Bases 501-1030 reservations/statuses/primes

[MyDogBuster]

Riesel Base 834
Conjectured k = 166
Covering Set = 5, 167
Trivial Factors k == 1 mod 7(7) and k == 1 mod 11(11)

Found Primes: 129k's File attached

Remaining k's:
4*834^n-1 <------ Proven composite by partial algebraic factors
9*834^n-1 <------ Proven composite by partial algebraic factors
49*834^n-1 <------ Proven composite by partial algebraic factors
144*834^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 31k's

Conjecture Proven

[MyDogBuster]

Riesel Base 849
Conjectured k = 16
Covering Set = 5, 17
Trivial Factors k == 1 mod 2(2) and k == 1 mod 53(53)

Found Primes:
2*849^1-1
6*849^19-1
8*849^1-1
10*849^21-1
12*849^2-1
14*849^4114-1

Remaining k's:
4*849^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

[MyDogBuster]

Riesel Base 859
Conjectured k = 44
Covering Set = 5, 43
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 11(11) and k == 1 mod 13(13)

Found Primes: 11k's File attached

Remaining k's:
26*859^n-1

Trivial Factor Eliminations: 9k's

Base Released

[MyDogBuster]

Riesel Base 879
Conjectured k = 34
Covering Set = 5, 11
Trivial Factors k == 1 mod 2(2) and k == 1 mod 439(439)

Found Primes: 14k's File attached

Remaining k's: Tested to n=25K
4*879^n-1 <------ Proven composite by partial algebraic factors
24*879^n-1

Base Released

[MyDogBuster]

Reserving Riesel Bases 939, 949, 964, 969, 984

This is the last of b = 4 mod 5 algebraic factors that I have done

[gd_barnes]

Batalov sent me full results file on all of his bases. Here is some additional detail to add to his Sierp base 961 status in the Email that I posted above:

R1021 is at n=50K; released
S1002 is at n=27.7K; released

Here is the additional base 961 prime that had not yet been posted in the forum:
346*961^30374+1 is prime

He no longer has any bases > 500 reserved.

[gd_barnes]

Originally Posted by MyDogBuster

Reserving Riesel Bases 939, 949, 964, 969, 984

This is the last of b = 4 mod 5 algebraic factors that I have done

Don't forget Riesel base 799. It shouldn't be too bad.

[MyDogBuster]

Don't forget Riesel base 799. It shouldn't be too bad.

With a conjecture k of 1,885,767,686,976 it should only take me an hour or so to complete (if I don't test it above n=1). Your Excel spreadsheet formula will have a hard time finding the partial algebraic factors anyway. Maybe we can have a race to see who gets there first. Just kidding.

[gd_barnes]

Originally Posted by MyDogBuster

With a conjecture k of 1,885,767,686,976 it should only take me an hour or so to complete (if I don't test it above n=1). Your Excel spreadsheet formula will have a hard time finding the partial algebraic factors anyway. Maybe we can have a race to see who gets there first. Just kidding.

And here's the kicker: I bet you can't test it to n=1 in an hour, even if you put all of your machines on it at the same time. For speed, be sure and set no factoring with the -f0 switch. You can even forget about proving the PRPs. (I'm not sure if running at least 2 regular ABC2 PFGW scripts would be faster [one each for k==(0 mod 6) & (2 mod 6)]. Likely not since there's so many other trivial k's.)

Better yet, I'll give you a day with all of your machines and you still don't have to prove the PRPs. Just divide the k-value by 50 or whatever # of cores you have and split them up that way just like you'd do different P-ranges while sieveing.

Good luck!

Edit: I got to k=1M in just a few mins. of course that's < 1 one-millionth of the entire k-range. :-)


Gary

[Mini-Geek]

I wonder what would be the fastest way to go about doing something like that...my initial impression would be that sieving might be a good thing to do, since the numbers are so plentiful that anything where you look at them one at a time would be terribly slow, and so small that they might be easily TFd (or proven prime by TF).
I doubt any current sieving programs would be at all optimized for something like that, though.

[KEP]

I've done some testings on Riesel base 633 with a conjectured k=1004, it has by tonight been taken to n=25K, however I need some help on finding out, weather or not the k=64, has to be excluded from further testing (beyond n=25K) or it has to remain in the k's remaining list. Srsieve raised a warning, that k=64 for Riesel base 633, has algebraric factors, however I've never gotten the website used to testing for algebraric factors to work. 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?

Btw, consider it reserved, to n=25K, if I want to take it higher I'll let you all know

Regards

KEP