A method of obtaining uniform and independent random numbers is given (a) comprising two distinct odd primes p1, p2 that give mutually coprime integers q1=(p1−1)/2 and q2=(p2−1)/2 with different parity to form the modulus d=p1p2; (b) comprising primitive roots z1, z2 of primes p1, p2, respectively, giving congruence relations z≡zj mod(pj) for j=1, 2 that determine the multiplier z; and (c) comprising the initial value n coprime with d=p1p2. The method generates the coset sequence n ={r1=n, r2, r3, . . . } of period T=2q1q2 recursively by rj+1=zrj mod(d) for j=1, 2, . . . in the reduced residue class group Z*d, giving {v1=r1/d, v2=r2/d, . . . } for output.