Speaker: Igor Shparlinski (Macquarie) Title: TBA Time & Place: 2:35-3:30pm, Thursday 14 June, Carslaw 535 Afternoon Tea: 3:30-4pm Speaker: Richard Brent (ANU) Title: Using Magma to find good xorshift random number generators Time & Place: 4:05-5pm, Thursday 14 June, Carslaw 535 Abstract (Brent): Marsaglia recently introduced a class of ``xorshift’’ random number generators (RNGs) with periods $2^n - 1$ for $n = 32, 64$, etc. We describe a generalisation of Marsaglia’s xorshift generators in order to obtain fast and high-quality RNGs with extremely long periods. RNGs based on primitive trinomials may be unsatisfactory because a trinomial has very small weight (number of nonzero terms). In contrast, our generators can be chosen so that their minimal polynomials have large weight. A search using Magma has found good generators for $n$ a power of two up to 4096. These have been implemented in a free software package xorgens. Aspects of the search using Magma, and a connection with Fermat numbers, will be mentioned.