Bases 501-1030 reservations/statuses/primes

[Mini-Geek]

My first idea was to do it purely with a sieve program, but considering k's with trivial factors, MOBs, etc. I figured it'd be too complicated to bypass the PFGW script completely. So I decided to try using PFGW to n=0 (essentially just eliminating trivial factors and MOBs) followed by srsieve. Srsieve doesn't know to stop searching a number and declare it prime when it passes the square root of it, (only when you pass the number itself) so you have to manually set the max p to the square root of the largest number. That works, and is significantly faster (not drastically faster, but significant...maybe about 15% faster) than using PFGW to n=1, but doesn't eliminate the k's from the file by itself. And my remove-ks.pl script isn't very good at doing that many different k's. So in the end, I figured it's probably fastest (not to mention way easier!) to just use PFGW with the max n set to 1.
Here are the timings I found:

k=1 to 10,000:
PFGW n=0:
7 CPU seconds (checks for trivial factors and MOB)
PFGW n=1:
10 CPU seconds
srsieve:
<1 CPU second

k=1 to 100,000:
PFGW n=0: (no -f)
56 CPU seconds
PFGW n=0: (-f)
57 CPU seconds
srsieve:
24 CPU seconds (56+24=80 CPU seconds)
PFGW n=1: (no -f)
95 CPU seconds
PFGW n=1: (no -f, minimized to tray)
88 CPU seconds
PFGW n=1: (-f)
95 CPU seconds

k=1885767586974 to 1885767686974 (final 100k):
PFGW n=1: (no -f)
115 CPU seconds
PFGW n=1: (-f)
121 CPU seconds

If the time for each 100,000 range averaged 105 CPU seconds, my two cores could complete all the k's to n=1 in only about 31.4 years! See you June 2041!
Looks like there is no big difference between using -f and not for numbers this small.

For the record, I ran srsieve with these options:

srsieve -n1 -N1 -P8939 -q -Z -G pl_remain.txt

i.e. min and max n set to 1, min p defaulting to 3 and max p set to sqrt(100000*799-1) (rounded up), quiet so it doesn't fill the screen and so waste CPU time, higher priority, outputting to the .prp format, and reading the list of sequences from pl_remain.txt left from PFGW's run, and its output (in t17_b799.prp) is all the primes.

[MyDogBuster]

So can either Gary or Ian tell me weather or not it is composit for all n's for k=64 or it in fact is expected to have a prime eventually?

I'll let Gary handle that. I'm still learning this stuff and 633 is beyond my knowledge at the moment.

[MyDogBuster]

Riesel Base 919
Conjectured k = 24
Covering Set = 5, 23
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 17(17)

Found Primes:
2*919^4-1
6*919^11-1
8*919^1-1
12*919^1-1
14*919^2-1
20*919^1-1

Trivial Factor Eliminations: 5k's

Conjecture Proven

[MyDogBuster]

Riesel Base 924
Conjectured k = 36
Covering Set = 5, 37
Trivial Factors k == 1 mod 13(13) and k == 1 mod 71(71)

Found Primes: 30k's File attached

Remaining k's:
4*924^n-1 <------ Proven composite by partial algebraic factors
9*924^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 2k's

Conjecture Proven

[MyDogBuster]

Riesel Base 934
Conjectured k = 21
Covering Set = 5, 11
Trivial Factors k == 1 mod 3(3) and k == 1 mod 311(311)

Found Primes: 12k's File attached

Remaining k's:
9*934^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 6k's

Conjecture Proven

[henryzz]

Using maxima i have found the following algebraic factorizations:
64*633^(2*n)-1=(8*633^n-1)*(8*633^n+1)
64*633^(3*n)-1=(4*633^n-1)*(16*633^(2*n)+4*633^n+1)
which leaves 1 and 5 mod 6
n=1 and 5 mod 12 are divisible by 17
which leaves 7 and 11 mod 12
after that there doesnt seem to me anything else obvious that would form a covering set
basically one third of n values are left after algebraic factorizations and half of them are eliminated by the trivial factor 17 so it is possible to test just one sixth of candidates

[henryzz]

after a sieve to 1e8 there arent that many to remove anyway

Read 4985 terms for 1 sequence from NewPGen format file `t17_b633_k64.npg'.
64*633^n-1: n = 1*m+0, 4985 terms
  n = 3 (mod 12): 338 terms
  n = 4 (mod 12): 265 terms
  n = 7 (mod 12): 2258 terms
  n = 11 (mod 12): 2124 terms

only 12.1% of the file will be removed when removing ns with algebraic factors

[henryzz]

More discoveries
More sieving without removal decreases the percentage of candidates that have algebraic factors. At 1e10 only 10.2% of the file would be removed.
It is however worthwhile removing them as it doubles the speed of the sieve when using sr1sieve.
Are there any other bases with complex algebraic factors like riesel 633? If so what bases?

[KEP]

Originally Posted by henryzz

after a sieve to 1e8 there arent that many to remove anyway

Read 4985 terms for 1 sequence from NewPGen format file `t17_b633_k64.npg'.
64*633^n-1: n = 1*m+0, 4985 terms
  n = 3 (mod 12): 338 terms
  n = 4 (mod 12): 265 terms
  n = 7 (mod 12): 2258 terms
  n = 11 (mod 12): 2124 terms

only 12.1% of the file will be removed when removing ns with algebraic factors

Thanks for your input. Just call me an illiterate, but does all your explanation mean that the 1/6 that is left, has to be tested or does what you stated actually mean that the k has to be left out of the que? Also after sieving, does one have to remove n's manually or will the sieve rule out all n's with algebraric factors?

Again, for now, it is remaining in the test file, at least up to n=25K, so everything should be good and fine for now

Regards

KEP

[henryzz]

Originally Posted by KEP

Thanks for your input. Just call me an illiterate, but does all your explanation mean that the 1/6 that is left, has to be tested or does what you stated actually mean that the k has to be left out of the que? Also after sieving, does one have to remove n's manually or will the sieve rule out all n's with algebraric factors?

Again, for now, it is remaining in the test file, at least up to n=25K, so everything should be good and fine for now

Regards

KEP

1/3 needs to be sieved but half of that will quickly be sieved away by the factor 17
the k does need to be tested as far as i can tell although i wouldnt do anything serious until gary posts
to remove the ns with algebraic factors use the perl script in post #64 of this thread to remove ns that are 0 mod 2 and 0 mod 3
i have attached a file sieved to 1e10 for that k with the algebraic factors removed

[MyDogBuster]

Riesel Base 939
Conjectured k = 46
Covering Set = 5, 47
Trivial Factors k == 1 mod 2(2) and k == 1 mod 7(7) and k == 1 mod 67(67)

Found Primes: 18k's File attached

Remaining k's:
4*939^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 3k's

Conjecture Proven