M1865987 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	15.9240	68.6567%	500000	15000000	0.1015	5.0805%	16.0254	70.2491%	1.5924%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0279%	0.0116	64.2734%	1.1155%
GPU72	2⁶¹	0.1646	65.5738%	10000	150000	0.0014	1.6889%	0.1660	66.1552%	0.5814%
Difference	+6	+15.7593	+3.0829%	+490000	+14850000	+0.1001	+3.3916%	+15.8594	+4.0939%	+4.0939%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9240

68.6567%

500000

15000000

0.1015

5.0805%

16.0254

70.2491%

1.5924%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0279%

0.0116

64.2734%

1.1155%

GPU72

2⁶¹

0.1646

65.5738%

10000

150000

0.0014

1.6889%

0.1660

66.1552%

0.5814%

Difference

+15.7593

+3.0829%

+490000

+14850000

+0.1001

+3.3916%

+15.8594

+4.0939%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1865987	10705465976921	14	43.283	2868580 2² × 5 × 11 × 13 × 17 × 59	-	17	59	1.196e-6	1.517e-6	2.722e-6
1865987	4430289976752623	16	51.976	1187117053 1187117053	2014-07-18	1	1187117053	0.0003	5.0877	9.502
1865987	535579736393777428823	21	68.860	143511111383353 7² × 3137 × 933630281	2021-03-17	3137	933630281	61.990	4.0015	7.4733

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1865987

10705465976921

43.283

2868580
2² × 5 × 11 × 13 × 17 × 59

1.196e-6

1.517e-6

2.722e-6

1865987

4430289976752623

51.976

1187117053
1187117053

2014-07-18

1187117053

0.0003

5.0877

9.502

1865987

535579736393777428823

68.860

143511111383353
7² × 3137 × 933630281

2021-03-17

3137

933630281

61.990

4.0015

7.4733

exponent	prime factors	composite factor	digits	bits*
1865987	10705465976921 4430289976752623	47428318614019333563844213783	29	95.260
1865987	10705465976921 535579736393777428823	5733630645891902139600057238193983	34	112.143
1865987	4430289976752623 535579736393777428823	2372773537897164159633484328061052729	37	120.836
1865987	10705465976921 4430289976752623 535579736393777428823	25401646380896561926246187295409261107195678067409	50	164.119

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:31	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 10705465976921	-	-	0.101	-	-	5.080%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:37:31

alpertron

Manual testing

500000

15000000

skipped known factor: 10705465976921

0.101

-

-

5.080%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-07-18T11:29:00	ANONYMOUS	Manual testing	?	?	4430289976752623	51.976	16	0.000	0.216	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-07-18T11:29:00

ANONYMOUS

Manual testing

4430289976752623

51.976

0.000

0.216

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.768 GHz-days
Estimated T-Level:	24.625

Digits	B1	Curves	Complete	FacMiss
20	11000	259 / 100	2.590	7.405%
25	50000	259 / 280	0.925	39.588%

New Calculation Method

Total ECM effort:	19.768 GHz-days
Estimated T-Level:	24.625

Digits	B1	Complete	FacMiss
20	11000	8.818	0.015%
25	50000	0.799	44.992%
30	250000	0.049	95.180%
35	1000000	0.002	99.773%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		49	3.392
50000	5000000	535579736393777428823	2	0.138
50000	6600000		208	16.24

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T21:22:41	ATH	ec2-1xe	50000	5000000						3	0.208
2019-01-19T04:51:51	tottenhoff	Dell-Optiplex-380-01	50000	5000000						3	0.208
2020-07-04T21:39:45	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2020-08-06T14:04:08	Ahmed Azhad	c5.xlarge.az	50000	5000000						3	0.208
2020-10-12T06:36:39	nordi	sweet16	50000	5000000						7	0.485
2021-02-24T21:59:35	Dirk	Fliegender_Hollander	50000	5000000						7	0.485
2021-03-17T14:11:52	Chang Chia-Tche	exbpc13	50000	5000000	535579736393777428823	68.860	2	2	587749570579704	2	0.138
2021-04-18T08:55:42	MarkS	desktop-i7	50000	5000000						15	1.038
2021-11-04T15:26:29	MarkS	desktop-i7	50000	5000000						8	0.554
2021-11-11T10:32:46	TJAOI	Manual testing	50000	6600000						208	16.24

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T10:07:52

Oliver Kruse

GTX-0

10705465976921

4430289976752623

698B9AD248AEDC__

2017-11-07T15:45:06

kkmrkkblmbrbk

old

10705465976921

4430289976752623

698B9AD248AEDC__

2021-03-18T05:38:33

Nescro

Manual testing

10705465976921

4430289976752623

535579736393777428823

6BB1CB8953092452

2021-03-18T10:44:56

Oliver Kruse

Threadripper-PC

10705465976921

4430289976752623

535579736393777428823

6BB1CB8953092452

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

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