M1798999 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	16.5169	68.6567%	500000	15000000	0.1015	5.0582%	16.6184	70.2421%	1.5854%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	150000	0.0012	2.8698%	0.0119	64.2152%	1.0573%
GPU72	2⁶¹	0.1708	65.5738%	9000	130000	0.0012	1.5542%	0.1720	66.1088%	0.5350%
Difference	+6	+16.3462	+3.0829%	+491000	+14870000	+0.1002	+3.5040%	+16.4464	+4.1333%	+4.1333%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5169

68.6567%

500000

15000000

0.1015

5.0582%

16.6184

70.2421%

1.5854%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

150000

0.0012

2.8698%

0.0119

64.2152%

1.0573%

GPU72

2⁶¹

0.1708

65.5738%

9000

130000

0.0012

1.5542%

0.1720

66.1088%

0.5350%

Difference

+16.3462

+3.0829%

+491000

+14870000

+0.1002

+3.5040%

+16.4464

+4.1333%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1798999	233869871	9	27.801	65 5 × 13	-	5	13	1.008e-11	4.276e-7	8.005e-7
1798999	260671357103	12	37.923	72449 13 × 5573	2008-07-15	13	5573	1.711e-8	2.485e-5	4.464e-5
1798999	3549296546197030522183	22	71.588	986464291029909 3 × 829 × 396648287507	2020-09-18	829	396648287507	487.23	1,699.9	3,175.0

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1798999

233869871

27.801

65
5 × 13

1.008e-11

4.276e-7

8.005e-7

1798999

260671357103

37.923

72449
13 × 5573

2008-07-15

5573

1.711e-8

2.485e-5

4.464e-5

1798999

3549296546197030522183

71.588

986464291029909
3 × 829 × 396648287507

2020-09-18

829

396648287507

487.23

1,699.9

3,175.0

exponent	prime factors	composite factor	digits	bits*
1798999	233869871 260671357103	60963176659073543713	20	65.725
1798999	233869871 3549296546197030522183	830073525399845068806000848393	30	99.389
1798999	260671357103 3549296546197030522183	925199947458170679846155356115849	33	109.511
1798999	233869871 260671357103 3549296546197030522183	216376392361249154791602652980772666685479	42	137.313

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:35:33	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 233869871 skipped known factor: 260671357103	-	-	0.101	-	-	5.058%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	260671357103	37.923	12	6.93703e-9	0.209	1.48701e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:46:00

J Feitsma

Manual testing

260671357103

37.923

6.93703e-9

0.209

1.48701e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.268 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	18.268 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	8.548	0.019%
25	50000	0.773	46.181%
30	250000	0.048	95.354%
35	1000000	0.002	99.782%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		261	17.99
50000	5000000	3549296546197030522183	4	0.276

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-14T23:25:15	ATH	ec2-1xe	50000	5000000						3	0.207
2018-12-28T17:22:18	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-20T19:30:40	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-29T00:53:40	Greg	azure2	50000	5000000						3	0.207
2020-05-14T18:58:40	alpertron	laptop3	50000	5000000						3	0.207
2020-06-21T04:57:04	nordi	sweet16	50000	5000000						3	0.207
2020-07-18T17:21:17	nordi	sweet16	50000	5000000						3	0.207
2020-09-18T01:09:30	nordi	sweet16	50000	5000000	3549296546197030522183	71.588	4	2	6330229640047942	4	0.276
2020-10-31T06:56:51	nordi	sweet16	50000	5000000						7	0.483
2021-01-18T16:21:41	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-02-12T10:31:12	TJAOI	Manual testing	50000	5000000						226	15.58

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T18:11:57

Oliver Kruse

GTX-2

233869871

260671357103

9BA742858F2E47__

2017-11-05T13:11:55

kkmrkkblmbrbk

old

233869871

260671357103

9BA742858F2E47__

2020-09-18T08:33:29

M Miller

cruncher

233869871

260671357103

3549296546197030522183

71146821CEBEEC65

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

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