M6919567 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	2⁶⁸	8.6140	66.1765%	4000000	164511270	4.0298	9.5386%	12.6437	69.4028%	3.2263%
PrimeNet	2⁶³	0.2307	63.4921%	28000	700000	0.0204	3.1600%	0.2511	64.6457%	1.1536%
GPU72	2⁶⁷	4.2942	65.6716%	45000	900000	0.0290	2.2363%	4.3231	66.4393%	0.7677%
Difference	+1	+4.3198	+0.5048%	+3955000	+163611270	+4.0008	+7.3024%	+8.3206	+2.9635%	+2.9635%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

8.6140

66.1765%

4000000

164511270

4.0298

9.5386%

12.6437

69.4028%

3.2263%

PrimeNet

2⁶³

0.2307

63.4921%

28000

700000

0.0204

3.1600%

0.2511

64.6457%

1.1536%

GPU72

2⁶⁷

4.2942

65.6716%

45000

900000

0.0290

2.2363%

4.3231

66.4393%

0.7677%

Difference

+4.3198

+0.5048%

+3955000

+163611270

+4.0008

+7.3024%

+8.3206

+2.9635%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6919567	1065613319	10	29.989	77 7 × 11	-	7	11	1.051e-11	2.282e-6	4.504e-6
6919567	17277813881391942833	20	63.906	1248475076648 2³ × 29 × 5381358089	2017-06-07	29	5381358089	0.3933	92.701	173.14
6919567	200205724370654180831	21	67.440	14466636739745 5 × 2893327347949	2022-08-03	5	2893327347949	6.9917	49,842	93,090

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6919567

1065613319

29.989

77
7 × 11

1.051e-11

2.282e-6

4.504e-6

6919567

17277813881391942833

63.906

1248475076648
2³ × 29 × 5381358089

2017-06-07

5381358089

0.3933

92.701

173.14

6919567

200205724370654180831

67.440

14466636739745
5 × 2893327347949

2022-08-03

2893327347949

6.9917

49,842

93,090

exponent	prime factors	composite factor	digits	bits*
6919567	1065613319 17277813881391942833	18411468595214340542131392727	29	93.895
6919567	1065613319 200205724370654180831	213341886429411987836548088089	30	97.429
6919567	17277813881391942833 200205724370654180831	3459117243665417993405187256809196434223	40	131.346
6919567	1065613319 17277813881391942833 200205724370654180831	3686081406832437793474821704544953161995336216137	49	161.335

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-08-10T02:32:28	riccardo uberti	Colab_noGPU14	4000000	164511270		-	skipped known factor: 1065613319	-	-	4.030	-	-	9.539%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-08-13T04:46:45	riccardo uberti	Colab_noGPU15	4000000	80000000	2	7			-	-	3.205
2022-08-17T03:03:53	riccardo uberti	Colab_noGPU15	4600000	96000000	6	5			-	-	3.754

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-08-10T19:28:49	LordJulius	Manual testing	2¹	2⁶³	1065613319	29.989	10	1.05083e-11	3.296	2.29519e-11
2017-06-07T16:19:34	TJAOI	Manual testing	2⁶³	2⁶⁴*	17277813881391942833	63.906	20	0.163	3.065	0.330
2022-08-10T19:28:49	LordJulius	Manual testing	2⁶³	2⁶⁴	17277813881391942833	63.906	20	0.163	3.065	0.330
2022-08-04T14:08:18	J.R. Allen	Manual testing	2⁶⁴	2⁶⁵		-	-	0.540	-	-
2022-08-10T19:28:49	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.540	-	-
2022-08-10T19:28:49	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	1.080	-	-
2022-08-10T19:28:49	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	2.160	-	-
2022-08-03T11:18:52	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200205724370654180831	67.440	21	2.698	3.065	5.479
2022-08-10T19:28:49	LordJulius	Manual testing	2⁶⁷	2⁶⁸	200205724370654180831	67.440	21	2.698	3.065	5.479

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.417 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	6.417 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.500	60.653%
25	50000	0.048	95.284%
30	250000	0.003	99.688%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		10	6.417

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2022-08-10T22:13:38	riccardo uberti	Colab_noGPU12	50000	14400000						10	6.417

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-22T18:04:06

Oliver Kruse

GTX-0

1065613319

17277813881391942833

A9C8E18A9600F5__

2019-01-25T13:16:13

Chang Chia-Tche

exbbbe-lt

1065613319

17277813881391942833

A9C8E18A9600F506

2022-08-08T23:17:47

riccardo uberti

Colab_noGPU11

1065613319

17277813881391942833

200205724370654180831

A9C8E18A9600F506

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 = 4000000, B2 = 164511270 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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