M1786679 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	16.6308	68.6567%	500000	15000000	0.1015	5.0540%	16.7323	70.2408%	1.5841%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8135%	0.0119	64.1944%	1.0366%
GPU72	2⁶¹	0.1719	65.5738%	8000	130000	0.0012	1.4928%	0.1731	66.0877%	0.5139%
Difference	+6	+16.4589	+3.0829%	+492000	+14870000	+0.1003	+3.5612%	+16.5592	+4.1531%	+4.1531%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6308

68.6567%

500000

15000000

0.1015

5.0540%

16.7323

70.2408%

1.5841%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8135%

0.0119

64.1944%

1.0366%

GPU72

2⁶¹

0.1719

65.5738%

8000

130000

0.0012

1.4928%

0.1731

66.0877%

0.5139%

Difference

+16.4589

+3.0829%

+492000

+14870000

+0.1003

+3.5612%

+16.5592

+4.1531%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1786679	333686873659609	15	48.245	93381876 2² × 3³ × 7 × 149 × 829	-	149	829	3.205e-5	1.464e-5	2.385e-5
1786679	440977351399063	15	48.648	123406989 3 × 97 × 424079	2008-08-26	97	424079	3.084e-5	0.0018	0.0034
1786679	3285952672761194782541353	25	81.443	919569959897999244 2² × 3 × 76630829991499937	2020-06-08	4	76630829991499937	492,673	328,420,580	613,398,184

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1786679

333686873659609

48.245

93381876
2² × 3³ × 7 × 149 × 829

149

829

3.205e-5

1.464e-5

2.385e-5

1786679

440977351399063

48.648

123406989
3 × 97 × 424079

2008-08-26

424079

3.084e-5

0.0018

0.0034

1786679

3285952672761194782541353

81.443

919569959897999244
2² × 3 × 76630829991499937

2020-06-08

76630829991499937

492,673

328,420,580

613,398,184

exponent	prime factors	composite factor	digits	bits*
1786679	333686873659609 440977351399063	147148353743048137378983546367	30	96.893
1786679	333686873659609 3285952672761194782541353	1096479274367119319257478005076488310977	40	129.688
1786679	440977351399063 3285952672761194782541353	1449030706456903662250207567401202952239	40	130.090
1786679	333686873659609 440977351399063 3285952672761194782541353	48352252627437878757385167452024131289694033677041 4551	54	178.336

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:33:59	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 333686873659609 skipped known factor: 440977351399063	-	-	0.101	-	-	5.054%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	440977351399063	48.648	15	9.85314e-6	0.208	2.11047e-5

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

440977351399063

48.648

9.85314e-6

0.208

2.11047e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.290 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.290 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		239	16.46
50000	5000000	3285952672761194782541353	12	0.827

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-13T22:43:31	alpertron		50000	5000000						3	0.207
2018-09-28T16:54:50	alpertron	Manual testing	50000	5000000						3	0.207
2020-03-12T02:54:01	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-03T08:59:58	Daniil Tsarkov	9900	50000	5000000						3	0.207
2020-05-01T21:08:17	Greg	azure	50000	5000000						3	0.207
2020-06-08T18:21:09	nordi	sweet16	50000	5000000	3285952672761194782541353	81.443	12	2	8355518828296184	12	0.827
2020-10-23T07:51:34	TJAOI	Manual testing	50000	5000000						224	15.43

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T15:35:08

Oliver Kruse

GTX-2

333686873659609

440977351399063

21DE5C6D13B38B__

2017-11-05T02:35:27

kkmrkkblmbrbk

c4.xlarge

333686873659609

440977351399063

21DE5C6D13B38B__

2020-06-08T20:43:00

riccardo uberti

Colab_noGPU12

333686873659609

440977351399063

3285952672761194782541353

E0AEB7F5D1F62F21

2020-06-08T20:52:09

ATH

ec2-PRPCFDC

333686873659609

440977351399063

3285952672761194782541353

E0AEB7F5D1F62F21

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

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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