Quote:
Originally Posted by Dubslow
EWMayer has explicitly said that the (full) residue can be used to effect a primality test on the cofactor after finding a first factor.

the first m*y+z y>0 can be used so for 2^111 that means (194^22)%(2^111) = 788 can be used.
788%23 = 6 =((194%23)^22)%23 since these equal 23 is a factor of m*y at least and in this case a factor of m.