Thread: Octoproths
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Old 2005-04-07, 16:08   #8
robert44444uk
 
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Jun 2003
Oxford, UK

190310 Posts
Default Another way

I also use the bitwin option in NewPGen to reduce to an acceptable number of candidates. Sieving to 1 billion is fine, which is the minimum p which the large k range option NewPGen uses. My NewPgen splits the range into 120 or so smaller ranges and then batches all of the survivors together when each range is tested to 1 billion.

At the next stage, I do not check the output for primes. Instead I alter the first line of the NewPgen output file to make this into an ABC file, and use the & option to check for the four other values of the octoproth. This file is then put through pfgw, with the -f100 option, which, for n=50 checks around 10,000 values of k a second. The output file for this run can be inspected to see if there are any values where all four possibilities are prp. It is quicker this way because the pfgw will give up testing the value of k as soon as it spots a composite. If you test the original output file then a lot of values will have to be tested for all four options as none of them, if they are composite, have factors of less than 1 billion.

The final stage is to extract the few (maybe only ten values) where the output file shows the complete set is prp, and make this into a PFGW input file with the first line of the file the same as the output file from the bitwin output file. About half of the values will be octoproths.

Therefore almost all of the work is in the sieving because a very large number of k must be looked at, for a given n. My computer takes 8 hours to sieve k=2 to k=10^11 up to p=1 billion. A further 2 hours takes the file to p=30 billion.

I ran this range for n=50, and found about 8 octoproths. But it looks as if I have been overtaken by events. The bar has been raised!

Regards

Robert Smith
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