M4701589 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	6.3200	65.6716%	-	-	-	-	6.3200	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0653	62.2951%	20000	400000	0.0078	3.1221%	0.0731	63.4723%	1.1772%
GPU72	2⁶⁵	1.5518	64.6154%	30000	600000	0.0117	2.2328%	1.5634	65.4055%	0.7901%
Difference	+2	+4.7682	+1.0563%	-30000	-600000	-0.0117	-2.2328%	+4.7566	+0.2662%	+0.2662%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.3200

65.6716%

6.3200

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0653

62.2951%

20000

400000

0.0078

3.1221%

0.0731

63.4723%

1.1772%

GPU72

2⁶⁵

1.5518

64.6154%

30000

600000

0.0117

2.2328%

1.5634

65.4055%

0.7901%

Difference

+4.7682

+1.0563%

-30000

-600000

-0.0117

-2.2328%

+4.7566

+0.2662%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4701589	112838137	9	26.750	12 2² × 3	-	4	4	1.906e-12	7.637e-7	1.554e-6
4701589	6632435464208129	16	52.558	705339776 2⁷ × 31 × 149 × 1193	2014-08-16	149	1193	0.0002	3.931e-5	5.789e-5
4701589	100240635751994112383	21	66.442	10660293334019 7 × 619 × 2460256943	2020-03-26	619	2460256943	4.9569	25.591	47.796
4701589	64063318785900880229279	23	75.762	6812943324682451 11 × 619358484062041	2019-04-10	11	619358484062041	2,561.4	6,442,360	12,032,535

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4701589

112838137

26.750

12
2² × 3

1.906e-12

7.637e-7

1.554e-6

4701589

6632435464208129

52.558

705339776
2⁷ × 31 × 149 × 1193

2014-08-16

149

1193

0.0002

3.931e-5

5.789e-5

4701589

100240635751994112383

66.442

10660293334019
7 × 619 × 2460256943

2020-03-26

619

2460256943

4.9569

25.591

47.796

4701589

64063318785900880229279

75.762

6812943324682451
11 × 619358484062041

2019-04-10

619358484062041

2,561.4

6,442,360

12,032,535

exponent	prime factors	composite factor	digits	bits*
4701589	112838137 6632435464208129	748391661553975456615673	24	79.308
4701589	112838137 100240635751994112383	11310966589950609676266350471	29	93.192
4701589	112838137 64063318785900880229279	7228785541838157191731975213223	31	102.512
4701589	6632435464208129 100240635751994112383	664839547516295042966637533328161407	36	119.0005
4701589	6632435464208129 64063318785900880229279	424895827470479855697077255051695608991	39	128.320
4701589	100240635751994112383 64063318785900880229279	6421747803481371827954574195200055133061857	43	142.204
4701589	112838137 6632435464208129 100240635751994112383	75019255945661709790690332415025142801178759	44	145.750
4701589	112838137 6632435464208129 64063318785900880229279	47944453590842369412887033805107171209624889767	47	155.070
4701589	112838137 100240635751994112383 64063318785900880229279	72461805842868011127067867281464856351198704964040 9	51	168.954
4701589	6632435464208129 100240635751994112383 64063318785900880229279	42591827874010505123687198910444461811947491547285 679235553	59	194.762
4701589	112838137 6632435464208129 100240635751994112383 64063318785900880229279	48059825087280161165858180958029829128277992880189 63451719384684761	67	221.512

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-16T11:47:00	TJAOI	Manual testing	?	?	6632435464208129	52.558	16	0.000	1.324	0.000
2020-03-26T16:35:03	TJAOI	Manual testing	2⁶⁶	2⁶⁷*	100240635751994112383	66.442	21	1.816	1.259	3.692

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.394 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:	0.394 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	64063318785900880229279	2	0.394

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-04-10T21:26:49	ATH	ec2-ECMCF	50000	5000000	64063318785900880229279	75.762	2	2	4793311948465115	2	0.394

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-18T10:52:13

kkmrkkblmbrbk

c4.xlarge

112838137

6632435464208129

C988150CD0BB01__

2018-03-08T15:46:27

ATH

ec2-1xf

112838137

6632435464208129

C988150CD0BB01__

2019-04-11T16:23:10

Ruzovej

Masa_notebook

112838137

6632435464208129

64063318785900880229279

C988150CD0BB015B

2020-03-28T00:09:51

AbsolutXTR

750D

112838137

6632435464208129

100240635751994112383

64063318785900880229279

C988150CD0BB015B

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

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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