M1996303 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	14.8845	68.6567%	-	-	-	-	14.8845	68.6567%	0.0000%
PrimeNet	2⁵⁸	0.0192	63.7931%	8000	140000	0.0014	2.4780%	0.0207	64.6903%	0.8972%
GPU72	2⁶²	0.3077	66.1290%	8000	110000	0.0013	1.2362%	0.3090	66.5477%	0.4187%
Difference	+5	+14.5767	+2.5277%	-8000	-110000	-0.0013	-1.2362%	+14.5754	+2.1090%	+2.1090%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.8845

68.6567%

14.8845

68.6567%

0.0000%

PrimeNet

2⁵⁸

0.0192

63.7931%

8000

140000

0.0014

2.4780%

0.0207

64.6903%

0.8972%

GPU72

2⁶²

0.3077

66.1290%

8000

110000

0.0013

1.2362%

0.3090

66.5477%

0.4187%

Difference

+14.5767

+2.5277%

-8000

-110000

-0.0013

-1.2362%

+14.5754

+2.1090%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1996303	233232072097	12	37.763	58416 2⁴ × 3 × 1217	-	16	1217	1.508e-8	7.764e-6	1.182e-5
1996303	38695020478748233	17	55.103	9691670172 2² × 3 × 23 × 3613 × 9719	2015-01-05	3613	9719	0.0027	0.0004	0.0007
1996303	5862974155086904849337	22	72.312	1468457983353956 2² × 7 × 173 × 303149872699	2021-03-22	173	303149872699	484.86	1,574.6	2,941.0

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1996303

233232072097

37.763

58416
2⁴ × 3 × 1217

1217

1.508e-8

7.764e-6

1.182e-5

1996303

38695020478748233

55.103

9691670172
2² × 3 × 23 × 3613 × 9719

2015-01-05

3613

9719

0.0027

0.0004

0.0007

1996303

5862974155086904849337

72.312

1468457983353956
2² × 7 × 173 × 303149872699

2021-03-22

173

303149872699

484.86

1,574.6

2,941.0

exponent	prime factors	composite factor	digits	bits*
1996303	233232072097 38695020478748233	9024919806094299335367354601	28	92.866
1996303	233232072097 5862974155086904849337	1367433610842076651121146106649689	34	110.075
1996303	38695020478748233 5862974155086904849337	226867904997459401755715859799219971521	39	127.415
1996303	233232072097 38695020478748233 5862974155086904849337	52912871574862797792119609794538016342148158749537	50	165.178

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-01-05T12:34:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	38695020478748233	55.103	17	0.000	0.281	0.001

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-01-05T12:34:00

TJAOI

Manual testing

2⁵⁵

2⁵⁶*

38695020478748233

55.103

0.000

0.281

0.001

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.464 GHz-days
Estimated T-Level:	1.950

Digits	B1	Curves	Complete	FacMiss
20	11000	39 / 100	0.390	67.573%
25	50000	39 / 280	0.139	86.976%

New Calculation Method

Total ECM effort:	3.464 GHz-days
Estimated T-Level:	1.950

Digits	B1	Complete	FacMiss
20	11000	1.289	27.549%
25	50000	0.117	88.948%
30	250000	0.007	99.280%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.691
50000	5000000	5862974155086904849337	5	0.423
50000	6717959		7	0.674
50000	6750000		7	0.676

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-24T02:59:21	ATH	ec2-1xe	50000	5000000						3	0.254
2019-05-04T15:33:12	J.R. Allen	lapdell	50000	5000000						3	0.254
2021-03-22T01:06:26	MarkS	laptop64	50000	5000000	5862974155086904849337	72.312	5	2	3392413478057796	5	0.423
2021-06-04T00:05:51	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.592
2021-09-04T01:36:34	Dylan Delgado	colab	50000	6750000						7	0.676
2022-01-03T01:57:08	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.592
2022-05-14T19:58:00	debrouxl	dl380g9-1	50000	6717959						7	0.674

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T17:35:27

Oliver Kruse

GTX-2

233232072097

38695020478748233

10A6B32E33D106__

2017-11-13T06:03:32

Chang Chia-Tche

exbpc13

233232072097

38695020478748233

10A6B32E33D106__

2021-03-22T09:15:17

MarkS

laptop64

233232072097

38695020478748233

5862974155086904849337

08A8DB5C8D8D4F2D

2021-03-22T22:23:45

MarkS

laptop64

233232072097

38695020478748233

5862974155086904849337

08A8DB5C8D8D4F2D

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

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