A method for determining, for use in ciphers, all of the prime numbers within the large numeric series: 5, 6, 7, 8, 9, 10, 11, 12, . . . , n, the method including steps of setting n'=.left brkt-top.n/6.left brkt-top.; establishing the small numeric series, 6(1)-1, 6(1)+1, 6(2)-1, 6(2)+1, 6(3)-1, 6(3)+1, . . . 6(n')-1, 6(n')+1, each member of the small numeric series being initially unlabeled, the small numeric series consisting of a "-1" subseries and a "+1" subseries; while .beta.-((.beta.+1)/6) is less than n', repeating sub-steps of First, setting .beta. to equal the least unlabeled member of the "-1" subseries, labeling that member as "prime", labeling as "non-prime" every .beta..sup.th member thereafter of the "-1" subseries, labeling as "non-prime" the (.beta.-((.beta.+1)/6)).sup.th member of the "+1" subseries, labeling as "non-prime" every .beta..sup.th member thereafter of the "+1" subseries, and Second, setting .beta. to equal the least unlabeled member of the "+1" subseries, labeling that member as "prime", labeling as "non-prime" every .beta..sup.th member thereafter of the "+1" subseries, labeling as "non-prime" the (.beta.-((.beta.-1)/6)).sup.th member of the "-1" subseries, and labeling as "non-prime" every .beta..sup.th member thereafter of the "-1" subseries; and labeling as "prime" each unlabeled member of the small numeric series.