M1652897 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	17.9769	68.6567%	500000	15000000	0.0880	5.0067%	18.0649	70.2260%	1.5693%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5643%	0.0125	64.1026%	0.9448%
GPU72	2⁶¹	0.1858	65.5738%	7000	70000	0.0007	1.1515%	0.1866	65.9702%	0.3964%
Difference	+6	+17.7910	+3.0829%	+493000	+14930000	+0.0873	+3.8552%	+17.8783	+4.2558%	+4.2558%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.9769

68.6567%

500000

15000000

0.0880

5.0067%

18.0649

70.2260%

1.5693%

PrimeNet

2⁵⁷

0.0116

63.1579%

7000

120000

0.0009

2.5643%

0.0125

64.1026%

0.9448%

GPU72

2⁶¹

0.1858

65.5738%

7000

70000

0.0007

1.1515%

0.1866

65.9702%

0.3964%

Difference

+17.7910

+3.0829%

+493000

+14930000

+0.0873

+3.8552%

+17.8783

+4.2558%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1652897	44876153551	11	35.385	13575 3 × 5² × 181	-	25	181	5.368e-9	2.286e-6	3.472e-6
1652897	205087825604663472839807	24	77.441	62038900670962399 59 × 22294763 × 47163847	2019-01-29	22294763	47163847	23,885	1.6139	3.0963

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1652897

44876153551

35.385

13575
3 × 5² × 181

181

5.368e-9

2.286e-6

3.472e-6

1652897

205087825604663472839807

77.441

62038900670962399
59 × 22294763 × 47163847

2019-01-29

22294763

47163847

23,885

1.6139

3.0963

exponent	prime factors	composite factor	digits	bits*
1652897	44876153551 205087825604663472839807	9203552753275587428840096957204657	34	112.826

exponent

prime factors

composite factor

digits

bits*

1652897

44876153551
205087825604663472839807

9203552753275587428840096957204657

112.826

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:17:55	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 44876153551	-	-	0.088	-	-	5.007%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.876 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.876 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	14.76
50000	5000000	205087825604663472839807	2	0.119

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-04-17T11:48:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-01-04T09:19:27	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-01-29T14:46:56	Chang Chia-Tche	exbpc13	50000	5000000	205087825604663472839807	77.441	2	2		2	0.119
2019-12-02T14:37:23	TJAOI	Manual testing	50000	5000000						245	14.52

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T19:01:52

Oliver Kruse

GTX-3

44876153551

574C396758A61A__

2017-11-02T09:04:03

kkmrkkblmbrbk

c4.xlarge

44876153551

574C396758A61A__

2019-01-29T19:40:13

Julian

martinpc

44876153551

205087825604663472839807

6D3C06318F1BE98C

2019-01-29T20:09:03

ATH

ec2-PRPCFDC

44876153551

205087825604663472839807

6D3C06318F1BE98C

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

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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