M1841447 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	16.1362	68.6567%	1000000	188329050	0.8815	8.2202%	17.0177	71.2332%	2.5765%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8825%	0.0117	64.2199%	1.0620%
GPU72	2⁶¹	0.1668	65.5738%	9000	140000	0.0013	1.5966%	0.1681	66.1234%	0.5497%
Difference	+6	+15.9694	+3.0829%	+991000	+188189050	+0.8802	+6.6236%	+16.8496	+5.1098%	+5.1098%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1362

68.6567%

1000000

188329050

0.8815

8.2202%

17.0177

71.2332%

2.5765%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8825%

0.0117

64.2199%

1.0620%

GPU72

2⁶¹

0.1668

65.5738%

9000

140000

0.0013

1.5966%

0.1681

66.1234%

0.5497%

Difference

+15.9694

+3.0829%

+991000

+188189050

+0.8802

+6.6236%

+16.8496

+5.1098%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1841447	2975778353	10	31.471	808 2³ × 101	-	8	101	1.825e-10	1.028e-6	1.281e-6
1841447	1607066314344700749833263	25	80.411	436359643895453073 3 × 883 × 43891 × 3753074147	2020-06-17	43891	3753074147	158,102	16.088	30.042

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1841447

2975778353

31.471

808
2³ × 101

101

1.825e-10

1.028e-6

1.281e-6

1841447

1607066314344700749833263

80.411

436359643895453073
3 × 883 × 43891 × 3753074147

2020-06-17

43891

3753074147

158,102

16.088

30.042

exponent	prime factors	composite factor	digits	bits*
1841447	2975778353 1607066314344700749833263	4782273150062453871616692394755839	34	111.881

exponent

prime factors

composite factor

digits

bits*

1841447

2975778353
1607066314344700749833263

4782273150062453871616692394755839

111.881

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-03T12:49:00	Jocelyn Larouche	Manual testing	1000000	188329050		-	skipped known factor: 2975778353	-	-	0.882	-	-	8.220%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.696 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.696 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.437	0.022%
25	50000	0.764	46.587%
30	250000	0.047	95.390%
35	1000000	0.002	99.783%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.415
50000	5000000	1607066314344700749833263	92	6.359
50000	6600000		153	11.92

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T15:29:00	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-11T18:19:02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-17T13:44:46	nordi	sweet16	50000	5000000	1607066314344700749833263	80.411	92	2	5689872255894939	92	6.359
2021-07-09T11:24:22	TJAOI	Manual testing	50000	6600000						153	11.92

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T04:06:13

Oliver Kruse

GTX-2

2975778353

6DE34F4D5A5EDF__

2017-11-06T13:40:51

kkmrkkblmbrbk

c4.xlarge

2975778353

6DE34F4D5A5EDF__

2020-06-18T11:46:06

mnd9

mnd

2975778353

1607066314344700749833263

ED42457AD4C75200

2020-06-20T01:08:36

AbsolutXTR

750D

2975778353

1607066314344700749833263

ED42457AD4C75200

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

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