a> prime test: i use Fermat thm and x^2==1(mod p) <==> x==1,p-1 (which can detected Carmichael Numbers);
b> Fator big int: i use Wheel Factorization!

but if all test data are number N (N=p*q,p,q is prime) 
you can pass it by div reverse from N^0.5! 
my team members tell me that you can first div frome 0 to 1/3*N^0.5(which can make sure N=p*q) then div from N^0.5 reverse!

the QS(or MPQS) was easy to understand but hard to programming! anyone who write it out can you post your problem out!!