Take for example 377 to test its primality. I will only test its divisibility with (3*5*7*....*125) (because 377/3=125.67, so here the multiplication series end with 125 ). 377 will be able to divide it. (Since I know 377=13*29, i.e in the numerator 13 & 29 will be divided by 377, hence the total is divisible by 377.) If a number is a prime, then the above method will not be divisible. I am aware for very very big number, the multiplication series product will be enormously large. But isn't it, theoritically, it will work? Thanks.