[quote=Batalov;208733]Reserving R361 with conjectured k=8870 as new to 25K.
At n=1500, there are only 45 [I]k[/I]'s left. 44... 43...
Initial files are attached.
[SIZE=1](Two R19 primes are included; they were the smallest for R19, so they are the smallest for R361 as well.)[/SIZE]
________

Gary, if you have all R19 primes, could please PM?
Of interest are somewhat larger even [I]n[/I]'s, except for two odd [I]n[/I]'s for k=138 and [strike]366[/strike]. The small primes of course will be soon rediscovered anyway.[/quote]

Here are n=2K to 30K attached. See the pages for the top 10, which include higher primes. k<10K was searched to n>=100K. See the base 19 reservations page for the exact search depths.

I'll post an update on the pages when you're at n>=10K for all k's.


Gary

Thank you for the R19 results.

For any reservations with unspecified limits, I expect to deliver towards the unwritten default of 25K.

Sierp Base 275
 

Sierp Base 275
Conjectured k = 22
Covering Set = 3, 23
Trivial Factors k == 1 mod 2(2) and k == 136 mod 137(137)

Found Primes:
2*275^3+1
4*275^158+1
6*275^4+1
8*275^19+1
10*275^2+1
12*275^1+1
14*275^1+1
16*275^4+1
18*275^1+1
20*275^1+1

Conjecture Proven

Sierp Base 281
 

Sierp Base 281
Conjectured k = 46
Covering Set = 3, 47
Trivial Factors k == 1 mod 2(2) and k == 4 mod 5(5) and k == 6 mod 7(7)

Found Primes:
2*281^1+1
8*281^1843+1
10*281^2+1
12*281^1+1
16*281^2+1
18*281^1+1
22*281^6+1
26*281^1+1
28*281^46+1
30*281^1+1
32*281^63+1
36*281^2+1
38*281^7+1
40*281^36+1
42*281^2+1

Trivial Factor Eliminations:
4
6
14
20
24
34
44

Conjecture Proven

Sierp Base 307
 

Sierp Base 307
Conjectured k = 34
Covering Set = 7, 11
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 16 mod 17(17)

Found Primes:
4*307^1+1
6*307^549+1
10*307^3423+1
12*307^490+1
18*307^1+1
22*307^24+1
24*307^1+1
28*307^1+1
30*307^4+1

Trivial Factor Eliminations:
2
8
14
16
20
26
32

Conjecture Proven

Oh boy, 2 new bases a day we get. I'll probably be doing about 2 a week. I'm in the process of returning to NPLB for their new k=301-399 n=1M-2M drive with about 16 cores.

Reserving R304 and S319 as new to n=25K.

[quote=MyDogBuster;209325]Oh boy, 2 new bases a day we get. I'll probably be doing about 2 a week. I'm in the process of returning to NPLB for their new k=301-399 n=1M-2M drive with about 16 cores.

Reserving R304 and S319 as new to n=25K.[/quote]

Do I sense a hint of sarcasm there? lol :smile:

Oops, I accidentally did three bases. :redface:

R265 is proven (c.k=20):
[CODE]2*265^2-1
6*265^2-1
8*265^71-1
14*265^1-1
18*265^2-1
4 - trivials
10
12
16[/CODE]

Riesel Base 304
 

Riesel Base 304
Conjectured k = 426
Covering Set = 5, 61
Trivial Factors k == 1 mod 3(3) and k == 1 mod 101(101)

Found Primes: 268k's - File attached

Remaining: 8k's - Tested to n=25K
131*304^n-1
284*304^n-1
294*304^n-1
339*304^n-1
374*304^n-1
389*304^n-1
404*304^n-1
411*304^n-1

k=9, 144, 324 proven composite by partial algebraic factors
k=171 proven composite by a difference of squares

Trivial Factor Eliminations: 144k's

Base Released

[QUOTE]Oops, I accidentally did three bases. :redface:[/QUOTE]

You did 3, I did 2 that's 5; / 2 or a 2.5 average.

We just slightly broke the rules:rofl:

Sierpinski Base 377
 

Primes found:

2*377^19+1
4*377^74+1
6*377^45+1

With a conjectured k of 8, this one is proven.