M1723247 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	17.2430	68.6567%	500000	15000000	0.0880	5.0320%	17.3310	70.2339%	1.5772%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0010	2.7943%	0.0122	64.1874%	1.0295%
GPU72	2⁶¹	0.1783	65.5738%	7000	110000	0.0009	1.3442%	0.1791	66.0365%	0.4628%
Difference	+6	+17.0647	+3.0829%	+493000	+14890000	+0.0872	+3.6878%	+17.1519	+4.1974%	+4.1974%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.2430

68.6567%

500000

15000000

0.0880

5.0320%

17.3310

70.2339%

1.5772%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0010

2.7943%

0.0122

64.1874%

1.0295%

GPU72

2⁶¹

0.1783

65.5738%

7000

110000

0.0009

1.3442%

0.1791

66.0365%

0.4628%

Difference

+17.0647

+3.0829%

+493000

+14890000

+0.0872

+3.6878%

+17.1519

+4.1974%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1723247	1492331903	10	30.475	433 433	-	1	433	9.079e-11	1.674e-6	3.029e-6
1723247	12327307611781023079	20	63.418	3576767466237 3 × 7² × 1009 × 24114719	2017-02-14	1009	24114719	1.2214	0.0897	0.1675
1723247	77063495248219393944287	23	76.028	22359967911802369 19 × 1310137 × 898257523	2019-06-02	1310137	898257523	13,473	3.4242	6.2376

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1723247

1492331903

30.475

433
433

433

9.079e-11

1.674e-6

3.029e-6

1723247

12327307611781023079

63.418

3576767466237
3 × 7² × 1009 × 24114719

2017-02-14

1009

24114719

1.2214

0.0897

0.1675

1723247

77063495248219393944287

76.028

22359967911802369
19 × 1310137 × 898257523

2019-06-02

1310137

898257523

13,473

3.4242

6.2376

exponent	prime factors	composite factor	digits	bits*
1723247	1492331903 12327307611781023079	18396434427155559390770989337	29	93.893
1723247	1492331903 77063495248219393944287	115004312515606705526384494688161	33	106.503
1723247	12327307611781023079 77063495248219393944287	949985411563825637504482625394237987199673	42	139.447
1723247	1492331903 12327307611781023079 77063495248219393944287	14176935370612821195772527273850193006725776490677 19	52	169.922

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:31:24	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1492331903	-	-	0.088	-	-	5.032%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:31:24

alpertron

Manual testing

500000

15000000

skipped known factor: 1492331903

0.088

-

-

5.032%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2017-02-14T17:30:51	TJAOI	Manual testing	2⁶³	2⁶⁴*	12327307611781023079	63.418	20	0.295	0.165	0.600

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2017-02-14T17:30:51

TJAOI

Manual testing

2⁶³

2⁶⁴*

12327307611781023079

63.418

0.295

0.165

0.600

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.120 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	15.120 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	14.94
50000	5000000	77063495248219393944287	3	0.179

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-09-17T23:03:43	Richard B. Woods	Puttputt	50000	5000000						1	0.060
2018-03-12T19:52:23	Chang Chia-Tche	exbpc13	50000	5000000						3	0.179
2019-06-03T02:38:19	Chang Chia-Tche	exbpc13	50000	5000000	77063495248219393944287	76.028	3	2		3	0.179
2020-02-11T07:11:50	kracker	O0	50000	5000000						3	0.179
2020-02-19T06:02:04	kracker	O0	50000	5000000						3	0.179
2020-02-27T06:04:04	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-03-08T10:31:37	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-03-21T08:48:29	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-04-27T10:16:20	TJAOI	Manual testing	50000	5000000						232	13.81

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T04:20:05

Oliver Kruse

GTX-2

1492331903

12327307611781023079

31DC58F087E8F3__

2017-11-03T15:48:51

kkmrkkblmbrbk

c4.xlarge

1492331903

12327307611781023079

31DC58F087E8F3__

2019-06-03T16:05:19

Niels_Mache_Nextcloud

SuperDry-X

1492331903

12327307611781023079

77063495248219393944287

1C69BD238A42A21D

2019-06-04T15:33:31

kkmrkkblmbrbk

c5.large

1492331903

12327307611781023079

77063495248219393944287

1C69BD238A42A21D

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

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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