Let p ( D ) p(D) be the period length of the continued fraction for D \sqrt D . Under the extended Riemann Hypothesis for Q ( D ) \mathcal {Q}(\sqrt D ) one would expect that p ( D ) = O ( D 1 / 2 log log D ) p(D) = O({D^{1/2}}\log \log D) . In order to test this it is necessary to find values of D for which p ( D ) p(D) is large. This, in turn, requires that we be able to find solutions to large sets of simultaneous linear congruences. The University of Manitoba Sieve Unit (UMSU), a machine similar to D. H. Lehmer’s DLS-127, was used to find such values of D. For example, if D = 46257585588439 D = 46257585588439 , then p ( D ) = 25679652 p(D) = 25679652 25679652. Some results are also obtained for the Voronoi continued fraction for 3 D ^3\sqrt D .