M1935181 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	15.3546	68.6567%	500000	15000000	0.1015	5.1028%	15.4561	70.2561%	1.5994%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4631%	0.0210	64.6849%	0.8918%
GPU72	2⁶²	0.3175	66.1290%	8000	90000	0.0010	1.1512%	0.3185	66.5190%	0.3899%
Difference	+5	+15.0371	+2.5277%	+492000	+14910000	+0.1005	+3.9516%	+15.1376	+3.7371%	+3.7371%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3546

68.6567%

500000

15000000

0.1015

5.1028%

15.4561

70.2561%

1.5994%

PrimeNet

2⁵⁸

0.0198

63.7931%

8000

140000

0.0012

2.4631%

0.0210

64.6849%

0.8918%

GPU72

2⁶²

0.3175

66.1290%

8000

90000

0.0010

1.1512%

0.3185

66.5190%

0.3899%

Difference

+15.0371

+2.5277%

+492000

+14910000

+0.1005

+3.9516%

+15.1376

+3.7371%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1935181	15533353424783	14	43.820	4013411 17 × 307 × 769	-	307	769	1.032e-6	2.613e-5	4.915e-5
1935181	1234771308458797707823	22	70.065	319032511289331 3 × 7 × 83 × 183036437917	2020-11-15	83	183036437917	152.12	784.45	1,465.1
1935181	1346986565304082850588159	25	80.156	348025989637166459 4933 × 268777 × 262487399	2022-03-17	268777	262487399	185,666	1.1449	2.1011

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1935181

15533353424783

43.820

4013411
17 × 307 × 769

307

769

1.032e-6

2.613e-5

4.915e-5

1935181

1234771308458797707823

70.065

319032511289331
3 × 7 × 83 × 183036437917

2020-11-15

183036437917

152.12

784.45

1,465.1

1935181

1346986565304082850588159

80.156

348025989637166459
4933 × 268777 × 262487399

2022-03-17

268777

262487399

185,666

1.1449

2.1011

exponent	prime factors	composite factor	digits	bits*
1935181	15533353424783 1234771308458797707823	19180139133072251472258987241177409	35	113.885
1935181	15533353424783 1346986565304082850588159	20923218377302865428996356888516944497	38	123.976
1935181	1234771308458797707823 1346986565304082850588159	1663220363716944147790998570575103136585467857	46	150.221
1935181	15533353424783 1234771308458797707823 1346986565304082850588159	25835389732911421289696436950342235836593322561119 313700031	59	194.041

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:41:03	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 15533353424783	-	-	0.101	-	-	5.103%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:41:03

alpertron

Manual testing

500000

15000000

skipped known factor: 15533353424783

0.101

-

-

5.103%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.461 GHz-days
Estimated T-Level:	24.464

Digits	B1	Curves	Complete	FacMiss
20	11000	250 / 100	2.500	8.106%
25	50000	250 / 280	0.893	40.883%

New Calculation Method

Total ECM effort:	20.461 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.825	0.015%
25	50000	0.785	45.619%
30	250000	0.049	95.249%
35	1000000	0.002	99.776%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		20	1.390
50000	5000000	1234771308458797707823	5	0.348
50000	6700000		7	0.553
50000	6750000		7	0.555
50000	7500000		106	8.849
50000	7500000	1346986565304082850588159	105	8.766

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T01:48:28	Oliver Kruse	O2.261	50000	5000000						3	0.209
2019-02-16T07:17:37	Yan Jinzhao	home	50000	5000000						3	0.209
2020-11-15T23:59:11	MarkS	desktop-i7	50000	5000000	1234771308458797707823	70.065	5	2	665228111457964	5	0.348
2021-01-22T09:51:02	nordi	sweet16	50000	6750000						7	0.555
2021-05-11T20:38:43	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.487
2021-08-15T17:47:46	Ahmed Azhad	c5.4xlarge.azf2	50000	6700000						7	0.553
2021-11-21T15:41:55	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-03-17T11:24:21	TJAOI	Manual testing	50000	7500000	1346986565304082850588159	80.156	105	2		105	8.766
2022-03-17T11:24:21	TJAOI	Manual testing	50000	7500000						106	8.849

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T02:04:08

Oliver Kruse

GTX-3

15533353424783

D5D69E0030E647__

2017-11-10T20:58:28

ATH

ec2-1xf

15533353424783

D5D69E0030E647__

2020-11-17T03:00:41

Poao

pc-Home

15533353424783

1234771308458797707823

7E84D1214D52D8C4

2022-03-20T08:43:56

SRJ2877

LTOS

15533353424783

1234771308458797707823

1346986565304082850588159

7E84D1214D52D8C4

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

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