Dual Sierpinski/Riesel conjectures in prime bases

[sweety439]

This is the dual (see http://www.kurims.kyoto-u.ac.jp/EMIS...rs/i61/i61.pdf and https://oeis.org/A076336/a076336c.html for the definition) conjectures for CRUS Sierpinski/Riesel conjectures, the form is k*b^n+-1 (+ for Sierpinski, - for Riesel), and the dual form is b^n+-k (+ for Sierpinski, - for Riesel), for composite bases b, gcd(k,b) may not be 1 even if k is not MOB (multiple of b), but for prime bases b, gcd(k,b) must be 1 if k is not MOB (multiple of b), thus in this project we only consider prime bases.

For the dual S2 conjecture, see https://oeis.org/A067760 and https://oeis.org/A123252, for the dual R2 conjecture, see https://oeis.org/A096502 and https://oeis.org/A096822

(in this project, we do not include "negative primes" of the form b^n-k, i.e. we do not include the n such that b^n<k, for b^n-k)

[sweety439]

dual S11 and dual R11 has the same CK as S11 and R11 (1490 and 862, respectively), and currently I only consider the k < CK, for dual S7 and dual R7, I consider k <= 5000

k-values divisible by the base should be excluded, as well as k-values with gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) > 1, as they have trivial prime factors and cannot be prime

Remain k-values with no known primes or PRPs: (for dual S7 and dual R7, all k <= 5000 have known primes)

11^n+430
11^n+1228
11^n-184
11^n-324

(unlike original Sierpinski/Riesel problems, for dual Sierpinski/Riesel problems when the prime is large their primality cannot be proven, since neither N-1 nor N+1 can be >= 25% factored)

Note: For even n, 11^n-324 has difference-of-squares algebraic factorization, thus only odd n should be considered (and when use srsieve to sieve with primes < certain limit (say 10^9), all even n should be removed)