Quote:
Originally Posted by sweety439
Of course,
* In the Riesel case if k and b are both rth powers for an r>1
* In the Sierpinski case if k and b are both rth powers for an odd r>1
* In the Sierpinski case if k is of the form 4*m^4, and b is 4th power
Then this k proven composite by full algebraic factors

There are many Riesel case for k=64 (since 64 = 4^3 = 8^2, thus n == 0 mod 2
or n == 0 mod 3 have algebra factors:
Bases 619, 1322, 2025, 2728, 3431, 4134, 4837, 5540, 6243, 6946, 7649, 8352, 9055, 9758, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 37
Bases 429, 1816, 3203, 4590, 5977, 7364, 8751, ...: n == 1 mod 3: factor of 19, n == 2 mod 3: factor of 73
Bases 391, 2462, 4533, 6604, 8675, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 109
Bases 159, 862, 1565, 2268, 2971, 3674, 4377, 5080, 5783, 6486, 7189, 7892, 8595, 9298, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 19
Bases 1232, 3933, 6634, 9335, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 73
Bases 936, 4969, 9002, ...: n == 1 mod 6: factor of 37, n == 5 mod 6: factor of 109
Bases 957, 2344, 3731, 5118, 6505, 7892, 9279, ...: n == 1 mod 3: factor of 73, n == 2 mod 3: factor of 19
Bases 1322, 4023, 6724, 9425, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 37
Bases 4315, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 109
Bases 482, 2553, 4624, 6695, 8766, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 19
Bases 3098, 7131, ...: n == 1 mod 6: factor of 109, n == 5 mod 6: factor of 37
Bases 4079, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 73