R236 is complete to n=25K; k=67 & 78 remaining; base released.

R248 is complete to n=25K; only k=56 remaining; base released.

Another big prime hole: R236 highest prime is currently 59*236^1786-1.

Riesel base 263, k=10
Primes:
2*263^2-1
4*263^1-1
6*263^2-1
8*263^2-1

Base proven.

R272 with CK=8 is complete to n=25K; only k=6 remains; base released.

Riesel Base 493
 

Riesel Base 493
Conjectured k = 170
Covering Set = 13, 19
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 and 41(41)

Found Primes: 54k's - File attached

Remaining k's: 1k - Tested to n=25K
92*493^n-1

Trivial Factor Eliminations: 29k's

Base Released

Sierp Base 409
 

Sierp Base 409
Conjectured k = 124
Covering Set = 5, 41
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 16 mod 17(17)

Found Primes: 36k's - File attached

Remaining k's: 1k - Tested to n=25K
6*409^n+1

Trivial Factor Eliminations: 24k's

Base Released

S356 and S437 k=8 conjectures proven and added to the pages.

Riesel bases 296 and 395
 

Primes found:
2*296^36-1
3*296^1-1
4*296^27-1
5*296^8-1
7*296^3-1
8*296^16-1
9*296^1-1

2*395^396-1
4*395^1-1
6*395^14-1
8*395^2-1

The other k have trivial factors. With a conjectured k of 10, these conjectures are proven.

S473 k=8 conjecture proven and added to the pages.

Riesel base 428
 

Primes found:

2*428^4-1
3*428^1-1
4*428^55-1
5*428^2-1
6*428^2-1
7*428^3-1
9*428^1-1

The other k have trivial factors. With a conjectured k of 10, this conjecture is proven.

Riesel Base 398
 

Reserving this base to at least n=25000.

Serge reported in a Mar. 29th Email that S405 k=106 is complete to n=50K. The base is now released.