M1990031 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	14.9314	68.6567%	-	-	-	-	14.9314	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0193	63.7931%	8000	140000	0.0014	2.4765%	0.0207	64.6898%	0.8966%
GPU72	2⁶²	0.3087	66.1290%	8000	100000	0.0012	1.1985%	0.3100	66.5350%	0.4059%
Difference	+5	+14.6227	+2.5277%	-8000	-100000	-0.0012	-1.1985%	+14.6214	+2.1217%	+2.1217%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.9314

68.6567%

14.9314

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0193

63.7931%

8000

140000

0.0014

2.4765%

0.0207

64.6898%

0.8966%

GPU72

2⁶²

0.3087

66.1290%

8000

100000

0.0012

1.1985%

0.3100

66.5350%

0.4059%

Difference

+14.6227

+2.5277%

-8000

-100000

-0.0012

-1.1985%

+14.6214

+2.1217%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1990031	827852897	9	29.625	208 2⁴ × 13	-	16	16	3.756e-11	1.525e-6	3.104e-6
1990031	5816372142697182161	19	62.335	1461377270680 2³ × 5 × 31 × 1178530057	2016-07-27	31	1178530057	0.5821	6.1216	11.433
1990031	48255948414955230024109961	26	85.319	12124421281617027580 2² × 5 × 3709 × 1258681 × 129854951	2022-06-27	1258681	129854951	5,352,265	0.7880	1.2598

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1990031

827852897

29.625

208
2⁴ × 13

3.756e-11

1.525e-6

3.104e-6

1990031

5816372142697182161

62.335

1461377270680
2³ × 5 × 31 × 1178530057

2016-07-27

1178530057

0.5821

6.1216

11.433

1990031

48255948414955230024109961

85.319

12124421281617027580
2² × 5 × 3709 × 1258681 × 129854951

2022-06-27

1258681

129854951

5,352,265

0.7880

1.2598

exponent	prime factors	composite factor	digits	bits*
1990031	827852897 5816372142697182161	4815100528361959645720570417	28	91.960
1990031	827852897 48255948414955230024109961	39948826692803245300760811060407017	35	114.944
1990031	5816372142697182161 48255948414955230024109961	280674554080177842486478177491567526711605721	45	147.654
1990031	827852897 5816372142697182161 48255948414955230024109961	23235724270945839717764064256367437005932767965162 3737	54	177.279

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2016-07-27T14:37:11	TJAOI	Manual testing	2⁶²	2⁶³*	5816372142697182161	62.335	19	0.273	0.266	0.555

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2016-07-27T14:37:11

TJAOI

Manual testing

2⁶²

2⁶³*

5816372142697182161

62.335

0.273

0.266

0.555

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.828 GHz-days
Estimated T-Level:	4.200

Digits	B1	Curves	Complete	FacMiss
20	11000	84 / 100	0.840	42.989%
25	50000	84 / 280	0.300	74.042%

New Calculation Method

Total ECM effort:	7.828 GHz-days
Estimated T-Level:	4.200

Digits	B1	Complete	FacMiss
20	11000	3.401	3.335%
25	50000	0.316	72.889%
30	250000	0.020	98.012%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		31	2.620
50000	6750000		7	0.675
50000	7050000	48255948414955230024109961	46	4.532

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-24T14:42:33	Oliver Kruse	ECM-HTC	50000	5000000						3	0.254
2019-04-25T12:02:02	ATH	ec2-ECMCF	50000	5000000						3	0.254
2021-03-06T21:37:39	zampel	goldammer	50000	5000000						7	0.592
2021-06-26T03:18:01	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.592
2021-09-20T13:45:56	Ahmed Azhad	c5.4xlarge.azf	50000	6750000						7	0.675
2022-01-25T08:26:20	MarkS	laptop64	50000	5000000						11	0.930
2022-06-27T07:00:04	debrouxl	athlon2	50000	7050000	48255948414955230024109961	85.319	46	2	7951345104547398	46	4.532

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T15:45:31

Oliver Kruse

GTX-3

827852897

5816372142697182161

A1BF519322AABC__

2017-11-12T20:21:01

kkmrkkblmbrbk

c4.xlarge

827852897

5816372142697182161

A1BF519322AABC__

2022-07-04T01:35:54

Ryan Propper

boulder

827852897

5816372142697182161

48255948414955230024109961

CDB04015E4C8CA59

2022-07-21T06:32:29

some-students

GIMPS_IN_SHANGHAI

827852897

5816372142697182161

48255948414955230024109961

CDB04015E4C8CA59

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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