Presuming since you're comparing all to zero, that all elements of the table are numeric, then simply
pTable=primersTable(:,~all(primersTable{:,:}==0));
will do the dirty...simple example--
>> t=table(zeros(5,1),rand(5,1),zeros(5,1)); % sample table w/ zero columns
>> t(:,~all(t{:,:}==0))
ans =
5×1 table
Var2
_______
0.54
0.93709
0.66096
0.39466
0.25899
>>