M1759249 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	16.8901	68.6567%	500000	15000000	0.1015	5.0445%	16.9916	70.2378%	1.5811%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8053%	0.0121	64.1914%	1.0335%
GPU72	2⁶¹	0.1746	65.5738%	8000	110000	0.0011	1.4142%	0.1757	66.0606%	0.4869%
Difference	+6	+16.7155	+3.0829%	+492000	+14890000	+0.1004	+3.6303%	+16.8159	+4.1772%	+4.1772%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.8901

68.6567%

500000

15000000

0.1015

5.0445%

16.9916

70.2378%

1.5811%

PrimeNet

2⁵⁷

0.0109

63.1579%

8000

140000

0.0012

2.8053%

0.0121

64.1914%

1.0335%

GPU72

2⁶¹

0.1746

65.5738%

8000

110000

0.0011

1.4142%

0.1757

66.0606%

0.4869%

Difference

+16.7155

+3.0829%

+492000

+14890000

+0.1004

+3.6303%

+16.8159

+4.1772%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1759249	233019567047	12	37.762	66227 7 × 9461	-	7	9461	1.389e-8	4.107e-5	7.573e-5
1759249	100144700439313	15	46.509	28462344 2³ × 3 × 1185931	2014-02-13	8	1185931	8.955e-6	0.0051	0.0095
1759249	9312547239060119248769	22	72.980	2646739386823616 2⁶ × 7 × 31 × 53 × 881 × 1619 × 2521	2015-05-29	1619	2521	698.48	0.0001	0.0003
1759249	32259369503645983231023737	26	84.738	9168505852112459132 2² × 7 × 43 × 61 × 1637 × 76259431819	2020-05-23	1637	76259431819	4,440,526	326.83	610.43

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1759249

233019567047

37.762

66227
7 × 9461

9461

1.389e-8

4.107e-5

7.573e-5

1759249

100144700439313

46.509

28462344
2³ × 3 × 1185931

2014-02-13

1185931

8.955e-6

0.0051

0.0095

1759249

9312547239060119248769

72.980

2646739386823616
2⁶ × 7 × 31 × 53 × 881 × 1619 × 2521

2015-05-29

1619

2521

698.48

0.0001

0.0003

1759249

32259369503645983231023737

84.738

9168505852112459132
2² × 7 × 43 × 61 × 1637 × 76259431819

2020-05-23

1637

76259431819

4,440,526

326.83

610.43

exponent	prime factors	composite factor	digits	bits*
1759249	233019567047 100144700439313	23335674738420225958118711	26	84.271
1759249	233019567047 9312547239060119248769	2170005725750524194552343267715143	34	110.741
1759249	100144700439313 9312547239060119248769	932602253582626989365415041834455697	36	119.489
1759249	233019567047 32259369503645983231023737	7517064314948782300453773374319994639	37	122.500
1759249	100144700439313 32259369503645983231023737	3230604895303736291631130665914630972681	40	131.247
1759249	233019567047 100144700439313 9312547239060119248769	217314573356880245702826086323726259161842616759	48	157.250
1759249	9312547239060119248769 32259369503645983231023737	300416902404998610631831186061185661443247029753	48	157.718
1759249	233019567047 100144700439313 32259369503645983231023737	75279415400359539423734739719851210951690310484300 7	51	169.009
1759249	233019567047 9312547239060119248769 32259369503645983231023737	70003016532013629298065834092769984080989744034912 787349391	59	195.479
1759249	100144700439313 9312547239060119248769 32259369503645983231023737	30085160698254915008388699211243273551633197306122 441481879689	62	204.227
1759249	233019567047 100144700439313 9312547239060119248769 32259369503645983231023737	70104311204467805036945170632914179975925536360249 78036478198226523008383	73	241.988

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-05-29T12:14:00	alpertron	Manual testing	500000	15000000	12		9312547239060119248769	22	72.980	0.039	0.191	0.079	5.045%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-05-29T12:14:00

alpertron

Manual testing

500000

15000000

9312547239060119248769

72.980

0.039

0.191

0.079

5.045%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-02-13T14:49:00	TJAOI	Manual testing	?	?	100144700439313	46.509	15	3.62624e-6	0.205	7.78273e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-02-13T14:49:00

TJAOI

Manual testing

100144700439313

46.509

3.62624e-6

0.205

7.78273e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:

23.519 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	342 / 100	3.420	3.215%
25	50000	342 / 280	1.221	29.416%

New Calculation Method

Total ECM effort:

23.519 GHz-days

Digits	B1	Complete	FacMiss
20	11000	11.032	0.002%
25	50000	0.997	36.895%
30	250000	0.061	94.045%
35	1000000	0.003	99.719%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.26
50000	5000000	32259369503645983231023737	91	6.258

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-04T11:32:49	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-21T02:51:02	ATH	ec2-ECMCF	50000	5000000						3	0.206
2019-08-02T12:34:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-27T16:28:36	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-09T03:38:53	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-22T06:15:14	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-30T00:39:55	Greg	azure2	50000	5000000						3	0.206
2020-05-23T06:58:50	nordi	sweet16	50000	5000000	32259369503645983231023737	84.738	91	2	3305469773205696	91	6.258
2020-08-21T10:53:56	TJAOI	Manual testing	50000	5000000						232	15.95

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T09:09:13

Oliver Kruse

GTX-2

233019567047

100144700439313

9312547239060119248769

457EFDD59F4AA038

2017-10-05T21:32:28

Oliver Kruse

Manual testing

233019567047

100144700439313

9312547239060119248769

457EFDD59F4AA0__

2017-11-10T20:52:10

kkmrkkblmbrbk

c4.xlarge

233019567047

100144700439313

9312547239060119248769

457EFDD59F4AA0__

2020-05-23T09:09:16

CrypticClue

cruncher

233019567047

100144700439313

9312547239060119248769

32259369503645983231023737

A9DA79F7F0956F7C

2020-05-24T06:55:24

marssystems

system03

233019567047

100144700439313

9312547239060119248769

32259369503645983231023737

A9DA79F7F0956F7C

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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