M1887079 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	15.7460	68.6567%	1000000	30000000	0.2029	6.2131%	15.9489	70.6041%	1.9474%
PrimeNet	2⁵⁷	0.0102	63.1579%	9000	160000	0.0014	3.0342%	0.0115	64.2758%	1.1179%
GPU72	2⁶¹	0.1628	65.5738%	10000	150000	0.0014	1.6927%	0.1642	66.1565%	0.5827%
Difference	+6	+15.5832	+3.0829%	+990000	+29850000	+0.2016	+4.5204%	+15.7848	+4.4476%	+4.4476%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.7460

68.6567%

1000000

30000000

0.2029

6.2131%

15.9489

70.6041%

1.9474%

PrimeNet

2⁵⁷

0.0102

63.1579%

9000

160000

0.0014

3.0342%

0.0115

64.2758%

1.1179%

GPU72

2⁶¹

0.1628

65.5738%

10000

150000

0.0014

1.6927%

0.1642

66.1565%

0.5827%

Difference

+15.5832

+3.0829%

+990000

+29850000

+0.2016

+4.5204%

+15.7848

+4.4476%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1887079	45289897	8	25.433	12 2² × 3	-	4	4	2.375e-12	3.146e-7	6.404e-7
1887079	510722834719	12	38.894	135321 3 × 43 × 1049	2008-07-15	43	1049	2.504e-8	7.694e-6	8.363e-6
1887079	5293827911126023809049	22	72.165	1402651375783956 2² × 3² × 31 × 1256856071491	2021-02-21	31	1256856071491	826.70	5,386.6	10,061

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1887079

45289897

25.433

12
2² × 3

2.375e-12

3.146e-7

6.404e-7

1887079

510722834719

38.894

135321
3 × 43 × 1049

2008-07-15

1049

2.504e-8

7.694e-6

8.363e-6

1887079

5293827911126023809049

72.165

1402651375783956
2² × 3² × 31 × 1256856071491

2021-02-21

1256856071491

826.70

5,386.6

10,061

exponent	prime factors	composite factor	digits	bits*
1887079	45289897 510722834719	23130584579971533943	20	64.326
1887079	45289897 5293827911126023809049	239756920830622772331376877953	30	97.597
1887079	510722834719 5293827911126023809049	2703678797284845279008591243572231	34	111.059
1887079	45289897 510722834719 5293827911126023809049	122449334250114522347235359536488254050207	42	136.491

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:16	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 45289897 skipped known factor: 510722834719	-	-	0.101	-	-	5.087%
2021-02-21T12:24:00	riccardo uberti	Colab_noGPU14	1000000	30000000	12	-	skipped known factor: 45289897 skipped known factor: 510722834719	-	-	0.203	-	-	6.213%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	510722834719	38.894	12	5.63249e-9	0.218	1.20127e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

510722834719

38.894

5.63249e-9

0.218

1.20127e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.799 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:	19.799 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.615	0.002%
25	50000	0.977	37.642%
30	250000	0.062	93.989%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		35	2.426
50000	5000000	5293827911126023809049	7	0.485
50000	6600000		216	16.89

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-02-01T18:19:08	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-22T21:51:02	Oliver Kruse	HTC5	50000	5000000						3	0.208
2020-07-20T06:57:08	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.208
2020-09-19T05:05:57	nordi	sweet16	50000	5000000						7	0.485
2020-11-22T22:22:50	MarkS	desktop-i7	50000	5000000						7	0.485
2021-02-21T04:29:23	Poao	justg-ZA	50000	5000000	5293827911126023809049	72.165	7	2	8718873265181544	7	0.485
2021-06-08T12:06:14	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-09-07T08:28:17	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.485
2021-10-28T13:39:54	TJAOI	Manual testing	50000	6600000						216	16.89

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T15:15:36

Oliver Kruse

GTX-0

45289897

510722834719

43F1C72265AC4F__

2017-11-08T15:48:31

Chang Chia-Tche

exbpc13

45289897

510722834719

43F1C72265AC4F__

2021-02-21T09:56:20

riccardo uberti

Colab_noGPU12

45289897

510722834719

5293827911126023809049

94FCDAB82DCC6088

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

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

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