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Old 2008-05-06, 01:46   #33
gd_barnes's Avatar
May 2007
Kansas; USA

2·23·233 Posts
Default Sierp base 3 k=110M-120M status

KEP reported completion of the k=110M-120M range on Sierp base 3 in an Email on April 25th.

KEP, there are some changes in your k's remaining for k=110M-120M on Sierp base 3. Many of the k's are divisible by powers of 3, which results in the following changes:

The following k's were removed:
k             comments
115381692     k/3^3=4273396 already found remaining by k<10M testing
117904734     k/3^4=1455614 already found prime at n=33885 by k<10M testing
k's divisible by 3^2 resulting in a k with no prime:
k             k changed to     comments
113061654     12562406       k not divisible by 3^3
113975118     12663902       (same)
118690038     13187782       (same)
119820906     13313434       (same)
k's divisible by 3^1 resulting in a k with no prime:
k             k changed to     comments
111055104     37018368       k/3^2=12339456 has a prime at n=1
                             k/3^3=4113152 has a prime at n=2
111190494     37063498       k not divisible by 3^2
111474414     37158138       k/3^2=12386046 has a prime at n=1
                             k/3^3=4128682 has a prime at n=2
111480438     37160146       k not divisible by 3^2
112607754     37535918       (same)
114584604     38194868       (same)
115059138     38353046       (same)
116413062     38804354       (same)
116433444     38811148       (same)
116849496     38949832       (same)
117573882     39191294       (same)
117860586     39286862       (same)
117965964     39321988       (same)
118295616     39431872       (same)
119429652     39809884       (same)
119503128     39834376       (same)
For the only remaining non-reduced k that is divisible by 3, k=114121992, k/3=38040664 gives a prime at n=1 so k=114121992 remains.

This leaves a total of 67 k's remaining for the range that you tested, although only 47 k's are technically remaining for n=110M-120M.

This was difficult to get exactly correct because we have the huge gap in k-range testing. Once we get contiguous testing up to n=50M, these higher ranges should be far easier. It will be easy to determine which k-values can be eliminated, either ahead of time, or before starting sieving and listing k's remaining.

These changes are reflected on the Sierp base 3 reservations page.

Anon, now, you can see why I didn't want to start any team sieve yet. This stuff is never as easy as it appears at a glance. Testing contiguous k-ranges is a must on large conjectures before beginning sieving. When we do start sieving, I will still recommend that we sieve only contiguous k-ranges, which when we hit 100 k's remaining, will likely be for k<30M. Another option is to sieve every k-range of 50M, which will likely have us sieving about 200 k's remaining at once, which wouldn't be bad for this very prime base. That would make the k-ranges nice and round.

Now: On to determining k's with algebraic factors on Siemelink's Riesel base 19. Whew, bases 3 and 19 are a lot of work to administer but FUN! :-)


Last fiddled with by gd_barnes on 2008-05-06 at 01:53
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