- Paul Underwood wrote:

> Bouk suggests having a look at 118080.

Did you mean 110880? I get an expected factorisation of

18.4% for that one, but only 9.7% for 118080. By my model,

110880 is the most promising exponent in (85680,750000]

Here's a list of exponents where each entry has a higher

expected factorisation yield than any larger:

Exponent, factors, expectation

1680,40,100.00%

1740,24,96.33%

1890,32,95.48%

2100,36,94.98%

2520,48,91.05%

2640,40,88.53%

2940,36,88.41%

3360,48,86.53%

3780,48,82.88%

3960,48,80.44%

4200,48,79.05%

4620,48,78.67%

5040,60,78.06%

5460,48,71.49%

5880,48,69.92%

6120,48,69.12%

7560,64,68.14%

7920,60,63.67%

9240,64,62.61%

10080,72,61.54%

10920,64,56.45%

12600,72,53.33%

13860,72,52.73%

15120,80,51.39%

16380,72,46.94%

18480,80,46.48%

20160,84,43.47%

21840,80,41.16%

27720,96,39.70%

30240,96,36.29%

32760,96,35.11%

36960,96,31.72%

37800,96,30.69%

40320,96,28.96%

41580,96,28.95%

42840,96,28.73%

55440,120,28.00%

65520,120,24.39%

75600,120,21.10%

83160,128,21.05%

85680,120,19.43%

110880,144,18.40%

131040,144,15.89%

138600,144,15.06%

166320,160,14.15%

171360,144,12.41%

196560,160,12.14%

221760,168,11.37%

240240,160,10.17%

277200,180,9.96%

332640,192,8.95%

360360,192,8.35%

393120,192,7.64%

415800,192,7.26%

443520,192,6.75%

471240,192,6.43%

480480,192,6.31%

498960,200,6.29%

554400,216,6.21%

556920,192,5.47%

720720,240,5.39%

739200,192,4.09%

742560,192,4.08%

748440,192,3.93%

749700,162,3.33%

HTH,

Andy - --- Andy Steward <aads@...> wrote:
> Paul Underwood wrote:

110880 it should be indeed. Moreover because phi(36960,2) is a prp.

>

> > Bouk suggests having a look at 118080.

>

> Did you mean 110880? I get an expected factorisation of

> 18.4% for that one, but only 9.7% for 118080. By my model,

> 110880 is the most promising exponent in (85680,750000]

36960 * 2 = 73920

2^73920-1 is already BLS

36960 * 3 = 110880

2^110880-1 is about 1300 digits short for Konyagin-Pomarance.

Bouk.

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http://faith.yahoo.com - --- Bouk de Water <bdewater@...> wrote:
> Moreover because phi(36960,2) is a prp.

^^^

> 36960 * 2 = 73920

Not yet... ;-)

>

> 2^73920-1 is already BLS

Phil

=====

First rule of Factor Club - you do not talk about Factor Club.

Second rule of Factor Club - you DO NOT talk about Factor Club.

Third rule of Factor Club - when the cofactor is prime, or you've trial-

divided up to the square root of the number, the factoring is over.

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http://faith.yahoo.com - Phil:

> Not yet... ;-)

True, oh sage.

But 2312 digits would be

a mere bagatelle for primo.

More significantly what "a" would make

2^a*(2^73920-1)-1

PrP?

On average you have to wait a long time

and by then 2^a gives you most of BLS anyway,

thus eroding you factorization work.

It was Paul U's a=15 that was really notable in

2^15*(2^64680-1)-1

David - Andy Steward wrote:

> Here's a list of exponents where each entry has a higher

[snip]

> expected factorisation yield than any larger:

>

> Exponent, factors, expectation

> 720720,240,5.39%

To be precise, 239 phi-factors and 5.895144%:

http://groups.yahoo.com/group/primenumbers/files/Factors/m720720.zip

Best,

Andrey

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