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# Random Number Generators for Ultracomputers

Random Number Generators for Ultracomputers
O E Percus
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. , etc. Such that 3 ', 5 ', 7 J, , . . , are of the order of v m /2, Let us note that the restriction *, - = i = 1, . . . , t is unnecessary. If *, o Â¥= for some i, then using (2. 3) we get -y, - = (a â€” I) x 0i + Â£>, â€¢ = rm + v, -, r integer and we will choose bj to guarantee that v, < "^ mil and g. C. D. (v, v, ) = 1 for all /#;' . Ultracomputer Note 114 Pa 8 e 17 5. Bounds for Multiplies The problem of creating a uniform distribution for a single 2-vector can be generalized in another direction. We will devise a method of choosing three bi's such that v 3 * = 0(m v3 ); of course, as explained in [10] (pages 90, 91) having a good lower bound for v 3 does not imply a good lower bound on v 2 . Taking this warning into account, we now present the following result: Theorem 2 Let x Qti = (1) for all i (5. 1) Define two finite sets of primes^ Set I = â–  pi : p i prime, p l = 0(m 2/3 ), and p t < m 2 ' 3 Set II = \p s : p s prime, p s = 0(m v3 ), and p s < m 1/3 [ Then v 2 (l, 2) ^ 0(m 1/3 ) (5.

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