## Re: 4-Brilliant results

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• ... Actually no. I worked more than my computer (for the larger numbers at least). When starting out, I used this technique: (for 10^29+ and 10^30+) 1. trial
Message 1 of 4 , Jun 3, 2002
--- In primenumbers@y..., "alpertron" <alpertron@h...> wrote:
>--- 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.

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