M1870859 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	15.8825	68.6567%	500000	15000000	0.1015	5.0821%	15.9840	70.2496%	1.5929%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0294%	0.0116	64.2740%	1.1161%
GPU72	2⁶¹	0.1642	65.5738%	10000	150000	0.0014	1.6898%	0.1656	66.1555%	0.5817%
Difference	+6	+15.7183	+3.0829%	+490000	+14850000	+0.1001	+3.3923%	+15.8184	+4.0941%	+4.0941%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.8825

68.6567%

500000

15000000

0.1015

5.0821%

15.9840

70.2496%

1.5929%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0294%

0.0116

64.2740%

1.1161%

GPU72

2⁶¹

0.1642

65.5738%

10000

150000

0.0014

1.6898%

0.1656

66.1555%

0.5817%

Difference

+15.7183

+3.0829%

+490000

+14850000

+0.1001

+3.3923%

+15.8184

+4.0941%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1870859	3741719	7	21.835	1 1	-	1	1	1.494e-13	7.866e-8	1.601e-7
1870859	29690922999034663	17	54.721	7935104409 3 × 421 × 6282743	2014-12-10	421	6282743	0.0014	0.0270	0.0503
1870859	164464498347225924007	21	67.156	43954274038617 3² × 439823 × 11104031	2015-08-15	439823	11104031	25.002	0.0803	0.0889
1870859	82631903043773373211633	23	76.129	22083947278702824 2³ × 3 × 920164469945951	2020-11-27	8	920164469945951	11,410	3,943,595	7,365,537

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1870859

3741719

21.835

1
1

1.494e-13

7.866e-8

1.601e-7

1870859

29690922999034663

54.721

7935104409
3 × 421 × 6282743

2014-12-10

421

6282743

0.0014

0.0270

0.0503

1870859

164464498347225924007

67.156

43954274038617
3² × 439823 × 11104031

2015-08-15

439823

11104031

25.002

0.0803

0.0889

1870859

82631903043773373211633

76.129

22083947278702824
2³ × 3 × 920164469945951

2020-11-27

920164469945951

11,410

3,943,595

7,365,537

exponent	prime factors	composite factor	digits	bits*
1870859	3741719 29690922999034663	111095090713024980205697	24	76.556
1870859	3741719 164464498347225924007	615379938291283837149548033	27	88.992
1870859	3741719 82631903043773373211633	309185361625044662240058217127	30	97.964
1870859	29690922999034663 164464498347225924007	4883102756502348507854672429196854641	37	121.877
1870859	29690922999034663 82631903043773373211633	2453417470536373220088291050483001834679	40	130.850
1870859	164464498347225924007 82631903043773373211633	13590014481570798737848914386546529586373431	44	143.285
1870859	3741719 29690922999034663 164464498347225924007	18271198362957210956461477067102025750467879	44	143.712
1870859	3741719 29690922999034663 82631903043773373211633	9179998764437887868695540301122207141853273201	46	152.685
1870859	3741719 164464498347225924007 82631903043773373211633	50850015395968607482585302089514494137395607867889	50	165.121
1870859	29690922999034663 164464498347225924007 82631903043773373211633	40350007352808456056437319254334638839906972183549 2031238753	60	198.006
1870859	3741719 29690922999034663 164464498347225924007 82631903043773373211633	15097838916214310338703658976300975050541787605165 75407634635636407	67	219.842

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-08-15T18:11:00	alpertron	Manual testing	500000	15000000	12		164464498347225924007	21	67.156	0.101	0.203	0.203	5.082%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2015-08-15T18:11:00

alpertron

Manual testing

500000

15000000

164464498347225924007

67.156

0.101

0.203

0.203

5.082%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-12-10T12:40:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	29690922999034663	54.721	17	8.57944e-5	0.214	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-12-10T12:40:00

TJAOI

Manual testing

2⁵⁴

2⁵⁵*

29690922999034663

54.721

8.57944e-5

0.214

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.796 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.796 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.810	0.015%
25	50000	0.798	45.022%
30	250000	0.049	95.183%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		38	2.631
50000	5000000	82631903043773373211633	1	0.069
50000	6433878		7	0.540
50000	6600000		212	16.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-05-26T16:08:48	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-11T17:41:44	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2019-11-04T14:02:12	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2020-07-24T02:31:39	argusdusty	Argus-PC	50000	5000000						3	0.208
2020-09-27T17:43:03	nordi	sweet16	50000	5000000						7	0.485
2020-11-27T05:57:21	MarkS	desktop-i7	50000	5000000	82631903043773373211633	76.129	1	2	2051050786738139	1	0.069
2020-12-05T21:15:36	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.485
2021-03-13T01:09:12	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						7	0.485
2021-07-09T09:58:28	Jonathan Webb	Desktop2021	50000	5000000						7	0.485
2021-09-22T13:05:07	Ahmed Azhad	c5.4xlarge.azf	50000	6433878						7	0.540
2021-09-29T12:09:39	TJAOI	Manual testing	50000	6600000						212	16.56

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:52

alpertron

Manual testing

3741719

29690922999034663

164464498347225924007

D227591CEDDDC9__

2017-10-19T21:44:46

Oliver Kruse

GTX-3

3741719

29690922999034663

164464498347225924007

D227591CEDDDC9__

2020-11-27T15:21:09

mrh

3741719

29690922999034663

164464498347225924007

82631903043773373211633

B36E81514A0CE9AC

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

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