M1569289 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	18.9346	68.6567%	500000	15000000	0.0835	4.9755%	19.0182	70.2162%	1.5595%
PrimeNet	2⁵⁷	0.0122	63.1579%	7000	110000	0.0008	2.4773%	0.0131	64.0706%	0.9127%
GPU72	2⁶¹	0.1957	65.5738%	6500	60000	0.0006	1.0518%	0.1964	65.9359%	0.3621%
Difference	+6	+18.7389	+3.0829%	+493500	+14940000	+0.0829	+3.9237%	+18.8218	+4.2803%	+4.2803%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.9346

68.6567%

500000

15000000

0.0835

4.9755%

19.0182

70.2162%

1.5595%

PrimeNet

2⁵⁷

0.0122

63.1579%

7000

110000

0.0008

2.4773%

0.0131

64.0706%

0.9127%

GPU72

2⁶¹

0.1957

65.5738%

6500

60000

0.0006

1.0518%

0.1964

65.9359%

0.3621%

Difference

+18.7389

+3.0829%

+493500

+14940000

+0.0829

+3.9237%

+18.8218

+4.2803%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1569289	6487440727	10	32.595	2067 3 × 13 × 53	-	13	53	5.277e-10	9.831e-7	1.714e-6
1569289	126850504772135330679671	24	76.747	40416553220004515 5 × 19 × 51461 × 8267181017	2017-12-04	51461	8267181017	16,285	29.175	54.485
1569289	43326551180555358016281479	26	85.163	13804516306606163051 307 × 74923 × 732943 × 818837	2022-05-26	732943	818837	7,728,614	0.0478	0.0966

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1569289

6487440727

32.595

2067
3 × 13 × 53

5.277e-10

9.831e-7

1.714e-6

1569289

126850504772135330679671

76.747

40416553220004515
5 × 19 × 51461 × 8267181017

2017-12-04

51461

8267181017

16,285

29.175

54.485

1569289

43326551180555358016281479

85.163

13804516306606163051
307 × 74923 × 732943 × 818837

2022-05-26

732943

818837

7,728,614

0.0478

0.0966

exponent	prime factors	composite factor	digits	bits*
1569289	6487440727 126850504772135330679671	822935130899258599006910236360817	33	109.342
1569289	6487440727 43326551180555358016281479	281078432689184760072890395960395233	36	117.758
1569289	126850504772135330679671 43326551180555358016281479	5495994887289203087273547129624301898837119113409	49	161.911
1569289	6487440727 126850504772135330679671 43326551180555358016281479	35654941067183750735752545038478644347459360475679 678408343	59	194.506

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:16:27	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 6487440727	-	-	0.084	-	-	4.975%

ECM factoring results:

Old Calculation Method

Total ECM effort:	31.292 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	31.292 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	13.88
50000	5000000	126850504772135330679671	3	0.168
250000	40000000		49	16.90
250000	40000000	43326551180555358016281479	1	0.345

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-04T18:37:08	Chang Chia-Tche	exbpc13	50000	5000000	126850504772135330679671	76.747	3	2		3	0.168
2018-11-13T17:48:22	rucio		50000	5000000						3	0.168
2019-08-19T13:18:32	TJAOI	Manual testing	50000	5000000						245	13.71
2022-05-26T10:14:39	TJAOI	Manual testing	250000	40000000	43326551180555358016281479	85.163	1	2		1	0.345
2022-05-26T10:14:39	TJAOI	Manual testing	250000	40000000						49	16.90

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T22:05:54

Oliver Kruse

GTX-0

6487440727

D00CA4F549B854__

2017-10-31T08:01:31

kkmrkkblmbrbk

old

6487440727

D00CA4F549B854__

2017-12-05T10:19:25

YarBer

Manual testing

6487440727

126850504772135330679671

5212A96F2C4416__

2017-12-05T13:41:10

Oliver Kruse

Threadripper

6487440727

126850504772135330679671

5212A96F2C4416__

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

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