6679617505067635978039	22	72.500	1777692068289543 3 × 7 × 84652003251883	2021-10-20	7	84652003251883	562.26	362,797	677,604

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1878733

188426878504223591

57.387

50147327615
5 × 7 × 11 × 3583 × 36353

2003-01-09

3583

36353

0.0196

0.0004

0.0006

1878733

792382272147931700993

69.425

210882087062912
2⁷ × 52709 × 31256831

2020-12-14

52709

31256831

78.864

0.1379

0.2502

1878733

6679617505067635978039

72.500

1777692068289543
3 × 7 × 84652003251883

2021-10-20

84652003251883

562.26

362,797

677,604

exponent	prime factors	composite factor	digits	bits*
1878733	188426878504223591 792382272147931700993	149306118122918959282509895351428725863	39	126.812
1878733	188426878504223591 6679617505067635978039	1258619476082064551094029442969621718049	40	129.887
1878733	792382272147931700993 6679617505067635978039	5292810495744592089454759112352634462492727	43	141.925
1878733	188426878504223591 792382272147931700993 6679617505067635978039	99730776022754568744628542395773001851313045330474 3619322657	60	199.312

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:39:09	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 188426878504223591	-	-	0.101	-	-	5.085%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:39:09

alpertron

Manual testing

500000

15000000

skipped known factor: 188426878504223591

0.101

-

-

5.085%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-09T00:00:00	ANONYMOUS	v4_computers	?	?	188426878504223591	57.387	18	0.009	0.207	0.019
2003-08-25T00:00:00	ANONYMOUS	v4_computers	?	?	188426878504223591	57.387	18	0.009	0.207	0.019

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-09T00:00:00

ANONYMOUS

v4_computers

188426878504223591

57.387

0.009

0.207

0.019

2003-08-25T00:00:00

ANONYMOUS

v4_computers

188426878504223591

57.387

0.009

0.207

0.019

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.824 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:	19.824 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.795	0.015%
25	50000	0.797	45.053%
30	250000	0.049	95.187%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	1.663
50000	5000000	792382272147931700993	6	0.416
50000	6600000		208	16.25
50000	6600000	6679617505067635978039	5	0.391
50000	6683997		7	0.550
50000	6750000		7	0.553

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-05T11:53:05	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-19T21:32:24	alpertron		50000	5000000						3	0.208
2018-09-28T16:57:58	alpertron	Manual testing	50000	5000000						3	0.208
2020-08-06T22:58:40	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.208
2020-10-12T12:26:03	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2020-12-14T08:53:10	MarkS	laptop64	50000	5000000	792382272147931700993	69.425	6	2	4529343395870904	6	0.416
2021-02-26T05:48:48	Deufo	Ryzen2600	50000	6750000						7	0.553
2021-07-06T10:51:26	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.485
2021-09-22T00:51:35	Ahmed Azhad	c5.4xlarge.azf	50000	6683997						7	0.550
2021-10-20T13:17:49	TJAOI	Manual testing	50000	6600000	6679617505067635978039	72.500	5	2		5	0.391
2021-10-20T13:17:50	TJAOI	Manual testing	50000	6600000						208	16.25

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	018D54D34B475A2C	0.102

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

018D54D34B475A2C

0.102

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T13:16:12

Oliver Kruse

GTX-0

188426878504223591

932F175F7D0217__

2017-11-08T05:49:13

kkmrkkblmbrbk

old

188426878504223591

932F175F7D0217__

2020-12-19T07:12:21

M8909387

188426878504223591

792382272147931700993

F27E0649921E29CE

2021-10-22T12:44:47

JackBlock

Win10

188426878504223591

792382272147931700993

6679617505067635978039

F27E0649921E29CE

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

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