Bases 501-1030 reservations/statuses/primes

[Batalov]

Reserving Riesel 1019 to 50K, and Riesel 1021 to 40K.

[Batalov]

A big fish. (176,647 digits)

2*704^62034-1 is 3-PRP! (605.8170s+0.0069s)
Done.
PFGW Version 20090928.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.13]
Output logging to file ../BR704a.txt
No factoring at all, not even trivial division
Primality testing 2*704^62034-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FFT length 48K on 2*704^62034-1
N+1: 2*704^62034-1 15000/586809 mro=0.052734375...
...a few hours later will submit to Top5000.

[gd_barnes]

Congratulations on a large proof Serge!

[Dougal]

doing some work on riesel base 1017 at the minute conjectured k is 900.

[Batalov]

I took Sierp. base 1002 (conj. k=1240) and apart from GFNs at k=1 and k=base, there are 10 k's left at 9.8K:
152 154 171 409 448 492 613 707 917 1106
I'll make a "Chris"-like zip file for every base, Gary, sometime this weekend.

[kar_bon]

Originally Posted by gd_barnes

Edit: There is only one such Riesel base <= 1024 remaining to be proven. The highest one: base 1019, which has currently been tested to n=25K. So there you go Karsten...another possible one to prove. Doing so would prove all Riesel bases <= 1024 where b==(29 mod 30). :-)

k=2 for Riesel Base 1019 at n=63.4k and continuing!

[Batalov]

Riesel Base 1002 is proven with conj. k=237.
Primes are attached.

[gd_barnes]

Originally Posted by Batalov

I took Sierp. base 1002 (conj. k=1240) and apart from GFNs at k=1 and k=base, there are 10 k's left at 9.8K:
152 154 171 409 448 492 613 707 917 1106
I'll make a "Chris"-like zip file for every base, Gary, sometime this weekend.

Serge,

This is a tremendous number of new bases and I have to check them all and subsequently update the pages, which I'm close to finishing now. The problem that I'm having is that I make it a rule to not list k's remaining until I can balance them; that is I have all of the primes. What I must have is a listing of the primes for n>2500 (preferrably n>1000). The biggest problem are the ones like the above where you're listing no primes or only primes for n>5000 (or 7000 or 10000). For those, I have to ignore them on the pages or make a note to myself to follow up on them. I have spare cores on a slower machine and can fairly quickly use it to test to n=2500 without sieving. But to test to n=5000 or 10000 to get that complete listing would require that I stop other efforts, sieve, and then test...too much personal time and CPU resources.

It would really help me out if you would post primes n>2500 and k's remaining at the same time. Otherwise I have to update the pages twice or just ignore the 1st posting of k's remaining, which means someone else may end up testing a base that you have already started on.

For now, I'm going to list what I can on the pages with a note to myself to follow up on primes needed for n=2500 to (the lower limit of what you're listing shows). In the future, I won't show them at all until I get the n>2500 primes, which means a base or two could get missed.


Thanks,
Gary

[Siemelink]

Hi all,

The riesel conjecture 12 for base 1000 is proven.
k = 1, 4, 7, 10 are eliminated because 1000-1 has 3 as a factor.
k = 8 can be eliminated because

All k = m^3 for all n; factors to (m*10^n - 1) *(m^2*100^n + m*10^n + 1)
( I stole this from base 27)

That leaves these primes:
2*1000^1-1
3*1000^1-1
5*1000^1-1
6*1000^998-1
9*1000^1-1
11*1000^3-1

Willem.

[TimSorbet]

Sierp Base 1000
Conjectured k = 12

Found Primes:

3*1000^1+1
4*1000^1+1
6*1000^3+1
7*1000^1+1
9*1000^1+1

Remaining k's: Tested to n=10K
10*1000^n+1

Trivial Factor Eliminations:
2
5
8
11

GFN Eliminations:
1

Base Released

(If k=10 can be eliminated for some algebraic/trivial reason, I don't see why. The automatic PFGW script didn't eliminate it and it's not a cube. It is equivalent to 10^(3*n+1)+1, but I don't know if that implies anything terribly interesting.)

[TimSorbet]

Riesel Base 701
Conjectured k = 14

Found Primes:

2*701^2-1
4*701^1-1
10*701^31-1
12*701^2-1

Trivial Factor Eliminations:
6
8

Conjecture Proven