M2128303 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	13.9613	67.1642%	500000	15000000	0.1230	5.1615%	14.0843	68.8590%	1.6948%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	160000	0.0016	2.6845%	0.0197	63.0872%	1.0183%
GPU72	2⁶²	0.2887	64.5161%	10000	140000	0.0016	1.4553%	0.2903	65.0325%	0.5164%
Difference	+5	+13.6727	+2.6481%	+490000	+14860000	+0.1214	+3.7062%	+13.7940	+3.8265%	+3.8265%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9613

67.1642%

500000

15000000

0.1230

5.1615%

14.0843

68.8590%

1.6948%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

160000

0.0016

2.6845%

0.0197

63.0872%

1.0183%

GPU72

2⁶²

0.2887

64.5161%

10000

140000

0.0016

1.4553%

0.2903

65.0325%

0.5164%

Difference

+13.6727

+2.6481%

+490000

+14860000

+0.1214

+3.7062%

+13.7940

+3.8265%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2128303	85132121	8	26.343	20 2² × 5	-	4	5	4.219e-12	3.865e-7	7.761e-7
2128303	11768838789647	14	43.420	2764841 2764841	2008-08-26	1	2764841	7.986e-7	0.0144	0.0268
2128303	195005522451758819756023	24	77.368	45812443635083637 3² × 23 × 20959 × 10559480549	2021-12-20	20959	10559480549	17,174	54.850	102.44

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2128303

85132121

26.343

20
2² × 5

4.219e-12

3.865e-7

7.761e-7

2128303

11768838789647

43.420

2764841
2764841

2008-08-26

2764841

7.986e-7

0.0144

0.0268

2128303

195005522451758819756023

77.368

45812443635083637
3² × 23 × 20959 × 10559480549

2021-12-20

20959

10559480549

17,174

54.850

102.44

exponent	prime factors	composite factor	digits	bits*
2128303	85132121 11768838789647	1001906207869721951287	22	69.763
2128303	85132121 195005522451758819756023	16601233733031348506286940514783	32	103.711
2128303	11768838789647 195005522451758819756023	2294988556825638152243830955158293881	37	120.788
2128303	85132121 11768838789647 195005522451758819756023	195377243513295603079038238378081448830851601	45	147.131

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T11:27:15	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 85132121 skipped known factor: 11768838789647	-	-	0.123	-	-	5.161%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	11768838789647	43.420	14	2.47999e-7	0.302	5.36087e-7

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.764 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	1.764 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.653	52.064%
25	50000	0.058	94.325%
30	250000	0.004	99.641%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.511
50000	5000000	195005522451758819756023	7	0.597
50000	6209182		7	0.656

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-07T23:49:17	ATH	ec2-1xe	50000	5000000						3	0.256
2019-10-11T09:29:25	ATH	ec2-ECMCF	50000	5000000						3	0.256
2021-12-20T08:33:49	MarkS	laptop64	50000	5000000	195005522451758819756023	77.368	7	2	5446849267851580	7	0.597
2022-05-11T01:07:06	debrouxl	dl380g9-1	50000	6209182						7	0.656

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T13:39:46

Oliver Kruse

GTX-3

85132121

11768838789647

90D01FE140A7C3__

2017-11-17T23:13:04

kkmrkkblmbrbk

c4.xlarge

85132121

11768838789647

90D01FE140A7C3__

2021-12-20T08:52:19

MarkS

desktop-i7

85132121

11768838789647

195005522451758819756023

027F9D9C4909958D

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

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