- --- jim_fougeron <jfoug@...> wrote:
> These are minimal 4 brilliant numbers:

[SNIP]

Grand work, Jim!

Do we yet have a heuristic for the delta from the power of ten for

each of the brilliant types. It appears that with the increased

choice of primes, there's a limited growth of the delta, and

sometimes it almost looks like it's hardly growing at all. However,

any formal attack evades me. Probably the 2 factor type is the most

attackable.

Phil

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http://fifaworldcup.yahoo.com - --- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:
> These are minimal 4 brilliant numbers:

[snip]

It appears that your computer worked a lot. Thanks a lot, Jim.

I've just uploaded you results to:

http://www.alpertron.com.ar/BRILLIANT.HTM

Best regards,

Dario Alejandro Alpern

Buenos Aires - Argentina

http://www.alpertron.com.ar/ENGLISH.HTM - --- In primenumbers@y..., "alpertron" <alpertron@h...> wrote:
>--- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:

Actually no. I worked more than my computer (for the larger numbers

>> These are minimal 4 brilliant numbers:

>

>[snip]

>

>It appears that your computer worked a lot. Thanks a lot, Jim.

at least).

When starting out, I used this technique: (for 10^29+ and 10^30+)

1. trial factor a 5000000 range with CPAPSieve up to prime 10000000

2. compute ceil((10^29)^.25) (17782795)

3. trial factor the values left over up to this point.

4. Whatever items factored out on step 2 (not too many) are the only

candidates which can be brilliant-4.

5. Check each of these by fully factoring until a brilliant was found

6. For 10^30+ step 2 is ceil((10^30)^.25) which is 31622776

For the larger numbers (where I show a lot of additional brilliants,

and "large enough" 4 factor results), I used this method: (10^35+)

1. trial factor a 5000000 range with CPAPSieve up to prime 100000000

2. modified CPAPSieve to not eliminate candidates, but to count how

many factors each had seen. Then simply run it to prime 1000000000

and output all candidates which 4 factors were found.

Method 2 is a constant time method, however, each time you increase

the size of the brilliant factors by 1 digit, this method take 10

times as long to complete.

Using something like the method 2 would quickly these brilliants while

the size of the factors are small.

Jim.

>I've just uploaded you results to:

>

>http://www.alpertron.com.ar/BRILLIANT.HTM

>

>Best regards,

>

>Dario Alejandro Alpern

>Buenos Aires - Argentina

>http://www.alpertron.com.ar/ENGLISH.HTM