M1822529 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	16.3037	68.6567%	500000	15000000	0.1015	5.0661%	16.4051	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	+16.1351	+3.0829%	+491000	+14870000	+0.1002	+3.5078%	+16.2354	+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

16.3037

68.6567%

500000

15000000

0.1015

5.0661%

16.4051

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

+16.1351

+3.0829%

+491000

+14870000

+0.1002

+3.5078%

+16.2354

+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
1822529	33747240959591	14	44.940	9258355 5 × 1851671	-	5	1851671	2.537e-6	0.0079	0.0148
1822529	911366691439897524761	21	69.627	250028035614220 2² × 5 × 23 × 37² × 397033753	2020-07-04	1369	397033753	86.522	1.7017	3.1781

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1822529

33747240959591

44.940

9258355
5 × 1851671

1851671

2.537e-6

0.0079

0.0148

1822529

911366691439897524761

69.627

250028035614220
2² × 5 × 23 × 37² × 397033753

2020-07-04

1369

397033753

86.522

1.7017

3.1781

exponent	prime factors	composite factor	digits	bits*
1822529	33747240959591 911366691439897524761	30756111338567442149018115322932751	35	114.566

exponent

prime factors

composite factor

digits

bits*

1822529

33747240959591
911366691439897524761

30756111338567442149018115322932751

114.566

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:38:20	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 33747240959591	-	-	0.101	-	-	5.066%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:38:20

alpertron

Manual testing

500000

15000000

skipped known factor: 33747240959591

0.101

-

-

5.066%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.744 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.744 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.812	0.015%
25	50000	0.798	45.010%
30	250000	0.049	95.182%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.554
50000	5000000	911366691439897524761	1	0.069
50000	6600000		220	17.12

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-07-26T07:59:54	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-03T20:03:05	Ismo Laitela	6600K	50000	5000000						3	0.207
2019-10-14T00:38:44	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-05-05T07:14:05	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-09T10:07:50	nordi	sweet16	50000	5000000						3	0.207
2020-07-04T02:08:21	nordi	sweet16	50000	5000000	911366691439897524761	69.627	1	2	3991836479456922	1	0.069
2020-07-17T13:37:09	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-09-07T03:09:24	MarkS	desktop-i7	50000	5000000						7	0.483
2020-11-19T18:59:14	nordi	sweet16	50000	5000000						7	0.483
2021-02-13T09:30:50	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.483
2021-03-26T16:50:38	TJAOI	Manual testing	50000	6600000						220	17.12

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T23:43:34

Oliver Kruse

GTX-0

33747240959591

E3E9A1185366AF__

2017-11-06T01:35:41

kkmrkkblmbrbk

c4.xlarge

33747240959591

E3E9A1185366AF__

2020-07-04T05:43:18

CrypticClue

Manual testing

33747240959591

911366691439897524761

5189CE9B7EB82BA8

2020-07-04T18:14:34

pew

10980xe_1

33747240959591

911366691439897524761

5189CE9B7EB82BA8

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

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