M1749959 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	16.9798	68.6567%	500000	15000000	0.1015	5.0413%	17.0813	70.2368%	1.5801%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8025%	0.0122	64.1904%	1.0325%
GPU72	2⁶¹	0.1755	65.5738%	8000	110000	0.0011	1.4127%	0.1766	66.0601%	0.4863%
Difference	+6	+16.8042	+3.0829%	+492000	+14890000	+0.1004	+3.6287%	+16.9047	+4.1767%	+4.1767%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9798

68.6567%

500000

15000000

0.1015

5.0413%

17.0813

70.2368%

1.5801%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8025%

0.0122

64.1904%

1.0325%

GPU72

2⁶¹

0.1755

65.5738%

8000

110000

0.0011

1.4127%

0.1766

66.0601%

0.4863%

Difference

+16.8042

+3.0829%

+492000

+14890000

+0.1004

+3.6287%

+16.9047

+4.1767%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1749959	194962932191	12	37.504	55705 5 × 13 × 857	-	13	857	1.106e-8	4.640e-6	6.871e-6
1749959	526220013211673399882737	24	78.800	150352097738196552 2³ × 3 × 11 × 569515521735593	2020-07-03	11	569515521735593	60,968	2,440,801	4,558,737

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1749959

194962932191

37.504

55705
5 × 13 × 857

857

1.106e-8

4.640e-6

6.871e-6

1749959

526220013211673399882737

78.800

150352097738196552
2³ × 3 × 11 × 569515521735593

2020-07-03

569515521735593

60,968

2,440,801

4,558,737

exponent	prime factors	composite factor	digits	bits*
1749959	194962932191 526220013211673399882737	102593396753334605190976481082486767	36	116.304

exponent

prime factors

composite factor

digits

bits*

1749959

194962932191
526220013211673399882737

102593396753334605190976481082486767

116.304

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:33	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 194962932191	-	-	0.101	-	-	5.041%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:33

alpertron

Manual testing

500000

15000000

skipped known factor: 194962932191

0.101

-

-

5.041%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.938 GHz-days
Estimated T-Level:	24.661

Digits	B1	Curves	Complete	FacMiss
20	11000	261 / 100	2.610	7.257%
25	50000	261 / 280	0.932	39.305%

New Calculation Method

Total ECM effort:	17.938 GHz-days
Estimated T-Level:	24.661

Digits	B1	Complete	FacMiss
20	11000	8.419	0.022%
25	50000	0.761	46.723%
30	250000	0.047	95.422%
35	1000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		260	17.87
50000	5000000	526220013211673399882737	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-08T14:32:58	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-21T09:18:02	BanWaiLun	asia-northeast1-b	50000	5000000						3	0.206
2019-07-17T11:16:32	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-24T02:21:36	nordi	sweet16	50000	5000000						3	0.206
2020-03-03T04:50:55	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-15T13:20:30	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-12T08:42:26	Oliver Kruse	IOS-2	50000	5000000						3	0.206
2020-06-07T10:04:56	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-06-18T08:52:47	Ondrej Vainlich	Intel_Core_i3_CAD	50000	5000000						3	0.206
2020-07-03T05:31:10	nordi	sweet16	50000	5000000	526220013211673399882737	78.800	1	2	4435235280640942	1	0.069
2020-07-15T23:52:54	kracker	O0	50000	5000000						3	0.206
2020-08-14T09:31:12	TJAOI	Manual testing	50000	5000000						203	13.95
2020-08-14T09:32:19	TJAOI	Manual testing	50000	5000000						29	1.993

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T06:23:00

Oliver Kruse

GTX-2

194962932191

B33C1C6D4F6EA4__

2017-11-03T22:06:24

kkmrkkblmbrbk

old

194962932191

B33C1C6D4F6EA4__

2020-07-03T07:36:46

CrypticClue

Manual testing

194962932191

526220013211673399882737

D2033848192CA92D

2020-07-04T02:44:43

marssystems

system03

194962932191

526220013211673399882737

D2033848192CA92D

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