M28 429 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
Actual	unknown	3000000000	925584566816910	40,279.8493	70.9023%	40,279.8493	70.9023%
Target	2⁴⁴	0.0001	65.9091%	500	80000	0.0000	1.7310%	0.0001	66.4992%
Difference	-44	-0.0001	-65.9091%	+2999999500	+925584566736910	+40,279.8493	+69.1713%	+40,279.8492	+4.4031%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

3000000000

925584566816910

40,279.8493

70.9023%

40,279.8493

70.9023%

Target

2⁴⁴

0.0001

65.9091%

500

80000

0.0000

1.7310%

0.0001

66.4992%

Difference

-44

-0.0001

-65.9091%

+2999999500

+925584566736910

+40,279.8493

+69.1713%

+40,279.8492

+4.4031%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
28429	1223044950568481	16	50.119	21510516560 2⁴ × 5 × 13 × 2089 × 9901	2014-04-23	2089	9901	0.0104	2.008e-6	3.396e-6
28429	10884458649339538001	20	63.239	191432316461000 2³ × 5³ × 423299 × 452239	2008-08-26	423299	452239	94.109	0.0003	0.0007

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

28429

1223044950568481

50.119

21510516560
2⁴ × 5 × 13 × 2089 × 9901

2014-04-23

2089

9901

0.0104

2.008e-6

3.396e-6

28429

10884458649339538001

63.239

191432316461000
2³ × 5³ × 423299 × 452239

2008-08-26

423299

452239

94.109

0.0003

0.0007

exponent	prime factors	composite factor	digits	bits*
28429	1223044950568481 10884458649339538001	13312182190746150724891334852346481	35	113.358

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-12-28	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 1223044950568481 skipped known factor: 10884458649339538001	-	-	0.813	-	-	42.829%
2022-10-13	nordi	sweet16_ccx3	3000000000	3000000000		-	skipped known factor: 1223044950568481 skipped known factor: 10884458649339538001	-	-	2.396	-	-	36.676%
2023-02-18	nordi	sweet16_30.8b14	3000000000	925584566816910		-	skipped known factor: 1223044950568481 skipped known factor: 10884458649339538001	-	-	40,280	-	-	70.902%

ECM factoring results:

Total ECM effort:	22.835 GHz-days
Estimated T-Level:	35.692

Digits	B1	Complete	FacMiss
20	11000	183.414	0.000%
25	50000	41.385	0.000%
30	250000	7.378	0.063%
35	1000000	1.099	33.319%
40	3000000	0.138	87.078%
45	11000000	0.015	98.482%
50	44000000	0.001	99.854%

ECM Summary

B1	B2	factor	curves	GHz-days
		10884458649339538001	1	0.00000e+0
50000	5000000		164	0.094
250000	25000000		608	1.747
1000000	100000000		11	0.126
3000000	300000000		500	17.24
3000000	348000000		100	3.627

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			10884458649339538001	63.239		1		1	-
2009-04-04	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2010-04-18	James Hintz	10_122109	50000	5000000						3	0.002
2010-04-19	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-20	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-21	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-22	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-23	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-24	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-25	James Hintz	14_091909	50000	5000000						32	0.018
2010-04-25	James Hintz	10_122109	50000	5000000						11	0.006
2010-04-26	James Hintz	10_122109	50000	5000000						11	0.006
2011-03-20	James Hintz	17_051310	250000	25000000						11	0.032
2014-11-19	James Hintz	08_04_2014	250000	25000000						567	1.629
2014-11-19	James Hintz	08_04_2014	1000000	100000000						11	0.126
2018-02-13	nordi	nordiputer	3000000	300000000						500	17.24
2022-09-19	nordi	sweet16_ccx3	3000000	348000000						100	3.627

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

1223044950568481

10884458649339538001

C6B7ABEECA9053__

2017-09-21

Oliver Kruse

Manual testing

1223044950568481

10884458649339538001

C6B7ABEECA9053__

2017-10-12

kkmrkkblmbrbk

Manual testing

1223044950568481

10884458649339538001

C6B7ABEECA9053__

2020-04-17

Oliver Kruse

Manual testing

1223044950568481

10884458649339538001

2A8F69AD8420DC__

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 = 3000000000, B2 = 925584566816910 (P-1 stage 2)

B1 = 3000000000 (P-1 stage 1)

B1 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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