M1752721 Mersenne number exponent details

Residue

Status

L-L

C31FE037E07D8361

double-checked

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	16.9530	68.6567%	500000	15000000	0.1015	5.0423%	17.0545	70.2371%	1.5804%
PrimeNet	2⁵⁷	0.0110	63.1579%	8000	140000	0.0012	2.8033%	0.0121	64.1907%	1.0328%
GPU72	2⁶¹	0.1753	65.5738%	8000	110000	0.0011	1.4131%	0.1763	66.0603%	0.4865%
Difference	+6	+16.7778	+3.0829%	+492000	+14890000	+0.1004	+3.6292%	+16.8782	+4.1769%	+4.1769%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.9530

68.6567%

500000

15000000

0.1015

5.0423%

17.0545

70.2371%

1.5804%

PrimeNet

2⁵⁷

0.0110

63.1579%

8000

140000

0.0012

2.8033%

0.0121

64.1907%

1.0328%

GPU72

2⁶¹

0.1753

65.5738%

8000

110000

0.0011

1.4131%

0.1763

66.0603%

0.4865%

Difference

+16.7778

+3.0829%

+492000

+14890000

+0.1004

+3.6292%

+16.8782

+4.1769%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1752721	877329968106781751	18	59.606	250276560875 5³ × 11 × 37 × 4919441	-	125	4919441	0.0777	0.0211	0.0394
1752721	6051948874329859182911	22	72.358	1726443876215855 5 × 191 × 1807794634781	2020-07-20	191	1807794634781	585.20	7,747.8	14,471
1752721	38074769690949935730569	23	75.011	10861617362646404 2² × 2715404340661601	2019-07-22	4	2715404340661601	5,427.9	11,637,544	21,735,692

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1752721

877329968106781751

59.606

250276560875
5³ × 11 × 37 × 4919441

125

4919441

0.0777

0.0211

0.0394

1752721

6051948874329859182911

72.358

1726443876215855
5 × 191 × 1807794634781

2020-07-20

191

1807794634781

585.20

7,747.8

14,471

1752721

38074769690949935730569

75.011

10861617362646404
2² × 2715404340661601

2019-07-22

2715404340661601

5,427.9

11,637,544

21,735,692

exponent	prime factors	composite factor	digits	bits*
1752721	877329968106781751 6051948874329859182911	5309556112899689076151235091982665857161	40	131.964
1752721	877329968106781751 38074769690949935730569	33404136478634167580623520382439622046319	41	134.617
1752721	6051948874329859182911 38074769690949935730569	230426559571513103954770680720799454185106359	45	147.369
1752721	877329968106781751 6051948874329859182911 38074769690949935730569	20216012615983103671217161372385264016546573585579 6447135254609	63	206.975

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:29:30	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 877329968106781751	-	-	0.101	-	-	5.042%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:29:30

alpertron

Manual testing

500000

15000000

skipped known factor: 877329968106781751

0.101

-

-

5.042%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-01-25T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.022

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.667 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	17.667 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.290	0.025%
25	50000	0.749	47.271%
30	250000	0.046	95.491%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		252	17.32
50000	5000000	6051948874329859182911	2	0.137
50000	5000000	38074769690949935730569	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-04-24T22:23:45	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-19T21:16:06	ATH	ec2-ECMCF	50000	5000000						3	0.206
2019-07-22T11:17:26	Chang Chia-Tche	exbpc13	50000	5000000	38074769690949935730569	75.011	3	2		3	0.206
2020-02-25T04:54:47	kracker	O0	50000	5000000						3	0.206
2020-03-04T19:20:58	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-17T15:35:11	Hans Loeblich	crow	50000	5000000						3	0.206
2020-04-16T13:36:22	Oliver Kruse	Melissa	50000	5000000						3	0.206
2020-05-07T02:18:21	kracker	O0	50000	5000000						3	0.206
2020-06-13T18:50:48	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.206
2020-07-09T05:22:29	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-07-20T13:08:06	TJAOI	Manual testing	50000	5000000	6051948874329859182911	72.358	2	2		2	0.137
2020-07-20T13:08:06	TJAOI	Manual testing	50000	5000000						227	15.60

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	Stephen Wood	v4_computers	024E18C7DAE9F9__	0.095
1999-06-06T00:00:00	Nayan Hajratwala	v4_computers	C31FE037E07D8361	0.095

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

Stephen Wood

v4_computers

024E18C7DAE9F9__

0.095

1999-06-06T00:00:00

Nayan Hajratwala

v4_computers

C31FE037E07D8361

0.095

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T07:09:40

Oliver Kruse

GTX-1

877329968106781751

36053C2EE70780__

2017-11-03T21:28:56

kkmrkkblmbrbk

c4.xlarge

877329968106781751

36053C2EE70780__

2019-07-23T02:11:41

Niels_Mache_Nextcloud

SuperDry-X

877329968106781751

38074769690949935730569

4FE85C01D57AD320

2019-07-24T21:35:13

arnaud

stm-11-010

877329968106781751

38074769690949935730569

4FE85C01D57AD320

2020-07-20T21:10:41

CrypticClue

Manual testing

877329968106781751

6051948874329859182911

38074769690949935730569

4FE85C01D57AD320

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

10¹⁶

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