M4339 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	6,848.1027	80.5970%	1000000000	201000000000	1.0484	16.8259%	6,849.1511	83.8617%	16.3617%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4422%	0.0000	68.2937%	0.7937%
GPU72	2⁴⁴	0.0005	70.4545%	500	10000	0.0000	0.9742%	0.0005	70.7424%	0.2878%
Difference	+23	+6,848.1021	+10.1425%	+999999500	+200999990000	+1.0484	+15.8517%	+6,849.1506	+13.1194%	+13.1194%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6,848.1027

80.5970%

1000000000

201000000000

1.0484

16.8259%

6,849.1511

83.8617%

16.3617%

PrimeNet

2⁴⁰

0.0000

67.5000%

500

10000

0.0000

2.4422%

0.0000

68.2937%

0.7937%

GPU72

2⁴⁴

0.0005

70.4545%

500

10000

0.0000

0.9742%

0.0005

70.7424%

0.2878%

Difference

+23

+6,848.1021

+10.1425%

+999999500

+200999990000

+1.0484

+15.8517%

+6,849.1506

+13.1194%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4339	36055069969873	14	45.035	4154767224 2³ × 3 × 17 × 1811 × 5623	1999-04-02	1811	5623	0.0014	1.779e-7	3.248e-7
4339	31656104144718898310053878501271041700569421852927 688143	56	184.369	36478571266096909783422307560810142545021228224161 89 3 × 21717767 × 9516829981168483 × 5883138672962295756507054883	2020-10-01	9516829981168483	5883138672962295756507054883	4.191e+13	2.825e+16	5.276e+16

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4339

36055069969873

45.035

4154767224
2³ × 3 × 17 × 1811 × 5623

1999-04-02

1811

5623

0.0014

1.779e-7

3.248e-7

4339

31656104144718898310053878501271041700569421852927
688143

184.369

36478571266096909783422307560810142545021228224161
89
3 × 21717767 × 9516829981168483 × 5883138672962295756507054883

2020-10-01

9516829981168483

5883138672962295756507054883

4.191e+13

2.825e+16

5.276e+16

exponent	prime factors	composite factor	digits	bits*
4339	36055069969873 31656104144718898310053878501271041700569421852927 688143	11413630499114265593239280437478292998791568714537 82528770882549315839	70	229.404

exponent

prime factors

composite factor

digits

bits*

4339

36055069969873
31656104144718898310053878501271041700569421852927
688143

11413630499114265593239280437478292998791568714537
82528770882549315839

229.404

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-05T22:58:06	ViliamF	3	1000000000	201000000000		-		-	-	1.048	-	-	16.826%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-07-05T22:58:06

ViliamF

1000000000

201000000000

1.048

-

-

16.826%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-04-02T00:00:00	ANONYMOUS	v4_computers	?	?	36055069969873	45.035	14	0.000	6.17107e-7	0.001
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	36055069969873	45.035	14	0.000	6.17107e-7	0.001

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-04-02T00:00:00

ANONYMOUS

v4_computers

36055069969873

45.035

0.000

6.17107e-7

0.001

2009-10-25T00:00:00

Carsten Kossendey

v4_computers

36055069969873

45.035

0.000

6.17107e-7

0.001

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Curves	Complete	FacMiss
20	11000	1204 / 100	12.040	0.001%
25	50000	1204 / 280	4.300	1.346%
30	250000	1204 / 640	1.881	15.218%
35	1000000	1100 / 1580	0.696	49.836%
40	3000000	1100 / 4700	0.234	79.131%
45	11000000	315 / 9700	0.032	96.805%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	20.529 GHz-days
Estimated T-Level:	33.481

Digits	B1	Complete	FacMiss
20	11000	263.067	0.000%
25	50000	74.344	0.000%
30	250000	17.149	0.000%
35	1000000	3.411	3.301%
40	3000000	0.597	55.058%
45	11000000	0.096	90.886%
50	44000000	0.014	98.606%
55	110000000	0.002	99.807%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		785	2.986
11000000	11000000		104	0.984
11000000	1100000000		114	1.590
44000000	4400000000		200	11.16
110000000	900514153782	31656104144718898310053878501271041700569421852927 688143	1	3.809

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-24T02:01:00	unconnected	E5430-next	44000000	4400000000						200	11.16
2009-10-13T13:41:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2010-06-24T16:26:00	James Hintz	NEW_OMFG	3000000	300000000						784	2.983
2011-01-02T06:47:00	James Hintz	OMFG	11000000	1100000000						3	0.042
2011-01-29T16:03:00	James Hintz	OMFG	11000000	1100000000						11	0.153
2016-10-03T18:21:45	kkmrkkblmbrbk	kel1	11000000	11000000						104	0.984
2020-03-24T12:28:07	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.395
2020-10-01T12:04:37	Ryan Propper	Manual testing	110000000	900514153782	31656104144718898310053878501271041700569421852927 688143	184.369	1	2	846077765664756712	1	3.809

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:51

Oliver Kruse

Oliver-PC

36055069969873

6B17848EB55F79__

2017-09-21T19:21:11

Oliver Kruse

Manual testing

36055069969873

6B17848EB55F79__

2017-10-12T13:52:42

kkmrkkblmbrbk

Manual testing

36055069969873

6B17848EB55F79__

2020-04-17T12:32:23

Oliver Kruse

IOS-1

36055069969873

BBF4A10A4FC9A9__

2020-10-01T15:22:06

mnd9

36055069969873

31656104144718898310053878501271041700569421852927
688143

BBF4A10A4FC9A9F6

2020-10-02T02:23:09

tottenhoff

3-of-4-Ryzen-5-3600

36055069969873

31656104144718898310053878501271041700569421852927
688143

BBF4A10A4FC9A9F6

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 = 1000000000, B2 = 201000000000 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

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