Bases 501-1030 reservations/statuses/primes

[gd_barnes]

I'm done with Riesel and Sierp bases 512 and 1024. These got a little tricky, especially on the Sierp side. There was both algebraic factors and unusual GFNs as well as testing from RPS and ProthSearch that helped eliminate some k's that I didn't. I only tested them to n=2500 but with testing from other projects, all of the remaining k's are at n>=145K. 2 are proven, one has 1 k remaining, and another has 2 k's remaining.

Particulars:

Riesel base 512 with a conjecture of k=14 is proven. Although cubed k's would have full algebraic factors, k=1 & 8 were already eliminated with a trivial factor of 7. This was the easy one.

Riesel base 1024 with a conjecture of k=81 has k=29 & 74 remaining. All squared k's have full algebraic factors, which eliminates k=9 & 36. After testing to n=2500, I had k=29, 39, & 74 remaining. For odd k's, base 2 Riesel primes convert to base 1024 Riesel primes if n==(0 mod 10). 39*2^40700-1 is prime, which converts to 39*1024^4070-1 so it is eliminated. For k=29, it has been tested to n=2M base 2 with no n==(0 mod 10) primes so it remains at n=200K base 1024. For k's==(2 mod 4), base 2 Riesel primes convert if n==(1 mod 10) where n>1. For k=74, it has been tested to n=1.45M base 2 with no n==(1 mod 10) n>1 primes so it remains at n=145K base 1024.

Sierp base 512 with a conjecture of k=18 has k=5 remaining and was the most unusual. Since 512=2^9, k=1, 2, 4, 8, & 16 are all GFN's. All cubed k's have full algebraic factors and in this case, it eliminates two of the GFN's, k=1 & 8, so we can't say that "k=1 and 8 are GFn's with no known prime" since it is mathematically impossible for them to have a prime. k=2, 4, & 16 have no known prime so are the only GFN's shown as such. As for k=5 remaining, the base 2 ProthSearch project has searched it to n=5.33M with no n==(0 mod 9) prime, which is the requirement for a base 512 prime. Hence k=5 remains at n=592.2K base 512. (I also updated the search limit for Sierp base 128 k=40.)

Sierp base 1024 with a conjecture of k=81 is proven and was a little unusual on its GFN elimination. Since 1024=2^10, k=1, 2, 4, 8, 16, 32, & 64 are all GFN's. k=2, 8 & 32 were eliminated by a trivial factor of 3. All k's that are perfect 5th powers have full algebraic factors, which eliminates k=1. k=64 has a prime at n=1; the only GFN on either of these bases with a known prime. This leaves only k=4 & 16 as GFN's with no known prime.

Bottom line:
Riesel base 1024 has the following remaining:
29 (200K)
74 (145K)

Sierp base 512 has the following remaining:
5 (592.2K)

I had hoped to open up some more power-of-2 bases testing but this didn't do it. What is remaining is being searched by RPS and ProthSearch. Like Sierp base 128, these aren't worth messing with.

The pages will shortly be updated for these bases.


Gary

[rogue]

Completed to n=20000 and released. k=70 remains. Here are the primes.

2*605^5+1
4*605^2+1
6*605^1+1
8*605^23+1
10*605^12394+1
12*605^5+1
14*605^3+1
16*605^2+1
18*605^1+1
20*605^1+1
22*605^4+1
24*605^3+1
26*605^1+1
28*605^2+1
30*605^34+1
32*605^13+1
34*605^2+1
36*605^5+1
38*605^3+1
40*605^86+1
42*605^1+1
44*605^11+1
46*605^2068+1
48*605^29+1
50*605^11+1
52*605^6+1
54*605^5+1
56*605^3+1
58*605^6+1
60*605^3+1
62*605^1+1
64*605^10+1
66*605^13+1
68*605^1+1
72*605^10+1
74*605^1+1
76*605^4+1
78*605^16+1
80*605^3+1
82*605^2+1
84*605^1+1
86*605^5+1
88*605^2+1
90*605^2+1
92*605^1+1
94*605^4+1
96*605^12+1
98*605^3+1

