M3204251 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	18.6018	67.6471%	1150000	116447100	0.9172	7.5885%	19.5190	70.1021%	2.4551%
PrimeNet	2⁶⁰	0.0479	63.3333%	13000	240000	0.0031	2.6581%	0.0511	64.3080%	0.9746%
GPU72	2⁶⁴	1.1108	65.6250%	16000	260000	0.0036	1.6161%	1.1144	66.1805%	0.5555%
Difference	+4	+17.4910	+2.0221%	+1134000	+116187100	+0.9135	+5.9723%	+18.4045	+3.9216%	+3.9216%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.6018

67.6471%

1150000

116447100

0.9172

7.5885%

19.5190

70.1021%

2.4551%

PrimeNet

2⁶⁰

0.0479

63.3333%

13000

240000

0.0031

2.6581%

0.0511

64.3080%

0.9746%

GPU72

2⁶⁴

1.1108

65.6250%

16000

260000

0.0036

1.6161%

1.1144

66.1805%

0.5555%

Difference

+17.4910

+2.0221%

+1134000

+116187100

+0.9135

+5.9723%

+18.4045

+3.9216%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3204251	6408503	7	22.612	1 1	-	1	1	1.744e-13	1.234e-7	2.512e-7
3204251	11669113121761	14	43.408	1820880 2⁴ × 3⁴ × 5 × 281	2013-12-20	81	281	4.132e-7	1.134e-5	2.034e-5
3204251	66429630578580601663	20	65.848	10365859381581 3² × 11 × 19 × 463 × 11902427	2018-09-02	463	11902427	4.2259	0.0801	0.1495

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3204251

6408503

22.612

1
1

1.744e-13

1.234e-7

2.512e-7

3204251

11669113121761

43.408

1820880
2⁴ × 3⁴ × 5 × 281

2013-12-20

281

4.132e-7

1.134e-5

2.034e-5

3204251

66429630578580601663

65.848

10365859381581
3² × 11 × 19 × 463 × 11902427

2018-09-02

463

11902427

4.2259

0.0801

0.1495

exponent	prime factors	composite factor	digits	bits*
3204251	6408503 11669113121761	74781546448144733783	20	66.019
3204251	6408503 66429630578580601663	425714486851725521499140489	27	88.460
3204251	11669113121761 66429630578580601663	775174873858250669292087558088543	33	109.256
3204251	6408503 11669113121761 66429630578580601663	4967710504645220988910350992273102081129	40	131.868

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-05-07T05:29:21	Jocelyn Larouche	Manual testing	320425	3204251	6	-	skipped known factor: 6408503 skipped known factor: 11669113121761	-	-	0.059	-	-	3.368%
2022-01-06T19:16:02	Jocelyn Larouche	Manual testing	1150000	116447100		-	skipped known factor: 6408503 skipped known factor: 11669113121761 skipped known factor: 66429630578580601663	-	-	0.917	-	-	7.588%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2013-12-20T18:24:00	TJAOI	Manual testing	?	?	11669113121761	43.408	14	4.74937e-8	0.602	1.04764e-7
2021-09-12T11:34:19	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.329	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.235 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.235 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	66429630578580601663	2	0.235

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-09-02T07:39:56	ATH	ec2-ECMCF	50000	5000000	66429630578580601663	65.848	2	2		2	0.235

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-01T15:56:44

Oliver Kruse

GTX-0

6408503

11669113121761

301077BD29A82B__

2017-12-13T05:58:12

kkmrkkblmbrbk

c4.xlarge

6408503

11669113121761

301077BD29A82B__

2018-09-02T14:50:35

Oliver Kruse

GTX-6

6408503

11669113121761

66429630578580601663

301077BD29A82B__

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 = 320425, B2 = 3204251 (P-1 stage 2)

B1 = 320425 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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