On the basis of a high degree of theory, prime numbers are derived through effective processing and steps so as to achieve a remarkable reduction in the processing time taken for the derivation. With respect to an arbitrary prime number rank entered, (1) numerical values are added in sequence to a prime number of the anterior rank to calculate prime number candidates of the next rank; (2) the thus calculated prime number candidate is divided by known prime numbers to verify whether it is a prime number or not; and (3) processing for reducing the verification time is iterated when the thus calculated prime number candidate is larger than a certain value, to thereby derive prime numbers until the entered rank is reached.