M9874103 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

4E4D486D5BBDBB__

unverified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	3.0093	64.1791%	-	-	-	-	3.0093	64.1791%	0.0000%
PrimeNet	2⁶⁴	0.3605	62.5000%	45000	1200000	0.0456	3.6719%	0.4061	63.8770%	1.3770%
GPU72	2⁶⁸	6.0365	64.7059%	65000	1500000	0.0606	2.5628%	6.0970	65.6104%	0.9045%
Difference	-1	-3.0272	-0.5268%	-65000	-1500000	-0.0606	-2.5628%	-3.0878	-1.4313%	-1.4313%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.0093

64.1791%

3.0093

64.1791%

0.0000%

PrimeNet

2⁶⁴

0.3605

62.5000%

45000

1200000

0.0456

3.6719%

0.4061

63.8770%

1.3770%

GPU72

2⁶⁸

6.0365

64.7059%

65000

1500000

0.0606

2.5628%

6.0970

65.6104%

0.9045%

Difference

-1

-3.0272

-0.5268%

-65000

-1500000

-0.0606

-2.5628%

-3.0878

-1.4313%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9874103	19748207	8	24.235	1 1	-	1	1	2.264e-13	4.229e-7	8.607e-7
9874103	2018128415759	13	40.876	102193 7 × 13 × 1123	2008-09-30	13	1123	1.661e-8	3.107e-5	4.827e-5
9874103	649323225493129179265951	24	79.103	32880112020966825 3⁴ × 5² × 59 × 11261 × 24438767	2022-07-30	11261	24438767	20,250	0.5676	1.0517

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9874103

19748207

24.235

1
1

2.264e-13

4.229e-7

8.607e-7

9874103

2018128415759

40.876

102193
7 × 13 × 1123

2008-09-30

1123

1.661e-8

3.107e-5

4.827e-5

9874103

649323225493129179265951

79.103

32880112020966825
3⁴ × 5² × 59 × 11261 × 24438767

2022-07-30

11261

24438767

20,250

0.5676

1.0517

exponent	prime factors	composite factor	digits	bits*
9874103	19748207 2018128415759	39854417706990794113	20	65.111
9874103	19748207 649323225493129179265951	12822969466945992109884108399857	32	103.339
9874103	2018128415759 649323225493129179265951	1310417652379972712091529602160521809	37	119.979
9874103	19748207 2018128415759 649323225493129179265951	25878399055653743772734929530093631912146463	44	144.215

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-07-30T03:25:00	riccardo uberti	Colab_noGPU15	2000000	50000000	2	7	649323225493129179265951	P-1	24	79.103	2.370
2022-08-01T02:10:12	riccardo uberti	Colab_noGPU15	2300000	60000000	6	5			-	-	2.781

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T23:58:00	markr	Manual testing	?	?	2018128415759	40.876	13	1.77562e-9	6.216	3.83260e-9

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.168 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	17.168 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.097	90.790%
30	250000	0.006	99.377%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		20	17.17

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2020-10-09T23:12:33	riccardo uberti	Colab_noGPU9	50000	14400000						10	8.584
2022-08-02T16:39:58	riccardo uberti	Colab_noGPU12	50000	14400000						10	8.584

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-10T07:49:57

riccardo uberti

Nomad2C

19748207

2018128415759

4E4D486D5BBDBB__

2021-02-09T21:31:36

Oliver Kruse

IOS-5

19748207

2018128415759

4E4D486D5BBDBB73

2022-07-31T04:30:32

riccardo uberti

Nomad2C

19748207

2018128415759

649323225493129179265951

4E4D486D5BBDBB73

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 = 50000000 (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