M1850357 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	16.0585	68.6567%	500000	15000000	0.1015	5.0753%	16.1600	70.2475%	1.5908%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0232%	0.0117	64.2717%	1.1138%
GPU72	2⁶¹	0.1660	65.5738%	9000	150000	0.0013	1.6310%	0.1673	66.1353%	0.5615%
Difference	+6	+15.8925	+3.0829%	+491000	+14850000	+0.1002	+3.4443%	+15.9926	+4.1122%	+4.1122%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0585

68.6567%

500000

15000000

0.1015

5.0753%

16.1600

70.2475%

1.5908%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0232%

0.0117

64.2717%

1.1138%

GPU72

2⁶¹

0.1660

65.5738%

9000

150000

0.0013

1.6310%

0.1673

66.1353%

0.5615%

Difference

+15.8925

+3.0829%

+491000

+14850000

+0.1002

+3.4443%

+15.9926

+4.1122%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1850357	7653076553	10	32.833	2068 2² × 11 × 47	-	11	47	4.476e-10	1.020e-6	1.761e-6
1850357	63219297263	11	35.880	17083 11 × 1553	2008-07-15	11	1553	4.200e-9	7.474e-6	1.246e-5
1850357	252592685260414357193	21	67.775	68255121919828 2² × 17063780479957	2020-10-17	4	17063780479957	22.240	73,131	136,589

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1850357

7653076553

32.833

2068
2² × 11 × 47

4.476e-10

1.020e-6

1.761e-6

1850357

63219297263

35.880

17083
11 × 1553

2008-07-15

1553

4.200e-9

7.474e-6

1.246e-5

1850357

252592685260414357193

67.775

68255121919828
2² × 17063780479957

2020-10-17

17063780479957

22.240

73,131

136,589

exponent	prime factors	composite factor	digits	bits*
1850357	7653076553 63219297263	483822121580602374439	21	68.713
1850357	7653076553 252592685260414357193	1933111157025785816098315195729	31	100.609
1850357	63219297263 252592685260414357193	15968732055937533813937329262759	32	103.655
1850357	7653076553 63219297263 252592685260414357193	122209928878435024464088439192261678989727	42	136.488

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:41	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 7653076553 skipped known factor: 63219297263	-	-	0.101	-	-	5.075%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:41

alpertron

Manual testing

500000

15000000

skipped known factor: 7653076553
skipped known factor: 63219297263

0.101

-

-

5.075%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:47:00	J Feitsma	Manual testing	?	?	63219297263	35.880	11	1.72574e-9	0.214	3.68732e-9

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:47:00

J Feitsma

Manual testing

63219297263

35.880

1.72574e-9

0.214

3.68732e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.366 GHz-days
Estimated T-Level:	24.714

Digits	B1	Curves	Complete	FacMiss
20	11000	264 / 100	2.640	7.042%
25	50000	264 / 280	0.943	38.886%

New Calculation Method

Total ECM effort:	20.366 GHz-days
Estimated T-Level:	24.714

Digits	B1	Complete	FacMiss
20	11000	9.048	0.012%
25	50000	0.820	44.041%
30	250000	0.051	95.052%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	1.521
50000	5000000	252592685260414357193	3	0.207
50000	6525716		14	1.086
50000	6600000		218	17.00
50000	6750000		7	0.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-17T10:30:09	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-01-14T21:36:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-16T07:18:35	nordi	sweet16	50000	5000000						3	0.207
2020-07-12T13:02:21	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-08-14T12:11:00	volki	home	50000	5000000						3	0.207
2020-10-17T15:23:33	nordi	sweet16	50000	5000000	252592685260414357193	67.775	3	2	8918225344355869	3	0.207
2020-11-01T21:26:04	Chang Chia-Tche	exbpc13	50000	5000000						7	0.484
2021-01-28T09:01:24	seatsea	dt	50000	6525716						7	0.543
2021-05-19T06:28:29	Dylan Delgado	laptop-i78750	50000	6750000						7	0.552
2021-07-09T11:25:19	TJAOI	Manual testing	50000	6600000						218	17.00
2021-07-14T09:03:45	seatsea	Manual testing	50000	6525716						7	0.543

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T06:16:22

Oliver Kruse

GTX-1

7653076553

63219297263

115581B0140220__

2017-11-06T22:54:01

ATH

ec2-1xf

7653076553

63219297263

115581B0140220__

2020-10-18T07:15:44

mrh.org

7653076553

63219297263

252592685260414357193

6BD9F6FC44A95EC9

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

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