M1822517 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	16.3038	68.6567%	500000	15000000	0.1015	5.0661%	16.4053	70.2446%	1.5879%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8769%	0.0118	64.2178%	1.0599%
GPU72	2⁶¹	0.1685	65.5738%	9000	130000	0.0012	1.5583%	0.1698	66.1102%	0.5365%
Difference	+6	+16.1352	+3.0829%	+491000	+14870000	+0.1002	+3.5078%	+16.2355	+4.1343%	+4.1343%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3038

68.6567%

500000

15000000

0.1015

5.0661%

16.4053

70.2446%

1.5879%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8769%

0.0118

64.2178%

1.0599%

GPU72

2⁶¹

0.1685

65.5738%

9000

130000

0.0012

1.5583%

0.1698

66.1102%

0.5365%

Difference

+16.1352

+3.0829%

+491000

+14870000

+0.1002

+3.5078%

+16.2355

+4.1343%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1822517	142156327	9	27.083	39 3 × 13	-	3	13	9.894e-12	2.788e-7	4.803e-7
1822517	3586713457	10	31.740	984 2³ × 3 × 41	2008-07-15	8	41	1.904e-10	7.707e-7	1.281e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1822517

142156327

27.083

39
3 × 13

9.894e-12

2.788e-7

4.803e-7

1822517

3586713457

31.740

984
2³ × 3 × 41

2008-07-15

1.904e-10

7.707e-7

1.281e-6

exponent	prime factors	composite factor	digits	bits*
1822517	142156327 3586713457	509874011048592439	18	58.823

exponent

prime factors

composite factor

digits

bits*

1822517

142156327
3586713457

509874011048592439

58.823

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:38:20	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 142156327 skipped known factor: 3586713457	-	-	0.101	-	-	5.066%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	3586713457	31.740	10	3.34330e-11	0.212	7.15581e-11

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

3586713457

31.740

3.34330e-11

0.212

7.15581e-11

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.266 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.266 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	10.913	0.002%
25	50000	1.004	36.632%
30	250000	0.064	93.827%
35	1000000	0.003	99.701%

ECM Summary

B1	B2	curves	GHz-days
50000	4850000	7	0.477
50000	5000000	33	2.278
50000	6600000	225	17.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-26T07:59:52	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-04T18:11:39	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-10-13T23:25:56	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-05T06:13:48	Greg Hogan	azure	50000	5000000						3	0.207
2020-06-09T07:57:29	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-07-04T01:07:06	nordi	sweet16	50000	5000000						3	0.207
2020-08-05T06:58:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-10-11T18:22:30	nordi	sweet16	50000	5000000						7	0.483
2020-12-11T20:35:36	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-03-16T08:09:30	Ducho_YYZ	Dutch	50000	4850000						7	0.477
2021-03-19T18:35:20	TJAOI	Manual testing	50000	6600000						225	17.51

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

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