M1840829 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	16.1416	68.6567%	1000000	188329050	0.8815	8.2200%	17.0231	71.2331%	2.5764%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8823%	0.0117	64.2198%	1.0619%
GPU72	2⁶¹	0.1669	65.5738%	9000	140000	0.0013	1.5965%	0.1681	66.1234%	0.5496%
Difference	+6	+15.9747	+3.0829%	+991000	+188189050	+0.8802	+6.6234%	+16.8550	+5.1097%	+5.1097%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1416

68.6567%

1000000

188329050

0.8815

8.2200%

17.0231

71.2331%

2.5764%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8823%

0.0117

64.2198%

1.0619%

GPU72

2⁶¹

0.1669

65.5738%

9000

140000

0.0013

1.5965%

0.1681

66.1234%

0.5496%

Difference

+15.9747

+3.0829%

+991000

+188189050

+0.8802

+6.6234%

+16.8550

+5.1097%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1840829	2234766407	10	31.057	607 607	-	1	607	1.758e-10	2.676e-6	4.833e-6
1840829	47600272292631781944905423	26	85.299	12929031510431382259 28463 × 454239943450493	2020-06-05	28463	454239943450493	6,872,345	1,946,759	3,636,003

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1840829

2234766407

31.057

607
607

607

1.758e-10

2.676e-6

4.833e-6

1840829

47600272292631781944905423

85.299

12929031510431382259
28463 × 454239943450493

2020-06-05

28463

454239943450493

6,872,345

1,946,759

3,636,003

exponent	prime factors	composite factor	digits	bits*
1840829	2234766407 47600272292631781944905423	106375489483626379911023764112525161	36	116.357

exponent

prime factors

composite factor

digits

bits*

1840829

2234766407
47600272292631781944905423

106375489483626379911023764112525161

116.357

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-03T12:48:57	Jocelyn Larouche	Manual testing	1000000	188329050		-	skipped known factor: 2234766407	-	-	0.882	-	-	8.220%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.837 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:	19.837 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.828	0.015%
25	50000	0.800	44.932%
30	250000	0.049	95.171%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.415
50000	5000000	47600272292631781944905423	25	1.728
50000	6600000		220	17.14
50000	6750000		7	0.551

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T11:19:49	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-10T17:10:59	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-05T13:14:41	nordi	sweet16	50000	5000000	47600272292631781944905423	85.299	25	2	8835264633798401	25	1.728
2021-04-10T17:13:19	John Burroughs		50000	6750000						7	0.551
2021-05-21T15:33:05	TJAOI	Manual testing	50000	6600000						220	17.14

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T04:03:59

Oliver Kruse

GTX-3

2234766407

2A240FEB48A7FA__

2017-11-06T17:38:43

kkmrkkblmbrbk

old

2234766407

2A240FEB48A7FA__

2020-06-06T12:09:24

Yuji Hasegawa

vj22m

2234766407

47600272292631781944905423

D5E4DF932A0D41F7

2020-06-07T09:58:26

marssystems

system03

2234766407

47600272292631781944905423

D5E4DF932A0D41F7

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 = 1000000, B2 = 188329050 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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