M1866869 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	15.9164	68.6567%	500000	15000000	0.1015	5.0808%	16.0179	70.2492%	1.5925%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0282%	0.0116	64.2735%	1.1156%
GPU72	2⁶¹	0.1645	65.5738%	10000	150000	0.0014	1.6891%	0.1659	66.1553%	0.5815%
Difference	+6	+15.7519	+3.0829%	+490000	+14850000	+0.1001	+3.3917%	+15.8520	+4.0939%	+4.0939%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9164

68.6567%

500000

15000000

0.1015

5.0808%

16.0179

70.2492%

1.5925%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0282%

0.0116

64.2735%

1.1156%

GPU72

2⁶¹

0.1645

65.5738%

10000

150000

0.0014

1.6891%

0.1659

66.1553%

0.5815%

Difference

+15.7519

+3.0829%

+490000

+14850000

+0.1001

+3.3917%

+15.8520

+4.0939%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1866869	102697911301293719	18	56.511	27505387711 17 × 1617963983	-	17	1617963983	0.0058	6.9342	12.951
1866869	2830992842209793999449	22	71.262	758219468588796 2² × 3 × 63184955715733	2020-12-23	4	63184955715733	464.36	270,795	505,770

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1866869

102697911301293719

56.511

27505387711
17 × 1617963983

1617963983

0.0058

6.9342

12.951

1866869

2830992842209793999449

71.262

758219468588796
2² × 3 × 63184955715733

2020-12-23

63184955715733

464.36

270,795

505,770

exponent	prime factors	composite factor	digits	bits*
1866869	102697911301293719 2830992842209793999449	290737051803858829375516463356873160831	39	127.773

exponent

prime factors

composite factor

digits

bits*

1866869

102697911301293719
2830992842209793999449

290737051803858829375516463356873160831

127.773

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:38	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.081%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:38

alpertron

Manual testing

500000

15000000

0.101

-

-

5.081%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.744 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:	19.744 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.796	0.015%
25	50000	0.797	45.076%
30	250000	0.049	95.191%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.284
50000	5000000	2830992842209793999449	12	0.831
50000	6600000		213	16.63

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T21:36:20	Oliver Kruse	ECM-HTC	50000	5000000						3	0.208
2019-01-19T04:37:05	tottenhoff	2011pc	50000	5000000						3	0.208
2020-07-06T14:58:06	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.208
2020-08-08T21:20:28	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.208
2020-10-13T18:23:06	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2020-12-23T02:09:58	MarkS	laptop64	50000	5000000	2830992842209793999449	71.262	12	2	5356145815986903	12	0.831
2021-06-01T19:12:44	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-09-03T08:17:02	TJAOI	Manual testing	50000	6600000						213	16.63
2021-09-03T14:08:13	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T10:30:48

Oliver Kruse

GTX-0

102697911301293719

4A676810478AA1__

2017-11-07T12:33:41

kkmrkkblmbrbk

c4.xlarge

102697911301293719

4A676810478AA1__

2020-12-23T19:24:50

Maciej Kmieciak

Asrock

102697911301293719

2830992842209793999449

4242ADFE5DC0EFE8

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 = 15000000 (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

10¹¹

10¹²

10¹³

10¹⁴

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