M6736739 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	2⁶³	0.2369	63.4921%	-	-	-	-	0.2369	63.4921%	0.0000%
PrimeNet	2⁶³	0.2369	63.4921%	28000	700000	0.0204	3.1462%	0.2573	66.6383%	3.1462%
GPU72	2⁶⁷	4.4107	65.6716%	40000	900000	0.0275	2.1659%	4.4382	67.8375%	2.1659%
Difference	-4	-4.1738	-2.1796%	-40000	-900000	-0.0275	-2.1659%	-4.2013	-4.3454%	-4.3454%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶³

0.2369

63.4921%

0.2369

63.4921%

0.0000%

PrimeNet

2⁶³

0.2369

63.4921%

28000

700000

0.0204

3.1462%

0.2573

66.6383%

3.1462%

GPU72

2⁶⁷

4.4107

65.6716%

40000

900000

0.0275

2.1659%

4.4382

67.8375%

2.1659%

Difference

-4

-4.1738

-2.1796%

-40000

-900000

-0.0275

-2.1659%

-4.2013

-4.3454%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
6736739	13473479	8	23.684	1 1	1	1	-	1.659e-13	3.162e-7	6.435e-7
6736739	279668982847	12	38.025	20757 3 × 11 × 17 × 37	17	37	2008-09-08	8.115e-9	5.720e-6	1.094e-5
6736739	270339475107071	15	47.942	20064565 5 × 787 × 5099	787	5099	2014-03-21	5.509e-6	0.0003	0.0005
6736739	771286490035159489	18	59.420	57244795296 2⁵ × 3 × 13 × 47 × 975941	47	975941	2015-11-19	0.0152	0.0168	0.0314

GHz-days

exponent

factor

digits

bits*

min B1

min B2

date found

min. TF

min. P-1

normal P-1

6736739

13473479

23.684

1
1

1.659e-13

3.162e-7

6.435e-7

6736739

279668982847

38.025

20757
3 × 11 × 17 × 37

2008-09-08

8.115e-9

5.720e-6

1.094e-5

6736739

270339475107071

47.942

20064565
5 × 787 × 5099

787

5099

2014-03-21

5.509e-6

0.0003

0.0005

6736739

771286490035159489

59.420

57244795296
2⁵ × 3 × 13 × 47 × 975941

975941

2015-11-19

0.0152

0.0168

0.0314

exponent	prime factors	composite factor	digits	bits*
6736739	13473479 279668982847	3768114167340414713	19	61.709
6736739	13473479 270339475107071	3642413240726143870009	22	71.625
6736739	13473479 771286490035159489	10391912326472430636692231	26	83.104
6736739	279668982847 270339475107071	75605566026586422987411137	26	85.967
6736739	279668982847 771286490035159489	215704908151765855556050285183	30	97.445
6736739	270339475107071 771286490035159489	208509184873280163572082836646719	33	107.362
6736739	13473479 279668982847 270339475107071	1018670006142325611806001218735623	34	109.650
6736739	13473479 279668982847 771286490035159489	2906295550179746067751476840357161657	37	121.129
6736739	13473479 270339475107071 771286490035159489	2809344123697257945005023085819998865401	40	131.045
6736739	279668982847 270339475107071 771286490035159489	58313551647767341934666189090214359009828993	44	145.387
6736739	13473479 279668982847 270339475107071 771286490035159489	78568641354160867844254427071703227161739173077664 7	51	169.070

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T02:55:00	Will Edgington	Manual testing	?	?	279668982847	38.025	12	2.67901e-9	3.220	5.87307e-9
2014-03-21T11:53:00	TJAOI	Manual testing	?	?	270339475107071	47.942	15	2.72584e-6	3.220	5.97571e-6
2015-11-19T12:27:04	TJAOI	Manual testing	2⁵⁹	2⁶⁰	771286490035159489	59.420	18	0.004	3.198	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-17T06:09:31

kkmrkkblmbrbk

c4.xlarge

13473479

279668982847

270339475107071

771286490035159489

DC26915D4EE18B__

2018-12-08T09:34:52

Oliver Kruse

GTX-7

13473479

279668982847

270339475107071

771286490035159489

DC26915D4EE18B61

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

10⁰

10¹

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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	<	123M	PrimeNet wavefront