M27067 Mersenne number exponent details

is 2 ²⁷⁰⁶⁷ - 1

has 8148 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	1,097.7913	77.6119%	500000000	10000000000	0.6681	13.6065%	1,098.4594	80.6582%	3.0462%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.9970%	0.0000	63.9989%	1.4989%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7061%	0.0001	66.4907%	0.5816%
Difference	+23	+1,097.7912	+11.7028%	+499999500	+9999990000	+0.6681	+11.9004%	+1,098.4593	+14.1675%	+14.1675%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27067	898604532823	12	39.709	16599633 3 × 17 × 167 × 1949	-	167	1949	5.396e-6	1.734e-7	2.231e-7
27067	72726237038951	14	46.048	1343448425 5² × 11 × 227 × 21521	2008-08-26	227	21521	0.0006	9.107e-7	1.438e-6
27067	559863370256975086095817920861703	33	108.787	10342176271049157388994308953 3 × 97 × 1283 × 27700798630382392505201	2018-04-27	1283	27700798630382392505201	6.885e+12	9.908e+11	1.851e+12
27067	15021033803699159980877285173903129	35	113.533	277478734320374625575004344292 2² × 3⁶ × 13 × 19 × 84648023 × 4551226113078577	2018-04-26	84648023	4551226113078577	5.273e+12	162,795	304,055

exponent	prime factors	composite factor	digits	bits*
27067	898604532823 72726237038951	65352126258361322208988673	26	85.756
27067	898604532823 559863370256975086095817920861703	503095762274479370698282665790001809907177569	45	148.496
27067	898604532823 15021033803699159980877285173903129	13497969063691574343853770457387765546502903167	47	153.241
27067	72726237038951 559863370256975086095817920861703	40716756174734759149379295399953660437095193553	47	154.834
27067	72726237038951 15021033803699159980877285173903129	1092423264977920873158082889889016309504273777679	49	159.580
27067	898604532823 72726237038951 559863370256975086095817920861703	36588261660465528801367406613304271972924704381872 326490119	59	194.543
27067	898604532823 72726237038951 15021033803699159980877285173903129	98165649767046092363407931589502925112111551271312 7160257817	60	199.289
27067	559863370256975086095817920861703 15021033803699159980877285173903129	84097266100829616280168754163899522753588900240562 29368479527968687	67	222.319
27067	898604532823 559863370256975086095817920861703 15021033803699159980877285173903129	75570184516227512150163398415052866615901412247268 83223145478552141543807713401	79	262.028
27067	72726237038951 559863370256975086095817920861703 15021033803699159980877285173903129	61160777087766731821040255990473466794024492702395 3163705416670830505434727327337	81	268.367
27067	898604532823 72726237038951 559863370256975086095817920861703 15021033803699159980877285173903129	54959351522044266516447407276195736767021582832855 5160402138787086202307590112502056281682351	93	308.076

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-12-22T01:05:42	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 898604532823 skipped known factor: 72726237038951	-	-	0.668	-	-	13.607%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-02T00:00:00	ANONYMOUS	v4_computers	?	?	72726237038951	46.048	14	0.000	2.51787e-5	0.000
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	72726237038951	46.048	14	0.000	2.51787e-5	0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.788 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1303 / 100	13.030	0.000%
25	50000	1303 / 280	4.654	0.945%
30	250000	1113 / 640	1.739	17.545%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	15.788 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	157.906	0.000%
25	50000	31.938	0.000%
30	250000	5.496	0.410%
35	1000000	0.796	45.098%
40	3000000	0.098	90.626%
45	11000000	0.011	98.945%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		189	0.089
200000	20000000		1	0.002
250000	25000000		602	1.422
1000000	100000000		11	0.104
3000000	300000000		33	0.935
3000000	300000000	559863370256975086095817920861703	161	4.563
3000000	300000000	15021033803699159980877285173903129	306	8.673

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06T12:37:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.014
2009-05-10T17:31:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.071
2010-04-18T18:47:00	James Hintz	10_122109	50000	5000000						3	0.001
2010-04-19T03:33:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-19T23:35:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-20T18:32:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-21T13:05:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-21T17:45:00	James Hintz	14_091909	50000	5000000						11	0.005
2010-04-21T21:52:00	James Hintz	14_091909	50000	5000000						11	0.005
2010-04-22T02:14:00	James Hintz	14_091909	50000	5000000						11	0.005
2010-04-22T06:35:00	James Hintz	14_091909	50000	5000000						11	0.005
2010-04-22T08:17:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-22T10:57:00	James Hintz	14_091909	50000	5000000						11	0.005
2010-04-23T05:25:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-23T23:46:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-24T18:45:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-25T13:52:00	James Hintz	10_122109	50000	5000000						11	0.005
2010-04-28T22:55:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-04-29T16:16:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-04-29T18:28:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-04-29T20:58:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-05T15:23:00	Rob_Dee	twopc	200000	20000000						1	0.002
2010-05-05T18:53:00	Rob_Dee	twopc	50000	5000000						1	0.000
2010-05-05T21:47:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-06T15:48:00	Rob_Dee	twopc	250000	25000000						1	0.002
2010-05-07T15:20:00	Rob_Dee	twopc	250000	25000000						1	0.002
2011-03-21T03:34:00	James Hintz	17_051310	250000	25000000						11	0.026
2014-11-09T14:28:00	James Hintz	08_04_2014	250000	25000000						555	1.311
2014-11-09T14:50:00	James Hintz	08_04_2014	1000000	100000000						11	0.104
2018-04-26T19:20:02	nordi	nordiputer	3000000	300000000	15021033803699159980877285173903129	113.533	306	2		306	8.673
2018-04-27T10:21:25	nordi	nordiputer	3000000	300000000	559863370256975086095817920861703	108.787	161	2		161	4.563
2018-04-27T20:53:50	nordi	nordiputer	3000000	300000000						33	0.935

Lucas-Lehmer results:
No L-L results for M27067

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:36:47

Oliver Kruse

Ollaptop

898604532823

72726237038951

78D7916CA0FCF6__

2017-09-21T20:27:15

Oliver Kruse

Manual testing

898604532823

72726237038951

78D7916CA0FCF6__

2017-10-12T16:30:04

kkmrkkblmbrbk

Manual testing

898604532823

72726237038951

78D7916CA0FCF6__

2018-04-28T16:31:55

Oliver Kruse

GTX-5

898604532823

72726237038951

15021033803699159980877285173903129

84DE477A0BB838__

2018-04-29T01:33:50

ANONYMOUS

dory

898604532823

72726237038951

559863370256975086095817920861703

15021033803699159980877285173903129

84DE477A0BB838__

2018-04-29T11:30:48

Oliver Kruse

GTX-0

898604532823

72726237038951

559863370256975086095817920861703

15021033803699159980877285173903129

84DE477A0BB838__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10¹

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10³

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10⁸

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10¹⁰

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10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

TF factor-bounds graph:

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2018-04-29T11:30:48+00:00

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