M2936753 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	10.1179	67.1642%	-	-	-	-	10.1179	67.1642%	0.0000%
PrimeNet	2⁵⁹	0.0261	62.7119%	13000	260000	0.0033	3.0712%	0.0294	63.8570%	1.1452%
GPU72	2⁶³	0.5435	65.0794%	17000	300000	0.0040	1.9460%	0.5475	65.7589%	0.6795%
Difference	+4	+9.5745	+2.0848%	-17000	-300000	-0.0040	-1.9460%	+9.5705	+1.4053%	+1.4053%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.1179

67.1642%

10.1179

67.1642%

0.0000%

PrimeNet

2⁵⁹

0.0261

62.7119%

13000

260000

0.0033

3.0712%

0.0294

63.8570%

1.1452%

GPU72

2⁶³

0.5435

65.0794%

17000

300000

0.0040

1.9460%

0.5475

65.7589%

0.6795%

Difference

+9.5745

+2.0848%

-17000

-300000

-0.0040

-1.9460%

+9.5705

+1.4053%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2936753	1920636463	10	30.839	327 3 × 109	-	3	109	5.216e-11	1.083e-6	1.316e-6
2936753	42136160814926777	17	55.226	7173936796 2² × 13 × 31 × 4450333	2015-07-21	31	4450333	0.0019	0.0299	0.0559
2936753	11161535679980353169	20	63.275	1900319107528 2³ × 6703 × 35437847	2017-01-17	6703	35437847	0.6430	0.2391	0.4450

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2936753

1920636463

30.839

327
3 × 109

109

5.216e-11

1.083e-6

1.316e-6

2936753

42136160814926777

55.226

7173936796
2² × 13 × 31 × 4450333

2015-07-21

4450333

0.0019

0.0299

0.0559

2936753

11161535679980353169

63.275

1900319107528
2³ × 6703 × 35437847

2017-01-17

6703

35437847

0.6430

0.2391

0.4450

exponent	prime factors	composite factor	digits	bits*
2936753	1920636463 42136160814926777	80928246871980162581269751	26	86.065
2936753	1920636463 11161535679980353169	21437252410045765419999001247	29	94.114
2936753	42136160814926777 11161535679980353169	470304262353195256042383671334906313	36	118.501
2936753	1920636463 42136160814926777 11161535679980353169	903283514979864993313623152601628949436690919	45	149.340

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-01-13T12:23:00	TJAOI	Manual testing	2⁵⁵	2⁵⁶*	42136160814926777	55.226	17	0.000	0.531	0.001
2022-03-10T18:31:22	LordJulius	Manual testing	2¹	2⁶²	1920636463	30.839	10	5.21550e-11	0.534	1.11479e-10
2022-03-10T18:31:23	LordJulius	Manual testing	2¹	2⁶²	42136160814926777	55.226	17	0.002	0.531	0.004
2022-03-10T18:31:23	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.334	-	-
2017-01-17T17:27:55	TJAOI	Manual testing	2⁶³	2⁶⁴*	11161535679980353169	63.275	20	0.100	0.508	0.202

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.347 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.347 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.347

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-05-30T16:47:23	ATH	ec2-ECMCF	50000	5000000						3	0.347

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-25T05:40:00

Oliver Kruse

GTX-3

1920636463

42136160814926777

11161535679980353169

1B8742BDE9564D__

2017-12-09T17:02:59

trebor

Laptop

1920636463

42136160814926777

11161535679980353169

1B8742BDE9564D__

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

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁵⁶

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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