M3249583 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	2⁶⁹	36.7391	68.1159%	1150000	116447100	0.9172	6.9730%	37.6563	70.3392%	2.2233%
PrimeNet	2⁶⁰	0.0473	63.3333%	14000	260000	0.0034	2.7708%	0.0506	64.3493%	1.0160%
GPU72	2⁶⁴	1.0953	65.6250%	16000	280000	0.0037	1.6548%	1.0991	66.1938%	0.5688%
Difference	+5	+35.6438	+2.4909%	+1134000	+116167100	+0.9134	+5.3182%	+36.5572	+4.1454%	+4.1454%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

36.7391

68.1159%

1150000

116447100

0.9172

6.9730%

37.6563

70.3392%

2.2233%

PrimeNet

2⁶⁰

0.0473

63.3333%

14000

260000

0.0034

2.7708%

0.0506

64.3493%

1.0160%

GPU72

2⁶⁴

1.0953

65.6250%

16000

280000

0.0037

1.6548%

1.0991

66.1938%

0.5688%

Difference

+35.6438

+2.4909%

+1134000

+116167100

+0.9134

+5.3182%

+36.5572

+4.1454%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3249583	76794145457	11	36.160	11816 2³ × 7 × 211	-	8	211	4.388e-9	2.352e-6	2.702e-6
3249583	322240192798817	15	48.195	49581776 2⁴ × 37 × 61 × 1373	2014-03-27	61	1373	2.292e-5	1.635e-5	1.728e-5
3249583	483370707525981912655471	24	78.677	74374267025335545 3³ × 5 × 550920496483967	2018-09-21	27	550920496483967	20,245	3,704,267	6,918,539

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3249583

76794145457

36.160

11816
2³ × 7 × 211

211

4.388e-9

2.352e-6

2.702e-6

3249583

322240192798817

48.195

49581776
2⁴ × 37 × 61 × 1373

2014-03-27

1373

2.292e-5

1.635e-5

1.728e-5

3249583

483370707525981912655471

78.677

74374267025335545
3³ × 5 × 550920496483967

2018-09-21

550920496483967

20,245

3,704,267

6,918,539

exponent	prime factors	composite factor	digits	bits*
3249583	76794145457 322240192798817	24746160237884076635524369	26	84.355
3249583	76794145457 483370707525981912655471	37120040423403259607215309100845247	35	114.838
3249583	322240192798817 483370707525981912655471	155761469986472994996408498412137377807	39	126.873
3249583	76794145457 322240192798817 483370707525981912655471	11961568982737347000156627419652631325577321672799	50	163.033

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-08-03T14:28:36	Jocelyn Larouche	Manual testing	324958	3249583	6	-	skipped known factor: 76794145457 skipped known factor: 322240192798817	-	-	0.060	-	-	3.049%
2022-01-06T19:15:41	Jocelyn Larouche	Manual testing	1150000	116447100		-	skipped known factor: 76794145457 skipped known factor: 322240192798817	-	-	0.917	-	-	6.973%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-03-27T11:47:00	TJAOI	Manual testing	?	?	322240192798817	48.195	15	1.13794e-5	0.609	2.50401e-5
2021-09-11T10:41:50	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.198	-	-
2021-11-14T23:34:16	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.353 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:	0.353 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	483370707525981912655471	3	0.353

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-21T07:35:10	ATH	ec2-ECMCF	50000	5000000	483370707525981912655471	78.677	3	2		3	0.353

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-02T14:58:30

Oliver Kruse

GTX-3

76794145457

322240192798817

C32D55120ECCC5__

2017-12-13T19:45:55

kkmrkkblmbrbk

c4.xlarge

76794145457

322240192798817

C32D55120ECCC5__

2018-09-21T09:15:00

ATH

ec2-PRPCF

76794145457

322240192798817

483370707525981912655471

C32D55120ECCC5__

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 = 1150000, B2 = 116447100 (P-1 stage 2)

B1 = 1150000 (P-1 stage 1)

B1 = 324958, B2 = 3249583 (P-1 stage 2)

B1 = 324958 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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