M1848281 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	16.0765	68.6567%	500000	2835864570	12.1910	10.3827%	28.2675	71.9110%	3.2543%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0226%	0.0117	64.2715%	1.1136%
GPU72	2⁶¹	0.1662	65.5738%	9000	150000	0.0013	1.6306%	0.1675	66.1351%	0.5614%
Difference	+6	+15.9103	+3.0829%	+491000	+2835714570	+12.1897	+8.7521%	+28.1000	+5.7759%	+5.7759%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0765

68.6567%

500000

2835864570

12.1910

10.3827%

28.2675

71.9110%

3.2543%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0226%

0.0117

64.2715%

1.1136%

GPU72

2⁶¹

0.1662

65.5738%

9000

150000

0.0013

1.6306%

0.1675

66.1351%

0.5614%

Difference

+15.9103

+3.0829%

+491000

+2835714570

+12.1897

+8.7521%

+28.1000

+5.7759%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1848281	14786249	8	23.818	4 2²	-	4	4	6.051e-13	3.146e-7	6.404e-7
1848281	166600469242115255407	21	67.175	45069031506063 3 × 79 × 653 × 291216983	2020-07-06	653	291216983	27.219	1.2481	2.3311

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1848281

14786249

23.818

4
2²

6.051e-13

3.146e-7

6.404e-7

1848281

166600469242115255407

67.175

45069031506063
3 × 79 × 653 × 291216983

2020-07-06

653

291216983

27.219

1.2481

2.3311

exponent	prime factors	composite factor	digits	bits*
1848281	14786249 166600469242115255407	2463396021730757453146498343	28	90.993

exponent

prime factors

composite factor

digits

bits*

1848281

14786249
166600469242115255407

2463396021730757453146498343

90.993

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-11T18:11:50	Lisander Viaene	Desktop	500000	2835864570		-	skipped known factor: 14786249 skipped known factor: 166600469242115255407	-	-	12.19	-	-	10.383%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.261 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:	19.261 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.577	0.019%
25	50000	0.777	45.976%
30	250000	0.048	95.307%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.282
50000	5000000	166600469242115255407	2	0.138
50000	6600000		216	16.84

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-16T06:58:51	ATH	ec2-1xe	50000	5000000						3	0.207
2019-01-15T01:08:12	tottenhoff	i3-8100-01	50000	5000000						3	0.207
2020-06-12T13:25:02	nordi	sweet16	50000	5000000						3	0.207
2020-07-06T20:40:05	Chang Chia-Tche	exbpc13	50000	5000000	166600469242115255407	67.175	2	2		2	0.138
2020-07-25T12:58:20	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-10-02T02:37:13	nordi	sweet16	50000	5000000						7	0.484
2020-11-30T05:21:49	nordi	sweet16	50000	5000000						7	0.484
2021-02-27T06:04:20	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.484
2021-06-11T13:32:21	TJAOI	Manual testing	50000	6600000						216	16.84

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T05:45:09

Oliver Kruse

GTX-3

14786249

7B26336DEFB856__

2017-11-06T21:21:12

kkmrkkblmbrbk

c4.xlarge

14786249

7B26336DEFB856__

2020-07-07T18:55:55

mnd9

50871

14786249

166600469242115255407

8F2340C0DACD016F

2020-07-07T20:28:14

atrench

Desktop

14786249

166600469242115255407

8F2340C0DACD016F

2020-07-09T19:25:43

nordi

sweet16

14786249

166600469242115255407

8F2340C0DACD016F

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 = 2835864570 (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

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