M2116783 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	14.0373	67.1642%	500000	15000000	0.1230	5.1581%	14.1603	68.8579%	1.6937%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6818%	0.0198	63.0862%	1.0172%
GPU72	2⁶²	0.2902	64.5161%	10000	140000	0.0016	1.4537%	0.2919	65.0319%	0.5158%
Difference	+5	+13.7471	+2.6481%	+490000	+14860000	+0.1214	+3.7045%	+13.8684	+3.8259%	+3.8259%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0373

67.1642%

500000

15000000

0.1230

5.1581%

14.1603

68.8579%

1.6937%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6818%

0.0198

63.0862%

1.0172%

GPU72

2⁶²

0.2902

64.5161%

10000

140000

0.0016

1.4537%

0.2919

65.0319%

0.5158%

Difference

+13.7471

+2.6481%

+490000

+14860000

+0.1214

+3.7045%

+13.8684

+3.8259%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2116783	333883336596671	15	48.246	78865745 5 × 7² × 321901	-	49	321901	2.671e-5	0.0017	0.0031
2116783	574224618412297	15	49.029	135636156 2² × 3² × 3767671	2014-04-22	9	3767671	5.227e-5	0.0196	0.0366
2116783	6183994330445047	16	52.457	1460705781 3 × 23 × 21169649	2014-08-09	23	21169649	0.0003	0.1100	0.2054

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2116783

333883336596671

48.246

78865745
5 × 7² × 321901

321901

2.671e-5

0.0017

0.0031

2116783

574224618412297

49.029

135636156
2² × 3² × 3767671

2014-04-22

3767671

5.227e-5

0.0196

0.0366

2116783

6183994330445047

52.457

1460705781
3 × 23 × 21169649

2014-08-09

21169649

0.0003

0.1100

0.2054

exponent	prime factors	composite factor	digits	bits*
2116783	333883336596671 574224618412297	191724031551447923075475663287	30	97.275
2116783	333883336596671 6183994330445047	2064732660543888738177768638537	31	100.704
2116783	574224618412297 6183994330445047	3551001784663615194026547542959	31	101.486
2116783	333883336596671 574224618412297 6183994330445047	1185620324124221264658894907640768380228889489	46	149.732

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-25T16:40:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 333883336596671 skipped known factor: 574224618412297	-	-	0.123	-	-	5.158%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-08-09T10:56:00	ANONYMOUS	Manual testing	?	?	6183994330445047	52.457	16	2.33738e-5	0.301	5.04681e-5
2014-04-22T10:31:00	TJAOI	Manual testing	?	?	574224618412297	49.029	15	1.68402e-5	0.301	3.64209e-5

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.417 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.417 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	1.072	34.244%
25	50000	0.099	90.588%
30	250000	0.006	99.376%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	13	1.107
50000	5450000	7	0.618
50000	6944559	7	0.691

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-07T02:46:35	Gordon Spence	haswell	50000	5000000						3	0.256
2019-09-22T10:29:15	ATH	ec2-ECMCF	50000	5000000						3	0.256
2021-11-14T02:17:54	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596
2022-04-02T00:52:41	Eric	miniPCWindows	50000	5450000						7	0.618
2022-06-22T03:07:52	debrouxl	dl380g9-1	50000	6944559						7	0.691

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T05:34:41

Oliver Kruse

GTX-3

333883336596671

574224618412297

6183994330445047

99F2C77C9CB04774

2017-10-17T22:23:09

Oliver Kruse

GTX-0

333883336596671

574224618412297

6183994330445047

E14892E81E3A2D__

2017-11-17T19:27:04

kkmrkkblmbrbk

old

333883336596671

574224618412297

6183994330445047

E14892E81E3A2D__

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