M3096811 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	19.2472	67.6471%	1000000	119912100	0.9229	7.4807%	20.1701	70.0673%	2.4202%
PrimeNet	2⁶⁰	0.0496	63.3333%	12000	220000	0.0029	2.5299%	0.0525	64.2610%	0.9276%
GPU72	2⁶⁴	1.1494	65.6250%	14000	240000	0.0032	1.5068%	1.1526	66.1430%	0.5180%
Difference	+4	+18.0978	+2.0221%	+986000	+119672100	+0.9197	+5.9738%	+19.0175	+3.9243%	+3.9243%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.2472

67.6471%

1000000

119912100

0.9229

7.4807%

20.1701

70.0673%

2.4202%

PrimeNet

2⁶⁰

0.0496

63.3333%

12000

220000

0.0029

2.5299%

0.0525

64.2610%

0.9276%

GPU72

2⁶⁴

1.1494

65.6250%

14000

240000

0.0032

1.5068%

1.1526

66.1430%

0.5180%

Difference

+18.0978

+2.0221%

+986000

+119672100

+0.9197

+5.9738%

+19.0175

+3.9243%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3096811	543880528687	12	38.984	87813 3² × 11 × 887	-	11	887	1.191e-8	7.248e-6	1.110e-5
3096811	104268563471411028511	21	66.499	16834828388205 3 × 5 × 43 × 599 × 43573471	2018-07-14	599	43573471	7.3230	0.2930	0.5472

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3096811

543880528687

38.984

87813
3² × 11 × 887

887

1.191e-8

7.248e-6

1.110e-5

3096811

104268563471411028511

66.499

16834828388205
3 × 5 × 43 × 599 × 43573471

2018-07-14

599

43573471

7.3230

0.2930

0.5472

exponent	prime factors	composite factor	digits	bits*
3096811	543880528687 104268563471411028511	56709641426265046196445110395057	32	105.483

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-06T09:07:43	Jocelyn Larouche	Manual testing	309681	3406492	6	-	skipped known factor: 543880528687	-	-	0.059	-	-	3.387%
2021-03-06T21:38:21	Jocelyn Larouche	Manual testing	309681	6503303	6	-	skipped known factor: 543880528687	-	-	0.080	-	-	3.909%
2022-01-23T13:34:49	Jocelyn Larouche	Manual testing	1000000	119912100		-	skipped known factor: 543880528687 skipped known factor: 104268563471411028511	-	-	0.923	-	-	7.481%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-06-22T11:14:40	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	104268563471411028511	3	0.350

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-14T21:40:56	ATH	ec2-ECMCF	50000	5000000	104268563471411028511	66.499	3	2		3	0.350

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T14:26:11

alpertron

laptop2

543880528687

B8C8403CC00F81__

2017-11-17T23:30:35

Oliver Kruse

Threadripper

543880528687

B8C8403CC00F81__

2018-07-15T17:19:26

GunnarLu

Ribenboim

543880528687

104268563471411028511

B8C8403CC00F81__

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 = 309681, B2 = 6503303 (P-1 stage 2)

B1 = 309681, B2 = 3406492 (P-1 stage 2)

B1 = 309681 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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