2006-01-24, 18:44   #5
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

1,567 Posts

Here it is a program to find hexadecaproths!

There are 3869775 workunits in this search, from workunit=0 to workunit=3869774, to use it just type for example:
if you want to complete start_workunit=100 to end_workunit=104 ( this is 5 workunits ).
Each workunit has got the same probability that it is containing a hexadecaproth, and to finish this workunit has got the same running time.

Note that we are searching only for n=76, for this n there are about 16 hexadecaproth. If the program find some dodecaproth then these will be saved to results_ex.txt file, but won't display, I think that we can find also about 6728 dodecaproths in this search but not all of them because this is optimized for hexadecaproth search.

We are using primes only up to 1000. And in every cases 15 primes in the sieve reduction, but not the first 15 primes: we are using: 2,3,5,7,11,13,17,19,23,37,41,43,47,67,71, because using the first 15 primes is suboptimal.

Here it is my first completed workunit for this search:

You can also find the results in results_hexadeca.txt file ( These are 3-probable primes )
If the program find some dodecaproths then these will be saved to results_ex.txt file, but we won't display these
n=76, start_workunit=456789, end_workunit=456789, version=1.0
Starting the sieve...
Using 15 primes to reduce the size of the sieve array
The sieving is complete.
Number of Prp tests=16198758
Time=2769 sec.

It means that the average expected running time to find only one! hexadecaproth for n=76 is about 2769*3869775/16 sec.=21 years for Penitum 4 Celeron 1.7 GHz. In my previous prediction I've forgotten to multiply by about 10, the program isn't slow!

It isn't impossible to test this program, because it is possible to print the examined k values then I've checked that 16 forms hasn't got small prime factors for various k values, however as a subproject it would be good to find at least one dodecaproth by this program.

Note Kosmaj has found one dodecaproth for n=76, but that won't find this program because the remaining 4 forms has got small prime factors!

See my attachment for c code