M1841701 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	16.1340	68.6567%	1000000	188329050	0.8815	8.2204%	17.0155	71.2332%	2.5765%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8826%	0.0117	64.2199%	1.0620%
GPU72	2⁶¹	0.1668	65.5738%	9000	140000	0.0013	1.5967%	0.1681	66.1234%	0.5497%
Difference	+6	+15.9672	+3.0829%	+991000	+188189050	+0.8802	+6.6237%	+16.8474	+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

16.1340

68.6567%

1000000

188329050

0.8815

8.2204%

17.0155

71.2332%

2.5765%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8826%

0.0117

64.2199%

1.0620%

GPU72

2⁶¹

0.1668

65.5738%

9000

140000

0.0013

1.5967%

0.1681

66.1234%

0.5497%

Difference

+15.9672

+3.0829%

+991000

+188189050

+0.8802

+6.6237%

+16.8474

+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
1841701	3509468074159	13	41.674	952779 3 × 317593	-	3	317593	1.955e-7	0.0014	0.0025
1841701	7561125612558229009561	22	72.679	2052756015378780 2² × 3 × 5 × 193 × 283 × 626386427	2020-06-24	283	626386427	633.93	2.6846	5.0140

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1841701

3509468074159

41.674

952779
3 × 317593

317593

1.955e-7

0.0014

0.0025

1841701

7561125612558229009561

72.679

2052756015378780
2² × 3 × 5 × 193 × 283 × 626386427

2020-06-24

283

626386427

633.93

2.6846

5.0140

exponent	prime factors	composite factor	digits	bits*
1841701	3509468074159 7561125612558229009561	26535528941979017147431728668034199	35	114.353

exponent

prime factors

composite factor

digits

bits*

1841701

3509468074159
7561125612558229009561

26535528941979017147431728668034199

114.353

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-03T12:49:02	Jocelyn Larouche	Manual testing	1000000	188329050		-	skipped known factor: 3509468074159	-	-	0.882	-	-	8.220%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.195 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:	18.195 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.310	0.025%
25	50000	0.752	47.147%
30	250000	0.046	95.466%
35	1000000	0.002	99.787%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.415
50000	5000000	7561125612558229009561	149	10.30
50000	6600000		96	7.481

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T04:10:55	alpertron		50000	5000000						3	0.207
2018-09-28T16:54:55	alpertron	Manual testing	50000	5000000						3	0.207
2020-06-24T16:32:56	nordi	sweet16	50000	5000000	7561125612558229009561	72.679	149	2	7229338112899895	149	10.30
2021-06-18T16:47:10	TJAOI	Manual testing	50000	6600000						96	7.481

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T04:03:54

Oliver Kruse

GTX-2

3509468074159

4EC0F58BEB765F__

2017-11-11T01:38:15

kkmrkkblmbrbk

c4.xlarge

3509468074159

4EC0F58BEB765F__

2020-06-25T05:03:10

atrench

Desktop

3509468074159

7561125612558229009561

78DDFC48AD65BFDB

2020-06-27T05:12:45

oodaira

com1

3509468074159

7561125612558229009561

78DDFC48AD65BFDB

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

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