M9157219 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	3.2449	64.1791%	-	-	-	-	3.2449	64.1791%	0.0000%
PrimeNet	2⁶⁴	0.3887	62.5000%	40000	1000000	0.0370	3.4065%	0.4257	63.7774%	1.2774%
GPU72	2⁶⁸	6.5091	64.7059%	60000	1300000	0.0511	2.4065%	6.5602	65.5552%	0.8494%
Difference	-1	-3.2642	-0.5268%	-60000	-1300000	-0.0511	-2.4065%	-3.3153	-1.3761%	-1.3761%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.2449

64.1791%

3.2449

64.1791%

0.0000%

PrimeNet

2⁶⁴

0.3887

62.5000%

40000

1000000

0.0370

3.4065%

0.4257

63.7774%

1.2774%

GPU72

2⁶⁸

6.5091

64.7059%

60000

1300000

0.0511

2.4065%

6.5602

65.5552%

0.8494%

Difference

-1

-3.2642

-0.5268%

-60000

-1300000

-0.0511

-2.4065%

-3.3153

-1.3761%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9157219	198173772933098929	18	57.460	10820630856 2³ × 3 × 7 × 64408517	1999-01-17	8	64408517	0.0040	1.4063	2.6267
9157219	273777812617527802338049	24	77.857	14948742222804096 2⁷ × 3² × 7 × 509513 × 3638303	2021-11-09	509513	3638303	4,801.1	0.2725	0.4156

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9157219

198173772933098929

57.460

10820630856
2³ × 3 × 7 × 64408517

1999-01-17

64408517

0.0040

1.4063

2.6267

9157219

273777812617527802338049

77.857

14948742222804096
2⁷ × 3² × 7 × 509513 × 3638303

2021-11-09

509513

3638303

4,801.1

0.2725

0.4156

exponent	prime factors	composite factor	digits	bits*
9157219	198173772933098929 273777812617527802338049	54255582071786461641579468440185217849521	41	135.317

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-11-09T01:46:33	riccardo uberti	Colab_noGPU15	2000000	40000000	2	7	273777812617527802338049	P-1	24	77.857	2.031
2021-11-25T10:27:48	riccardo uberti	Colab_noGPU15	3000000	60000000	2	7			-	-	3.047
2021-11-27T03:53:58	riccardo uberti	Colab_noGPU15	3000000	60000000	6	5			-	-	3.047

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	delong	v4_computers	?	?	198173772933098929	57.460	18	0.002	5.525	0.004

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.134 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:	8.134 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.435	64.741%
25	50000	0.040	96.125%
30	250000	0.003	99.748%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		10	8.134

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2020-08-09T08:37:26	riccardo uberti	Colab_noGPU7	50000	14400000						10	8.134

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-31T22:39:36

riccardo uberti

Colab_noGPU12

198173772933098929

37709D5DE2EF8B__

2020-12-19T11:37:43

Oliver Kruse

IOS-5

198173772933098929

37709D5DE2EF8BAC

2021-11-09T17:00:46

riccardo uberti

Nomad2C

198173772933098929

273777812617527802338049

37709D5DE2EF8BAC

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 = 2000000, B2 = 40000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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