M1786331 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	16.6340	68.6567%	500000	15000000	0.1015	5.0538%	16.7355	70.2408%	1.5840%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8134%	0.0119	64.1944%	1.0365%
GPU72	2⁶¹	0.1720	65.5738%	8000	130000	0.0012	1.4927%	0.1731	66.0877%	0.5139%
Difference	+6	+16.4621	+3.0829%	+492000	+14870000	+0.1003	+3.5611%	+16.5624	+4.1531%	+4.1531%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6340

68.6567%

500000

15000000

0.1015

5.0538%

16.7355

70.2408%

1.5840%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8134%

0.0119

64.1944%

1.0365%

GPU72

2⁶¹

0.1720

65.5738%

8000

130000

0.0012

1.4927%

0.1731

66.0877%

0.5139%

Difference

+16.4621

+3.0829%

+492000

+14870000

+0.1003

+3.5611%

+16.5624

+4.1531%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1786331	3572663	7	21.769	1 1	-	1	1	1.564e-13	7.866e-8	1.601e-7
1786331	154367482823269871	18	57.099	43207972885 5 × 7² × 11² × 1457513	2015-06-21	121	1457513	0.0116	0.0063	0.0117
1786331	747407469350504083065311	24	79.306	209201841470171005 5 × 127 × 329451718850663	2020-05-29	127	329451718850663	94,723	1,411,948	2,637,125

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1786331

3572663

21.769

1
1

1.564e-13

7.866e-8

1.601e-7

1786331

154367482823269871

57.099

43207972885
5 × 7² × 11² × 1457513

2015-06-21

121

1457513

0.0116

0.0063

0.0117

1786331

747407469350504083065311

79.306

209201841470171005
5 × 127 × 329451718850663

2020-05-29

127

329451718850663

94,723

1,411,948

2,637,125

exponent	prime factors	composite factor	digits	bits*
1786331	3572663 154367482823269871	551502994285831807136473	24	78.868
1786331	3572663 747407469350504083065311	2670235011672179968916363193193	31	101.075
1786331	154367482823269871 747407469350504083065311	115375409686947541610136850867053871544881	42	136.405
1786331	3572663 154367482823269871 747407469350504083065311	412197457298399064851496352029241285875149188103	48	158.174

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
unknown			500000	15000000		-	skipped known factor: 3572663 MISSED FACTOR!	-	-	0.101	-	-	5.054%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

unknown

500000

15000000

skipped known factor: 3572663
MISSED FACTOR!

0.101

-

-

5.054%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-05-25T11:27:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	154367482823269871	57.099	18	0.001	0.197	0.002

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-05-25T11:27:00

TJAOI

Manual testing

2⁵⁷

2⁵⁸*

154367482823269871

57.099

0.001

0.197

0.002

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.290 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.290 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		131	9.024
50000	5000000	747407469350504083065311	120	8.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-13T21:13:13	alpertron		50000	5000000						3	0.207
2018-09-28T16:54:50	alpertron	Manual testing	50000	5000000						3	0.207
2020-03-11T19:08:17	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-01T13:55:38	Hans Loeblich	tomservo	50000	5000000						3	0.207
2020-05-02T01:23:47	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-05-29T16:46:51	nordi	sweet16	50000	5000000	747407469350504083065311	79.306	120	2	6633790270943815	120	8.266
2020-11-13T10:48:49	TJAOI	Manual testing	50000	5000000						116	7.991

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:43

alpertron

Manual testing

3572663

154367482823269871

9151E706EC444F__

2017-10-19T18:07:18

Oliver Kruse

GTX-3

3572663

154367482823269871

9151E706EC444F__

2020-05-30T19:01:45

mnd9

75211backdoor

3572663

154367482823269871

747407469350504083065311

6F704BCF1B396DF7

2020-05-31T18:17:37

Oliver Kruse

Threadripper-PC

3572663

154367482823269871

747407469350504083065311

6F704BCF1B396DF7

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