M18 869 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
Actual	unknown	5600000000	16709983434234090	388,328.3485	75.7290%	388,328.3485	75.7290%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.5324%	0.0001	66.4315%
Difference	-44	-0.0001	-65.9091%	+5599999500	+16709983434184090	+388,328.3485	+74.1966%	+388,328.3484	+9.2975%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

5600000000

16709983434234090

388,328.3485

75.7290%

388,328.3485

75.7290%

Target

2⁴⁴

0.0001

65.9091%

500

50000

0.0000

1.5324%

0.0001

66.4315%

Difference

-44

-0.0001

-65.9091%

+5599999500

+16709983434184090

+388,328.3485

+74.1966%

+388,328.3484

+9.2975%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
18869	264167	6	18.011	7 7	-	1	7	1.854e-12	5.660e-10	8.681e-10
18869	62907241961814071	17	55.804	1666946896015 5 × 311 × 653 × 1641641	2008-08-26	653	1641641	0.3697	3.841e-5	7.125e-5
18869	76341280181921928079556543656237759967	38	125.844	2022928617889711380559556512169107 11 × 183902601626337398232686955651737	2017-10-01	11	183902601626337398232686955651737	9.857e+12	4.274e+21	7.982e+21

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

18869

264167

18.011

7
7

1.854e-12

5.660e-10

8.681e-10

18869

62907241961814071

55.804

1666946896015
5 × 311 × 653 × 1641641

2008-08-26

653

1641641

0.3697

3.841e-5

7.125e-5

18869

76341280181921928079556543656237759967

125.844

2022928617889711380559556512169107
11 × 183902601626337398232686955651737

2017-10-01

183902601626337398232686955651737

9.857e+12

4.274e+21

7.982e+21

exponent	prime factors	composite factor	digits	bits*
18869	264167 62907241961814071	16618017387326537693857	23	73.815
18869	264167 76341280181921928079556543656237759967	20166846961817769974992213468037360337202489	44	143.855
18869	62907241961814071 76341280181921928079556543656237759967	48024193840788040500112809152774610482394855047810 95657	55	181.648
18869	264167 62907241961814071 76341280181921928079556543656237759967	12686407214339454294793300455461010527302801673415 07696422719	61	199.659

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 264167	-	-	2.13271e-5	-	-	6.534%
2023-04-18	JacobZ	GreatLakes	5600000000	16709983434234090		-	skipped known factor: 264167 skipped known factor: 62907241961814071	-	-	388,328	-	-	75.729%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06

Lisander Viaene

Manual testing

50000

skipped known factor: 264167

2.13271e-5

-

-

6.534%

2023-04-18

JacobZ

GreatLakes

5600000000

16709983434234090

skipped known factor: 264167
skipped known factor: 62907241961814071

388,328

-

-

75.729%

ECM factoring results:

Total ECM effort:	21.465 GHz-days
Estimated T-Level:	36.195

Digits	B1	Complete	FacMiss
20	11000	422.835	0.000%
25	50000	89.725	0.000%
30	250000	15.004	0.000%
35	1000000	2.066	12.669%
40	3000000	0.239	78.735%
45	11000000	0.024	97.615%
50	44000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
		62907241961814071	1	0.00000e+0
50000	5000000		148	0.045
250000	25000000		571	0.876
1000000	100000000		442	2.713
1000000	100000000	76341280181921928079556543656237759967	979	6.009
3000000	300000000		642	11.82

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			62907241961814071	55.804		1		1	-
2009-04-07	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.015
2009-06-08	unconnected	dual5430	250000	25000000						30	0.046
2009-06-14	Rob_Dee	twopc	50000	5000000						80	0.025
2009-06-28	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-29	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-29	Rob_Dee	twopc	50000	5000000						4	0.001
2009-06-30	Rob_Dee	twopc	50000	5000000						6	0.002
2009-07-12	Rob_Dee	twopc	250000	25000000						10	0.015
2011-04-03	James Hintz	17_051310	250000	25000000						11	0.017
2014-09-18	James Hintz	08_04_2014	250000	25000000						520	0.798
2014-09-18	James Hintz	08_04_2014	1000000	100000000						11	0.068
2017-10-01	kkmrkkblmbrbk	r4.16xlarge-64	1000000	100000000	76341280181921928079556543656237759967	125.844	979	2		979	6.009
2017-10-01	kkmrkkblmbrbk	r4.16xlarge-64	1000000	100000000						431	2.645
2019-09-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-01	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-08	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-12	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-10-15	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-10-29	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-02	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-05	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2019-11-09	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.055
2019-11-12	Niels_Mache_Nextcloud	SuperDry-Y	3000000	300000000						3	0.055
2020-06-26	James Hintz	work_lappy_5_16_2019	3000000	300000000						100	1.841
2022-02-22	nordi	sweet16_ccx2	3000000	300000000						500	9.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

264167

62907241961814071

0DDDF3BC8AA7CE__

2017-09-21

Oliver Kruse

Manual testing

264167

62907241961814071

0DDDF3BC8AA7CE__

2017-10-01

Oliver Kruse

GTX-3

264167

62907241961814071

76341280181921928079556543656237759967

22DA446EA6939A1B

2017-10-02

kkmrkkblmbrbk

Manual testing

264167

62907241961814071

76341280181921928079556543656237759967

22DA446EA6939A__

2017-10-09

Chang Chia-Tche

homura

22DA446EA6939A__

2017-10-13

Oliver Kruse

Threadripper

22DA446EA6939A__

2020-04-17

Oliver Kruse

Manual testing

264167

62907241961814071

76341280181921928079556543656237759967

2F8748A52CA60B__

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 = 5600000000, B2 = 16709983434234090 (P-1 stage 2)

B1 = 5600000000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

10²⁹

10³⁰

10³¹

10³²

10³³

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