M9544097 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	3.1133	64.1791%	-	-	-	-	3.1133	64.1791%	0.0000%
PrimeNet	2⁶⁴	0.3729	62.5000%	40000	1100000	0.0392	3.5031%	0.4121	63.8137%	1.3137%
GPU72	2⁶⁸	6.2452	64.7059%	60000	1400000	0.0533	2.4658%	6.2985	65.5762%	0.8703%
Difference	-1	-3.1319	-0.5268%	-60000	-1400000	-0.0533	-2.4658%	-3.1852	-1.3970%	-1.3970%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.1133

64.1791%

3.1133

64.1791%

0.0000%

PrimeNet

2⁶⁴

0.3729

62.5000%

40000

1100000

0.0392

3.5031%

0.4121

63.8137%

1.3137%

GPU72

2⁶⁸

6.2452

64.7059%

60000

1400000

0.0533

2.4658%

6.2985

65.5762%

0.8703%

Difference

-1

-3.1319

-0.5268%

-60000

-1400000

-0.0533

-2.4658%

-3.1852

-1.3970%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9544097	76352777	8	26.186	4 2²	-	4	4	9.375e-13	1.603e-6	3.262e-6
9544097	229058329	9	27.771	12 2² × 3	2008-09-08	4	4	1.878e-12	1.603e-6	3.262e-6
9544097	308566764232081	15	48.133	16165320 2³ × 3 × 5 × 23 × 5857	2014-03-27	23	5857	7.807e-6	0.0001	0.0002
9544097	32368319498777046658098551	26	84.743	1695724566649786075 5² × 13 × 470333 × 11093446667	2022-03-07	470333	11093446667	692,610	242.40	452.40

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9544097

76352777

26.186

4
2²

9.375e-13

1.603e-6

3.262e-6

9544097

229058329

27.771

12
2² × 3

2008-09-08

1.878e-12

1.603e-6

3.262e-6

9544097

308566764232081

48.133

16165320
2³ × 3 × 5 × 23 × 5857

2014-03-27

5857

7.807e-6

0.0001

0.0002

9544097

32368319498777046658098551

84.743

1695724566649786075
5² × 13 × 470333 × 11093446667

2022-03-07

470333

11093446667

692,610

242.40

452.40

exponent	prime factors	composite factor	digits	bits*
9544097	76352777 229058329	17489239514129633	17	53.957
9544097	76352777 308566764232081	23559929339023656838937	23	74.319
9544097	229058329 308566764232081	70679787399937442052649	23	75.904
9544097	76352777 229058329 308566764232081	5396598045754833326996331356273	31	102.090
9544097	76352777 32368319498777046658098551	2471411080554875616204393908526127	34	110.929
9544097	229058329 32368319498777046658098551	7414233176927987851059088409381279	34	112.514
9544097	308566764232081 32368319498777046658098551	9987787611367807202362160040617133814631	40	132.875
9544097	76352777 229058329 32368319498777046658098551	566097292383984201450623791144773503461783	42	138.700
9544097	76352777 308566764232081 32368319498777046658098551	762595320214128848300951878819550960527680080287	48	159.062
9544097	229058329 308566764232081 32368319498777046658098551	2287785940666811322167241231734332800348772611599	49	160.647
9544097	76352777 229058329 308566764232081 32368319498777046658098551	17467880975146827618251052647181683554881535743712 6060423	57	186.833

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-03-07T03:21:31	riccardo uberti	Colab_noGPU15	2000000	2000000	2	7	32368319498777046658098551	P+1	26	84.743	1.218
2022-03-11T20:13:58	riccardo uberti	Colab_noGPU15	2300000	48000000	6	5			-	-	2.379

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T05:32:00	Will Edgington	Manual testing	?	?	229058329	27.771	9	4.86607e-15	5.731	1.05727e-14
2014-03-27T11:19:00	TJAOI	Manual testing	?	?	308566764232081	48.133	15	3.87785e-6	5.731	8.42554e-6

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
2020-08-17T20:13:36	riccardo uberti	Colab_noGPU10	50000	14400000						10	8.134

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-12T01:35:32

riccardo uberti

Nomad2C

76352777

229058329

308566764232081

DF5206C1E24D3E__

2020-12-21T13:35:47

Oliver Kruse

IOS-5

76352777

229058329

308566764232081

DF5206C1E24D3ED2

2022-03-07T16:31:20

riccardo uberti

Nomad2C

76352777

229058329

308566764232081

32368319498777046658098551

DF5206C1E24D3ED2

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 (P+1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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