We propose three physical tests to measure correlations in random numb
ers used in Monte Carlo simulations. The first test uses autocorrelati
on times of certain physical quantities when the Ising model is simula
ted with the Wolff algorithm. The second test is based on random walks
and the third on blocks of n successive numbers. We apply the tests t
o show that recent errors in;high precision Ising simulations using ge
neralized feedback shift register algorithms are due to short range co
rrelations in random number sequences.