M1840781 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	16.1420	68.6567%	500000	15000000	0.1015	5.0722%	16.2435	70.2465%	1.5898%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8823%	0.0117	64.2198%	1.0619%
GPU72	2⁶¹	0.1669	65.5738%	9000	140000	0.0013	1.5965%	0.1681	66.1234%	0.5496%
Difference	+6	+15.9751	+3.0829%	+491000	+14860000	+0.1002	+3.4757%	+16.0753	+4.1231%	+4.1231%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1420

68.6567%

500000

15000000

0.1015

5.0722%

16.2435

70.2465%

1.5898%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8823%

0.0117

64.2198%

1.0619%

GPU72

2⁶¹

0.1669

65.5738%

9000

140000

0.0013

1.5965%

0.1681

66.1234%

0.5496%

Difference

+15.9751

+3.0829%

+491000

+14860000

+0.1002

+3.4757%

+16.0753

+4.1231%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1840781	11044687	8	23.397	3 3	-	1	3	6.075e-13	8.723e-8	1.601e-7
1840781	705637625417	12	39.360	191668 2² × 47917	2008-07-15	4	47917	5.915e-8	0.0002	0.0004
1840781	1723392653798249834951	22	70.546	468114526876975 5² × 11 × 349 × 11927 × 408943	2015-08-20	11927	408943	131.36	0.0026	0.0033

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1840781

11044687

23.397

3
3

6.075e-13

8.723e-8

1.601e-7

1840781

705637625417

39.360

191668
2² × 47917

2008-07-15

47917

5.915e-8

0.0002

0.0004

1840781

1723392653798249834951

70.546

468114526876975
5² × 11 × 349 × 11927 × 408943

2015-08-20

11927

408943

131.36

0.0026

0.0033

exponent	prime factors	composite factor	digits	bits*
1840781	11044687 705637625417	7793546708154009479	19	62.757
1840781	11044687 1723392653798249834951	19034332439301030574835455337	29	93.943
1840781	705637625417 1723392653798249834951	1216090699887298979325335812549567	34	109.906
1840781	11044687 705637625417 1723392653798249834951	13431341143866152502067805219500639500529	41	133.303

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-08-20T11:36:00	alpertron	Manual testing	500000	15000000	12		1723392653798249834951	22	70.546	0.039	0.200	0.079	5.072%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	705637625417	39.360	12	1.93591e-8	0.213	4.13879e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

705637625417

39.360

1.93591e-8

0.213

4.13879e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.231 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	19.231 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	10.324	0.003%
25	50000	0.950	38.672%
30	250000	0.060	94.148%
35	1000000	0.003	99.717%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	29	2.004
50000	6600000	214	16.68
50000	6750000	7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T01:42:41	alpertron		50000	5000000						3	0.207
2018-09-28T16:54:55	alpertron	Manual testing	50000	5000000						3	0.207
2020-05-27T10:45:06	kracker	O0	50000	5000000						3	0.207
2020-06-27T05:51:43	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-07-24T18:29:39	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-09-29T20:07:31	nordi	sweet16	50000	5000000						7	0.484
2020-11-28T02:41:36	nordi	sweet16	50000	5000000						7	0.484
2021-02-25T01:31:43	Deufo	Ryzen2600	50000	6750000						7	0.551
2021-05-21T15:33:05	TJAOI	Manual testing	50000	6600000						214	16.68

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T04:03:42

Oliver Kruse

GTX-0

11044687

705637625417

1723392653798249834951

EA89242CD1749BCF

2017-10-05T21:07:28

Oliver Kruse

Manual testing

11044687

705637625417

1723392653798249834951

EA89242CD1749B__

2017-11-11T04:19:14

kkmrkkblmbrbk

c4.xlarge

11044687

705637625417

1723392653798249834951

EA89242CD1749B__

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

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