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
.