M1774637 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	16.7437	68.6567%	500000	15000000	0.1015	5.0498%	16.8451	70.2395%	1.5828%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8099%	0.0120	64.1931%	1.0352%
GPU72	2⁶¹	0.1731	65.5738%	8000	120000	0.0011	1.4552%	0.1742	66.0747%	0.5010%
Difference	+6	+16.5706	+3.0829%	+492000	+14880000	+0.1004	+3.5947%	+16.6709	+4.1648%	+4.1648%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.7437

68.6567%

500000

15000000

0.1015

5.0498%

16.8451

70.2395%

1.5828%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8099%

0.0120

64.1931%

1.0352%

GPU72

2⁶¹

0.1731

65.5738%

8000

120000

0.0011

1.4552%

0.1742

66.0747%

0.5010%

Difference

+16.5706

+3.0829%

+492000

+14880000

+0.1004

+3.5947%

+16.6709

+4.1648%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1774637	213382352881	12	37.635	60120 2³ × 3² × 5 × 167	-	9	167	1.045e-8	1.385e-6	1.441e-6
1774637	178141472014347679	18	57.306	50190960747 3 × 19 × 433 × 2033587	2015-06-09	433	2033587	0.0143	0.0087	0.0163
1774637	172317443439660017329	21	67.224	48550053740472 2³ × 3⁴ × 1559 × 48058321	2020-05-13	1559	48058321	30.131	0.2061	0.3847

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1774637

213382352881

37.635

60120
2³ × 3² × 5 × 167

167

1.045e-8

1.385e-6

1.441e-6

1774637

178141472014347679

57.306

50190960747
3 × 19 × 433 × 2033587

2015-06-09

433

2033587

0.0143

0.0087

0.0163

1774637

172317443439660017329

67.224

48550053740472
2³ × 3⁴ × 1559 × 48058321

2020-05-13

1559

48058321

30.131

0.2061

0.3847

exponent	prime factors	composite factor	digits	bits*
1774637	213382352881 178141472014347679	38012246444106322335401313199	29	94.940
1774637	213382352881 172317443439660017329	36769501523593292248363253074849	32	104.858
1774637	178141472014347679 172317443439660017329	30696883028090134031106466085770929391	38	124.529
1774637	213382352881 178141472014347679 172317443439660017329	6550173126646708815300146977194831268241696425471	49	162.164

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
unknown			500000	15000000		-	skipped known factor: 213382352881 MISSED FACTOR!	-	-	0.101	-	-	5.050%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

unknown

500000

15000000

skipped known factor: 213382352881
MISSED FACTOR!

0.101

-

-

5.050%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-06-09T11:51:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	178141472014347679	57.306	18	0.003	0.196	0.007

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-06-09T11:51:00

TJAOI

Manual testing

2⁵⁷

2⁵⁸*

178141472014347679

57.306

0.003

0.196

0.007

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.277 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:	17.277 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		249	17.14
50000	5000000	172317443439660017329	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-08-24T06:02:54	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-29T02:08:45	Gordon Spence	haswell	50000	5000000						3	0.207
2019-08-28T00:50:58	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-07T18:00:54	-Anonymous-	aws-nano	50000	5000000						3	0.207
2020-03-20T12:13:43	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-29T00:38:03	Oliver Kruse	IOS-1	50000	5000000						3	0.207
2020-05-13T07:35:01	Chang Chia-Tche	exbpc13	50000	5000000	172317443439660017329	67.224	2	2		2	0.138
2020-06-09T18:41:15	kracker	O0	50000	5000000						3	0.207
2020-07-04T11:54:46	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.207
2020-08-05T17:03:55	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-10-09T08:35:18	TJAOI	Manual testing	50000	5000000						224	15.42

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T12:47:53

Oliver Kruse

GTX-0

213382352881

178141472014347679

0D61033DAE84D8__

2017-11-04T12:09:02

kkmrkkblmbrbk

c4.xlarge

213382352881

178141472014347679

0D61033DAE84D8__

2020-05-14T18:38:44

mnd9

mnd

213382352881

178141472014347679

172317443439660017329

4977151263531611

2020-05-19T09:18:04

AbsolutXTR

750D

213382352881

178141472014347679

172317443439660017329

4977151263531611

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

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