M1575083 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	18.8650	68.6567%	500000	15000000	0.0835	4.9777%	18.9485	70.2169%	1.5602%
PrimeNet	2⁵⁷	0.0122	63.1579%	7000	110000	0.0008	2.4791%	0.0130	64.0712%	0.9133%
GPU72	2⁶¹	0.1950	65.5738%	6500	60000	0.0006	1.0527%	0.1956	65.9362%	0.3624%
Difference	+6	+18.6700	+3.0829%	+493500	+14940000	+0.0829	+3.9250%	+18.7529	+4.2807%	+4.2807%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.8650

68.6567%

500000

15000000

0.0835

4.9777%

18.9485

70.2169%

1.5602%

PrimeNet

2⁵⁷

0.0122

63.1579%

7000

110000

0.0008

2.4791%

0.0130

64.0712%

0.9133%

GPU72

2⁶¹

0.1950

65.5738%

6500

60000

0.0006

1.0527%

0.1956

65.9362%

0.3624%

Difference

+18.6700

+3.0829%

+493500

+14940000

+0.0829

+3.9250%

+18.7529

+4.2807%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1575083	3150167	7	21.587	1 1	-	1	1	1.774e-13	6.477e-8	1.318e-7
1575083	885604230227911	15	49.654	281129385 3 × 5 × 1901 × 9859	2014-05-08	1901	9859	7.219e-5	0.0002	0.0003
1575083	94544808593761468177	20	66.358	30012643331736 2³ × 3 × 13 × 96194369653	2018-11-15	13	96194369653	13.147	339.44	633.98

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1575083

3150167

21.587

1
1

1.774e-13

6.477e-8

1.318e-7

1575083

885604230227911

49.654

281129385
3 × 5 × 1901 × 9859

2014-05-08

1901

9859

7.219e-5

0.0002

0.0003

1575083

94544808593761468177

66.358

30012643331736
2³ × 3 × 13 × 96194369653

2018-11-15

96194369653

13.147

339.44

633.98

exponent	prime factors	composite factor	digits	bits*
1575083	3150167 885604230227911	2789801221124367711137	22	71.241
1575083	3150167 94544808593761468177	297831936053383782922735559	27	87.945
1575083	885604230227911 94544808593761468177	83729282436723309699974358683688247	35	116.011
1575083	3150167 885604230227911 94544808593761468177	263761222465845358347639125571518153987249	42	137.598

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:16:33	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3150167 skipped known factor: 885604230227911	-	-	0.084	-	-	4.978%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-05-08T12:16:00	TJAOI	Manual testing	?	?	885604230227911	49.654	15	2.45797e-5	0.155	5.41461e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	31.305 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:	31.305 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		250	13.99
50000	5000000	94544808593761468177	1	0.056
250000	40000000		50	17.25

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-05T05:02:32	ATH	ec2-1xe	50000	5000000						3	0.168
2018-11-15T05:47:45	MarkS	laptop64	50000	5000000	94544808593761468177	66.358	1	2		1	0.056
2019-01-20T07:03:07	tottenhoff	i7-8700k-01	50000	5000000						3	0.168
2019-08-09T10:55:38	TJAOI	Manual testing	50000	5000000						244	13.66
2022-05-05T09:31:46	TJAOI	Manual testing	250000	40000000						50	17.25

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T23:07:09

Oliver Kruse

GTX-1

3150167

885604230227911

B0ECF0827DEE7E__

2017-10-31T09:34:00

kkmrkkblmbrbk

c4.xlarge

3150167

885604230227911

B0ECF0827DEE7E__

2018-11-15T05:57:33

ATH

ec2-PRPCF

3150167

885604230227911

94544808593761468177

457F1A09ACD316__

2018-11-18T11:32:56

Chang Chia-Tche

exbpc13

3150167

885604230227911

94544808593761468177

457F1A09ACD316__

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

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