M2036423 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	14.5912	68.6567%	500000	15000000	0.1230	5.1342%	14.7142	70.2659%	1.6092%
PrimeNet	2⁵⁸	0.0189	63.7931%	9000	160000	0.0016	2.6623%	0.0205	64.7570%	0.9639%
GPU72	2⁶²	0.3017	66.1290%	9000	120000	0.0014	1.3285%	0.3031	66.5790%	0.4500%
Difference	+5	+14.2895	+2.5277%	+491000	+14880000	+0.1216	+3.8057%	+14.4111	+3.6869%	+3.6869%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.5912

68.6567%

500000

15000000

0.1230

5.1342%

14.7142

70.2659%

1.6092%

PrimeNet

2⁵⁸

0.0189

63.7931%

9000

160000

0.0016

2.6623%

0.0205

64.7570%

0.9639%

GPU72

2⁶²

0.3017

66.1290%

9000

120000

0.0014

1.3285%

0.3031

66.5790%

0.4500%

Difference

+14.2895

+2.5277%

+491000

+14880000

+0.1216

+3.8057%

+14.4111

+3.6869%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2036423	43648690583	11	35.345	10717 7 × 1531	-	7	1531	2.966e-9	8.583e-6	1.489e-5
2036423	27680948520026930678634481	26	84.517	6796463337928055880 2³ × 3² × 5 × 11 × 4597 × 373347535499	2021-09-19	4597	373347535499	2,473,582	1,939.3	3,622.0

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2036423

43648690583

35.345

10717
7 × 1531

1531

2.966e-9

8.583e-6

1.489e-5

2036423

27680948520026930678634481

84.517

6796463337928055880
2³ × 3² × 5 × 11 × 4597 × 373347535499

2021-09-19

4597

373347535499

2,473,582

1,939.3

3,622.0

exponent	prime factors	composite factor	digits	bits*
2036423	43648690583 27680948520026930678634481	1208237156994607276018906670123792423	37	119.862

exponent

prime factors

composite factor

digits

bits*

2036423

43648690583
27680948520026930678634481

1208237156994607276018906670123792423

119.862

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:19:48	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 43648690583	-	-	0.123	-	-	5.134%

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.245 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	3.245 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.436	23.790%
25	50000	0.133	87.566%
30	250000	0.008	99.163%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.695
50000	6464464		7	0.664
50000	6900000	27680948520026930678634481	2	0.196
50000	7000000		7	0.690

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-28T09:13:45	ATH	ec2-1xe	50000	5000000						3	0.254
2019-06-21T02:58:55	Ducho_YYZ	Dutch	50000	5000000						3	0.254
2021-06-22T22:38:49	Jonathan Webb	Desktop2021	50000	5000000						7	0.593
2021-09-19T16:04:35	Ahmed Azhad	c5.azf2	50000	6900000	27680948520026930678634481	84.517	2	2	799707771235227	2	0.196
2021-10-08T12:27:20	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.593
2022-03-01T13:34:08	Team_Inspector	SpudBoy4	50000	7000000						7	0.690
2022-06-05T19:45:53	debrouxl	dl380g9-1	50000	6464464						7	0.664

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T04:42:48

Oliver Kruse

GTX-3

43648690583

C88FA61890E509__

2017-11-14T15:22:16

ATH

ec2-1xf

43648690583

C88FA61890E509__

2021-09-19T17:13:54

Ahmed Azhad

AzhadPC1

43648690583

27680948520026930678634481

FC659ABE563C4A32

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