M1891907 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	15.7058	68.6567%	500000	2903586840	12.4812	10.4318%	28.1870	71.9264%	3.2697%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0356%	0.0115	64.2763%	1.1184%
GPU72	2⁶¹	0.1624	65.5738%	10000	160000	0.0014	1.7259%	0.1638	66.1679%	0.5942%
Difference	+6	+15.5434	+3.0829%	+490000	+2903426840	+12.4798	+8.7059%	+28.0232	+5.7585%	+5.7585%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.7058

68.6567%

500000

2903586840

12.4812

10.4318%

28.1870

71.9264%

3.2697%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0356%

0.0115

64.2763%

1.1184%

GPU72

2⁶¹

0.1624

65.5738%

10000

160000

0.0014

1.7259%

0.1638

66.1679%

0.5942%

Difference

+15.5434

+3.0829%

+490000

+2903426840

+12.4798

+8.7059%

+28.0232

+5.7585%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1891907	1558931369	10	30.538	412 2² × 103	-	4	103	8.235e-11	7.389e-7	8.133e-7
1891907	480563568131083519	18	58.738	127005071637 3 × 167 × 253503137	2015-09-28	167	253503137	0.0253	1.0865	2.0292
1891907	182381809510748268823	21	67.306	48200521883673 3 × 16066840627891	2020-11-30	3	16066840627891	27.309	68,858	128,608
1891907	48838107157928333571673	23	75.370	12907110962094948 2² × 3² × 358530860058193	2021-11-19	9	358530860058193	5,714.9	1,536,574	2,869,892

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1891907

1558931369

30.538

412
2² × 103

103

8.235e-11

7.389e-7

8.133e-7

1891907

480563568131083519

58.738

127005071637
3 × 167 × 253503137

2015-09-28

167

253503137

0.0253

1.0865

2.0292

1891907

182381809510748268823

67.306

48200521883673
3 × 16066840627891

2020-11-30

16066840627891

27.309

68,858

128,608

1891907

48838107157928333571673

75.370

12907110962094948
2² × 3² × 358530860058193

2021-11-19

358530860058193

5,714.9

1,536,574

2,869,892

exponent	prime factors	composite factor	digits	bits*
1891907	1558931369 480563568131083519	749165621158114801728007511	27	89.275
1891907	1558931369 182381809510748268823	284320723981288018930619408687	30	97.843
1891907	1558931369 48838107157928333571673	76135257251077916258776849510337	32	105.908
1891907	480563568131083519 182381809510748268823	87646053140688771807660591864476828137	38	126.043
1891907	480563568131083519 48838107157928333571673	23469815036582250417057695323644735557287	41	134.108
1891907	182381809510748268823 48838107157928333571673	8907182356542796852661213927290257141850879	43	142.676
1891907	1558931369 480563568131083519 182381809510748268823	136634181610060696637044931162639124156391129553	48	156.581
1891907	1558931369 480563568131083519 48838107157928333571673	36587830885155952723764573922874385671964400835903	50	164.646
1891907	1558931369 182381809510748268823 48838107157928333571673	13885685985017908404608037520872467026507617993323 351	53	173.214
1891907	480563568131083519 182381809510748268823 48838107157928333571673	42804673352544394078843857456588549801263575767449 67392563201	61	201.413
1891907	1558931369 480563568131083519 182381809510748268823 48838107157928333571673	66729548029079851894607548642040446011408504100985 54581148911353952169	70	231.951

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-04-12T07:28:14	Lisander Viaene	Desktop	500000	2903586840		-	skipped known factor: 1558931369 skipped known factor: 480563568131083519	-	-	12.48	-	-	10.432%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-04-12T07:28:14

Lisander Viaene

Desktop

500000

2903586840

skipped known factor: 1558931369
skipped known factor: 480563568131083519

12.48

-

-

10.432%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2015-09-28T11:49:52	TJAOI	Manual testing	2⁵⁸	2⁵⁹*	480563568131083519	58.738	18	0.005	0.209	0.010

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2015-09-28T11:49:52

TJAOI

Manual testing

2⁵⁸

2⁵⁹*

480563568131083519

58.738

0.005

0.209

0.010

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.248 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:	19.248 GHz-days
Estimated T-Level:	24.464

Digits	B1	Complete	FacMiss
20	11000	8.543	0.019%
25	50000	0.774	46.108%
30	250000	0.048	95.323%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		28	1.941
50000	5000000	182381809510748268823	7	0.485
50000	6600000		36	2.816
50000	6600000	48838107157928333571673	172	13.45
50000	6750000		7	0.553

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-07T11:58:06	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-23T22:52:02	Dylan Delgado		50000	5000000						3	0.208
2020-07-25T08:03:23	Ahmed Azhad	c5.large.az	50000	5000000						3	0.208
2020-10-01T08:54:31	nordi	sweet16	50000	5000000						7	0.485
2020-11-30T04:47:56	Chang Chia-Tche	exbpc13	50000	5000000	182381809510748268823	67.306	7	2	1730276509208936	7	0.485
2021-02-26T23:29:18	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.485
2021-06-22T11:43:15	Daniil Tsarkov	9900KF	50000	5000000						7	0.485
2021-09-19T07:31:13	happy5214	Focus	50000	6750000						7	0.553
2021-11-19T10:19:04	TJAOI	Manual testing	50000	6600000	48838107157928333571673	75.370	172	2		172	13.45
2021-11-19T10:19:05	TJAOI	Manual testing	50000	6600000						36	2.816

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:49

alpertron

Manual testing

1558931369

480563568131083519

67ADBBACBFDA7B__

2017-10-20T03:03:45

Oliver Kruse

Threadripper

1558931369

480563568131083519

67ADBBACBFDA7B__

2020-12-01T01:39:22

Poao

pc-Home

1558931369

480563568131083519

182381809510748268823

E9A9483F919B0A52

2021-11-19T18:18:26

JackBlock

Win10

1558931369

480563568131083519

182381809510748268823

48838107157928333571673

E9A9483F919B0A52

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 = 2903586840 (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