M3047563 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	19.5582	67.6471%	1000000	119912100	0.9229	7.4679%	20.4812	70.0632%	2.4161%
PrimeNet	2⁶⁰	0.0504	63.3333%	12000	220000	0.0029	2.5224%	0.0533	64.2582%	0.9249%
GPU72	2⁶⁴	1.1679	65.6250%	13000	220000	0.0030	1.4307%	1.1709	66.1168%	0.4918%
Difference	+4	+18.3903	+2.0221%	+987000	+119692100	+0.9200	+6.0372%	+19.3102	+3.9463%	+3.9463%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.5582

67.6471%

1000000

119912100

0.9229

7.4679%

20.4812

70.0632%

2.4161%

PrimeNet

2⁶⁰

0.0504

63.3333%

12000

220000

0.0029

2.5224%

0.0533

64.2582%

0.9249%

GPU72

2⁶⁴

1.1679

65.6250%

13000

220000

0.0030

1.4307%

1.1709

66.1168%

0.4918%

Difference

+18.3903

+2.0221%

+987000

+119692100

+0.9200

+6.0372%

+19.3102

+3.9463%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3047563	76802805427193	14	46.126	12600692 2² × 13 × 443 × 547	-	443	547	4.376e-6	5.537e-5	0.0001

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3047563

76802805427193

46.126

12600692
2² × 13 × 443 × 547

443

547

4.376e-6

5.537e-5

0.0001

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-16T16:09:50	Jocelyn Larouche	Manual testing	304756	3047563	6	-	skipped known factor: 76802805427193	-	-	0.056	-	-	3.285%
2022-02-05T08:19:06	Jocelyn Larouche	Manual testing	1000000	119912100		-	skipped known factor: 76802805427193	-	-	0.923	-	-	7.468%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-05-17T16:57:22	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.81	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.699 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	0.699 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.699

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-06-27T05:56:05	alpertron		50000	5000000						3	0.349
2018-09-28T16:59:19	alpertron	Manual testing	50000	5000000						3	0.349

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-28T08:50:12

Oliver Kruse

GTX-1

76802805427193

7C3B9093C43996__

2017-12-10T23:32:26

kkmrkkblmbrbk

c4.xlarge

76802805427193

7C3B9093C43996__

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 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 304756, B2 = 3047563 (P-1 stage 2)

B1 = 304756 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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