  A prime $p$ is a Wolstenholme prime if $\binom{2p}{p}\equiv2$ mod $p^4$, or,
equivalently, if $p$ divides the numerator of the Bernoulli number $B_{p-3}$; a
Vandiver prime $p$ is one that divides the Euler number $E_{p-3}$. Only two
Wolstenholme primes and eight Vandiver primes are known. We increase the search
range in the first case by a factor of $6$, and show that no additional
Wolstenholme primes exist up to $60$ billion, and in the second case by a
factor of $8$, proving that no additional Vandiver primes occur up to $40$
billion. To facilitate this, we develop a number of new congruences for
Bernoulli and Euler numbers mod $p$ that are favorable for computation, and we
implement some highly parallel searches using GPUs.
