[quote=MyDogBuster;209388]You did 3, I did 2 that's 5; / 2 or a 2.5 average.

We just slightly broke the rules:rofl:[/quote]

Well, Mark just did 2 so now the average is 2-1/3. We need someone different to do one new base today. Then the average will be 2 and everything will be good in my world.

:missingteeth:

Sierp Base 319
 

Sierp Base 319
Conjectured k = 684
Covering Set = 5, 17, 73
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 52 mod 53(53)

Found Primes: 217k's File attached

Remaining k's: 6k's - Tested to n=25K
64*319^n+1
256*319^n+1
286*319^n+1
334*319^n+1
366*319^n+1
574*319^n+1

Trivial Factor Eliminations: 118k's

Base Released

[quote=MyDogBuster;209457]Sierp Base 319
Conjectured k = 684
Covering Set = 5, 17, 73
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 52 mod 53(53)

Found Primes: 217k's File attached

Remaining k's: 6k's - Tested to n=25K
64*319^n+1
256*319^n+1
286*319^n+1
334*319^n+1
366*319^n+1
574*319^n+1

Trivial Factor Eliminations: 118k's

Base Released[/quote]


Since the highest prime in the file is n=2817, I just thought I'd check and see if you might have missed including any higher primes.

These large bases go into these tremendous primeless gaps at times. It keeps me wondering.

[QUOTE]Since the highest prime in the file is n=2817, I just thought I'd check and see if you might have missed including any higher primes.[/QUOTE]

Just re-checked. Only 2 primes > n=2500. Another galactic void.

Reserving Sierp 373 and 379 as new to n=25K

Riesel base 302
 

Riesel base 302 is proven:
k n
2 6
3 4
4 3
5 98
6 1
7 1
8 trivial
9 5
10 1
11 74
12 1
13 conjecture

Willem.

Sierpinski Base 309
 

Primes found:

[code]
2*309^1+1
4*309^1+1
8*309^1+1
12*309^1+1
14*309^1+1
16*309^180+1
18*309^1+1
22*309^6+1
24*309^1+1
26*309^146+1
28*309^2+1
30*309^5+1
36*309^4+1
38*309^1+1
40*309^4+1
42*309^1+1
44*309^1+1
46*309^8+1
50*309^1+1
52*309^1+1
56*309^38+1
58*309^1+1
60*309^1+1
64*309^1+1
66*309^16+1
68*309^1+1
70*309^4+1
72*309^2+1
74*309^51+1
78*309^1+1
80*309^40+1
82*309^1+1
84*309^3+1
86*309^2+1
88*309^13+1
92*309^1+1
[/code]

The other k have trivial factors. With a conjectured k of 94, this conjecture is proven.

Sierp Base 373
 

Sierp Base 373
Conjectured k = 120
Covering Set = 11, 17
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 30 mod 31(31)

Found Primes: 36k's File attached

Remaining k's: Tested to n=25K
108*373^n+1
118*373^n+1

Trivial Factor Eliminations: 21k's

Base Released

Sierp Base 379
 

Sierp Base 379
Conjectured k = 246
Covering Set = 5, 19
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 6 mod 7(7)

Found Primes: 66k's - File attached

Remaining k's: Tested to n=25K
24*379^n+1
136*379^n+1
156*379^n+1

Trivial Factor Eliminations: 53k's

Base Released

Sierpinski base 272+278 is complete. Both is proven. Attached is a file with both bases. In the file is also all other k=8 sierpinski conjectures that I proved before trying to reserve them. Suite yourself, weather or not you will actually add them to the websites or not.

KEP

Ps. This also means, that even though I started and took these sierpinski conjectures bases to n=2500: 230, 335, 398, 440, 482, 587, 608, 632, 650, 797 and 818, that they are suspended and verified for deletion from my harddrive, since no further work appeared to be wanted or allowed. So for now and forward on my DualCore is focusing on PG work only :smile:

Riesel bases 293 and 335
 

Primes found:

2*293^2-1
4*293^1-1
6*293^6-1

2*335^2-1
4*335^3-1
6*335^2-1

With a conjectured k of 8, both of these are proven.