[TimSorbet]

Originally Posted by henryzz

do u mean a .prp file as .npg files are only single k values?
might be worth editing that in in the script thread

By NewPGen I meant the format LLR uses, which in srfile is -G and writes to a .prp file. Although it would work just fine on anything that has "k n", (or even "k n c" or any other number of specifiers - as long as the first two are k and n, separated by spaces) such as .prp, (LLR/NewPGen) .npg, (single-k NewPGen) and ABC files, for single-k files there'd be the useless overhead of specifying and filtering the k.
Besides, I can't edit the other post myself, as it's way past the 1 hour mark, and I'm not a mod here.

[gd_barnes]

Karsten reported:

50*601^30735-1 is prime

As far as I know, he has not reserved Riesel base 601.

[Batalov]

Originally Posted by gd_barnes

Karsten reported:

50*601^30735-1 is prime

As far as I know, he has not reserved Riesel base 601.

Actually,
BR601a.txt:120*601^4663-1 is 3-PRP! (4.1509s+0.0024s)
BR601a.txt:50*601^30735-1 is 3-PRP! (188.4408s+0.0183s)
BR601a.txt:624*601^44279-1 is 3-PRP! (564.9792s+0.0151s)

EDIT: The file is attached - it was running unattended and then interrupted at 45.36K and I will not continue anytime soon.

Overwhelmed by the deluge of new bases, I've stopped short of reporting those that I have reserved, but I'll try to organize and report them all now whereever they are stopped.

[gd_barnes]

Originally Posted by Batalov

Actually,
BR601a.txt:120*601^4663-1 is 3-PRP! (4.1509s+0.0024s)
BR601a.txt:50*601^30735-1 is 3-PRP! (188.4408s+0.0183s)
BR601a.txt:624*601^44279-1 is 3-PRP! (564.9792s+0.0151s)

OK, I have Riesel base 601 as unreserved. The status is:

k=300, 482, and 744 still remain and the testing limit on them is n=2500.


Gary

[kar_bon]

Originally Posted by gd_barnes

OK, I have Riesel base 601 as unreserved. The status is:

k=300, 482, and 744 still remain and the testing limit on them is n=2500.

you should set the test-limit to 45.36k as Serge's file show.

so i will stop testing k=300!

[gd_barnes]

OK, I will set the test limit on Riesel base 601 to n=45.36K on the remaining 3 k's. Since Serge states that he will not get back to it, I'll unreserve it.

Thanks for the results Serge. That helps a lot.


Gary

[MyDogBuster]

Sierp Base 729
Conjectured k = 74
Covering Set = 5,73
Trivial Factors k == 1 mod 2(2) and 6 mod 7(7) and 12 mod 13(13)

Found Primes:
2*729^1+1
4*729^1+1
10*729^2+1
14*729^3+1
16*729^2+1
18*729^53+1
22*729^2+1
24*729^1+1
26*729^2+1
28*729^3+1
30*729^1+1
32*729^6+1
36*729^2+1
40*729^3+1
42*729^24+1
44*729^1+1
46*729^2+1
50*729^1+1
52*729^16+1
54*729^1+1
56*729^28+1
58*729^1+1
60*729^3+1
66*729^6+1
68*729^4+1
70*729^1+1
72*729^1+1

Remaining k's:
8*729^n+1 <------- Proven composite by full algebraic factors

Trivial Factor Eliminations: 8k's

Conjecture Proven

[MyDogBuster]

Sierp Bases 869, 899, 914 and 1004 complete n=2.5K-25K

2*899^15731+1 is prime - Conjecture Proven

Bases Released - Results attached

[MyDogBuster]

Almost caught up on my new reservations so:

Reserving Riesel bases 529,676,784,900
to clean up some k's with full algebraic factors