Therefore, formula_1 divides formula_156 (also written formula_157). Suppose that we are able to obtain formula_50 and that it is even. (If formula_50 is odd, then by step 5, we have to restart the algorithm with a different random number formula_160) Now formula_161 is a square root of formula_13 modulo formula_1 that is different from formula_13. This is because formula_50 is the order of formula_35 modulo formula_1, so formula_168, or else the order of formula_35 in this group would be formula_170. If formula_171, then by step 6, we have to restart the algorithm with a different random number formula_35.