M3089027 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	2⁶⁸	19.2957	67.6471%	1050000	116447100	0.9055	7.4866%	20.2012	70.0692%	2.4221%
PrimeNet	2⁶⁰	0.0497	63.3333%	12000	220000	0.0029	2.5287%	0.0526	64.2605%	0.9272%
GPU72	2⁶⁴	1.1522	65.6250%	14000	240000	0.0032	1.5061%	1.1555	66.1427%	0.5177%
Difference	+4	+18.1434	+2.0221%	+1036000	+116207100	+0.9022	+5.9805%	+19.0457	+3.9265%	+3.9265%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.2957

67.6471%

1050000

116447100

0.9055

7.4866%

20.2012

70.0692%

2.4221%

PrimeNet

2⁶⁰

0.0497

63.3333%

12000

220000

0.0029

2.5287%

0.0526

64.2605%

0.9272%

GPU72

2⁶⁴

1.1522

65.6250%

14000

240000

0.0032

1.5061%

1.1555

66.1427%

0.5177%

Difference

+18.1434

+2.0221%

+1036000

+116207100

+0.9022

+5.9805%

+19.0457

+3.9265%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3089027	895817831	9	29.739	145 5 × 29	-	5	29	2.388e-11	7.784e-7	1.256e-6
3089027	65113513442546273	17	55.854	10539485968 2⁴ × 11 × 59883443	2015-07-21	16	59883443	0.0016	0.4026	0.7520
3089027	5035443497805617585383	22	72.093	815053331972433 3 × 604787 × 449223353	2018-07-12	604787	449223353	589.28	3.0910	5.6414

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3089027

895817831

29.739

145
5 × 29

2.388e-11

7.784e-7

1.256e-6

3089027

65113513442546273

55.854

10539485968
2⁴ × 11 × 59883443

2015-07-21

59883443

0.0016

0.4026

0.7520

3089027

5035443497805617585383

72.093

815053331972433
3 × 604787 × 449223353

2018-07-12

604787

449223353

589.28

3.0910

5.6414

exponent	prime factors	composite factor	digits	bits*
3089027	895817831 65113513442546273	58329846380891145395993863	26	85.592
3089027	895817831 5035443497805617585383	4510840072327281604953256364273	31	101.831
3089027	65113513442546273 5035443497805617585383	327875417883548304974824321353505927559	39	127.946
3089027	895817831 65113513442546273 5035443497805617585383	293716645686658853146273633160944664271546504529	48	157.685

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-07T11:57:36	Jocelyn Larouche	Manual testing	1050000	116447100		-	skipped known factor: 895817831 skipped known factor: 65113513442546273	-	-	0.905	-	-	7.487%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-02-19T12:03:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	65113513442546273	55.854	17	2.95960e-5	0.581	6.53631e-5
2022-03-15T22:34:36	LordJulius	Manual testing	2¹	2⁶²	65113513442546273	55.854	17	0.002	0.581	0.003
2022-03-15T22:34:36	LordJulius	Manual testing	2¹	2⁶²	895817831	29.739	9	2.38799e-11	0.584	5.30214e-11
2022-03-15T22:34:36	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.318	-	-
2022-03-15T22:34:36	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.636	-	-
2022-03-15T22:34:36	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.210	-	-
2022-03-15T22:34:36	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.419	-	-
2022-03-15T22:34:36	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.838	-	-
2021-06-20T23:51:56	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.68	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.233 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.233 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	5035443497805617585383	2	0.233

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-13T03:06:49	ATH	ec2-ECMCF	50000	5000000	5035443497805617585383	72.093	2	2		2	0.233

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T09:42:15

Oliver Kruse

GTX-0

895817831

65113513442546273

964060521D7D98__

2017-12-11T09:17:38

ATH

ec2-1xf

895817831

65113513442546273

964060521D7D98__

2018-07-15T01:34:26

Martin Russell

ThunderChoad

895817831

65113513442546273

5035443497805617585383

964060521D7D98__

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 = 1050000, B2 = 116447100 (P-1 stage 2)

B1 = 1050000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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