R361
 

Done with R361 to 25K.
For a CK of 8870, very few (15) [I]k[/I]'s remain (of which three are tested to higher limits for R19).
Results emailed to Gary. Base released.

Riesel base 443, k=28

Primes:
2*443^12-1
4*443^3-1
6*443^1-1
8*443^416-1
10*443^3-1
12*443^3-1
16*443^165-1
20*443^6-1
22*443^7-1
24*443^1-1
26*443^2-1

Trivially factors: k=14, 18
Base proven.

Riesel Base 253
 

Riesel Base 253
Conjectured k = 1904
Covering Set = 5, 13, 43
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 7(7)

Found Primes: 537k's - File attached

Remaining k's: 4's - Tested to n=25K
408*253^n-1
1650*253^n-1
1652*253^n-1
1854*253^n-1

Trivial Factor Eliminations: 408k's

MOB Eliminations: 2k's
506
1518

Base Released

S383 is at n=25K, 50 k's remaining. Continuing to n=100K, is going to e-mail residuals and remaining k's aswell as other script created files in a short while to Gary.

KEP

Sierp Base 343
 

Sierp Base 343
Conjectured k = 1936
Covering Set = 5, 13, 43
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 18 mod 19(19)

Found Primes: 598k's - File attached

Remaining k's: 11k's - File attached - Tested to n=25K

k=216 proven composite by full algebraic factors

Trivial Factor Eliminations: 357k's

Base Released

[quote=MyDogBuster;212781]Sierp Base 343
Remaining k's: 11k's - File attached - Tested to n=25K

...k=216 proven composite by full algebraic factors
[/quote]
And so do k=64 and k=1000. :ermm:

I would like to advance S343 to 50K.

Riesel base 447, k=148.
Primes attached.

Remaining k's:
78*447^n-1
118*447^n-1
146*447^n-1

Base completed to 25K and released.

Riesel bases 455, 413, and 340
 

I haven't posted any in a few days, so in keeping with an average of one per day...

Primes found:

2*455^2-1
4*455^3-1
6*455^1-1
8*455^2-1
10*455^1-1
12*455^8-1
14*455^20-1
16*455^5-1
18*455^198-1

With a conjectured k of 20, this conjecture is proven.

2*413^6-1
4*413^23-1
6*413^1-1
8*413^4-1
10*413^1-1
12*413^2-1
14*413^20-1
16*413^1-1
18*413^1-1
20*413^4-1

With a conjectured k of 22, this conjecture is proven.

2*340^60-1
3*340^1-1
5*340^1-1
6*340^1-1
8*340^1-1
9*340^3-1
11*340^1-1
12*340^1-1
14*340^1-1
15*340^1-1
17*340^1-1
18*340^22-1
20*340^12-1
21*340^2-1
23*340^3-1
24*340^4-1
26*340^1-1
27*340^2-1
29*340^1-1
30*340^2-1

The other k have trivial factors. With a conjectured k of 32, this conjecture is proven.

Riesel base 353, k=58.
Primes attached.

1k's remain: 52*353^n-1
Trivially factors: k=12,34,56.

Base completed to 25K and released.

Riesel base 373, k=74.
Primes:
2*373^3-1
6*373^1-1
8*373^4-1
12*373^3-1
14*373^8-1
20*373^1-1
24*373^1-1
26*373^1-1
30*373^15-1
36*373^5-1
38*373^1-1
42*373^3-1
44*373^1-1
48*373^1-1
50*373^10-1
54*373^4-1
56*373^1-1
60*373^11-1
62*373^2-1
66*373^31-1
68*373^14-1
72*373^3-1

1k's remain: 18*373^n-1
Trivially factors: 13 k's.

Base completed to 25K and released.