M3200929 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	18.6211	67.6471%	1000000	119912100	0.9229	7.5070%	19.5441	70.0758%	2.4287%
PrimeNet	2⁶⁰	0.0480	63.3333%	13000	240000	0.0031	2.6576%	0.0511	64.3078%	0.9744%
GPU72	2⁶⁴	1.1120	65.6250%	16000	260000	0.0036	1.6158%	1.1156	66.1804%	0.5554%
Difference	+4	+17.5092	+2.0221%	+984000	+119652100	+0.9193	+5.8912%	+18.4285	+3.8954%	+3.8954%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.6211

67.6471%

1000000

119912100

0.9229

7.5070%

19.5441

70.0758%

2.4287%

PrimeNet

2⁶⁰

0.0480

63.3333%

13000

240000

0.0031

2.6576%

0.0511

64.3078%

0.9744%

GPU72

2⁶⁴

1.1120

65.6250%

16000

260000

0.0036

1.6158%

1.1156

66.1804%

0.5554%

Difference

+17.5092

+2.0221%

+984000

+119652100

+0.9193

+5.8912%

+18.4285

+3.8954%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3200929	224065031	9	27.739	35 5 × 7	-	5	7	5.628e-12	6.305e-7	1.256e-6
3200929	52975739381041780993	20	65.522	8275056925824 2⁷ × 3² × 13 × 552554549	2018-08-30	128	552554549	3.9892	3.7153	6.9391

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3200929

224065031

27.739

35
5 × 7

5.628e-12

6.305e-7

1.256e-6

3200929

52975739381041780993

65.522

8275056925824
2⁷ × 3² × 13 × 552554549

2018-08-30

128

552554549

3.9892

3.7153

6.9391

exponent	prime factors	composite factor	digits	bits*
3200929	224065031 52975739381041780993	11870010686661047470491755783	29	93.261

exponent

prime factors

composite factor

digits

bits*

3200929

224065031
52975739381041780993

11870010686661047470491755783

93.261

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-25T11:56:46	Jocelyn Larouche	Manual testing	320092	3200929	6	-	skipped known factor: 224065031	-	-	0.059	-	-	3.366%
2022-02-09T23:48:31	Jocelyn Larouche	Manual testing	1000000	119912100		-	skipped known factor: 224065031	-	-	0.923	-	-	7.507%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-09-28T10:32:38	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.338	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.470 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	0.470 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.154	85.740%
25	50000	0.014	98.587%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.352
50000	5000000	52975739381041780993	1	0.117

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-08-30T13:27:25	ATH	ec2-ECMCF	50000	5000000	52975739381041780993	65.522	1	2		1	0.117
2019-04-07T17:56:20	ATH	ec2-ECMCF	50000	5000000						3	0.352

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-01T14:11:47

Oliver Kruse

GTX-0

224065031

BF6E258067B194__

2017-12-13T04:58:25

kkmrkkblmbrbk

c4.xlarge

224065031

BF6E258067B194__

2018-09-01T13:39:45

Oliver Kruse

GTX-1

224065031

52975739381041780993

BF6E258067B194__

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 = 320092, B2 = 3200929 (P-1 stage 2)

B1 = 320092 (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