There are 3 different problems:

(1) original Sierpinski problem, Which asks about the smallest k, such that k*2^n+1 is composite for all n. SB have sucessfully removed 5 hard candidates out of 17. (a really great work which must be continued)

(2) dual Sierpinski problem , Which asks the same question for the sequence k+2^n, which could be considered as the negative continuation of the Proth sequence k*2^n+1:

k*2^(-n)+1=k/2^n+1=(k+2^n)/2^n

for this problem there remains 8 candidates to be removed:
2131, 8543, 28433, 37967, 40291, 41693, 60451, 75353
see http://sierpinski.insider.com/dual

(3) mixed Sierpinski problem , asks the same question for both the sequences k*2^n+1 and k+2^n, simultaneosly.

for this special problem there remains only one candidate to be removed, namely k=28433.

Payam