M4915109 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	6.0454	65.6716%	-	-	-	-	6.0454	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0625	62.2951%	22000	450000	0.0091	3.3038%	0.0716	63.5408%	1.2457%
GPU72	2⁶⁵	1.4843	64.6154%	32000	700000	0.0137	2.3752%	1.4981	65.4559%	0.8405%
Difference	+2	+4.5611	+1.0563%	-32000	-700000	-0.0137	-2.3752%	+4.5473	+0.2158%	+0.2158%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.0454

65.6716%

6.0454

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0625

62.2951%

22000

450000

0.0091

3.3038%

0.0716

63.5408%

1.2457%

GPU72

2⁶⁵

1.4843

64.6154%

32000

700000

0.0137

2.3752%

1.4981

65.4559%

0.8405%

Difference

+4.5611

+1.0563%

-32000

-700000

-0.0137

-2.3752%

+4.5473

+0.2158%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4915109	173929372007615449	18	57.271	17693338236 2² × 3 × 7 × 109 × 1932431	-	109	1932431	0.0074	0.0212	0.0395
4915109	216147086177886089	18	57.585	21988025716 2² × 5497006429	2015-08-06	4	5497006429	0.0075	60.194	112.43
4915109	376726469889084870703	21	68.352	38323307772939 3 × 7 × 1019 × 1790892461	2019-08-05	1019	1790892461	18.706	19.611	36.627

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4915109

173929372007615449

57.271

17693338236
2² × 3 × 7 × 109 × 1932431

109

1932431

0.0074

0.0212

0.0395

4915109

216147086177886089

57.585

21988025716
2² × 5497006429

2015-08-06

5497006429

0.0075

60.194

112.43

4915109

376726469889084870703

68.352

38323307772939
3 × 7 × 1019 × 1790892461

2019-08-05

1019

1790892461

18.706

19.611

36.627

exponent	prime factors	composite factor	digits	bits*
4915109	173929372007615449 216147086177886089	37594326960195664858592404438588961	35	114.856
4915109	173929372007615449 376726469889084870703	65523798326454382434464350005510290647	38	125.623
4915109	216147086177886089 376726469889084870703	81428328752606836360485792896427350567	38	125.937
4915109	173929372007615449 216147086177886089 376726469889084870703	14162778083570563695856770552752295298769458694448 109583	56	183.208

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-07-01T11:25:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	216147086177886089	57.585	18	0.004	1.439	0.008

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.420 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.420 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	376726469889084870703	2	0.420

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-08-05T19:04:30	MarkS	laptop64	50000	5000000	376726469889084870703	68.352	2	2		2	0.420

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:45:23

kkmrkkblmbrbk

Manual testing

173929372007615449

216147086177886089

376953C020F574__

2018-04-09T09:27:50

Oliver Kruse

GTX-5

173929372007615449

216147086177886089

376953C020F574__

2019-08-06T07:50:17

Niels_Mache_Nextcloud

SuperDry-X

173929372007615449

216147086177886089

376726469889084870703

6298D9F2EF4BAC7D

2019-08-06T08:50:03

ATH

ec2-PRPCFDC

173929372007615449

216147086177886089

376726469889084870703

6298D9F2EF4BAC7D

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

10⁰

10¹

10²

10³

10⁴

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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