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Computer experiments reveal that twin primes tend to center on nonsquarefreemultiples of 6 more often than on squarefree multiples of 6 compared to whatshould be expected from the ratio of the number of nonsquarefree multiples of 6to the number of squarefree multiples of 6 equal $\pi^2/3-1$, or ca 2.290. Formultiples of 6 surrounded by twin primes, this ratio is 2.427, a relativedifference of ca $6.0\%$ measured against the expected value. A deviation fromthe expected value of this ratio, ca $1.9\%$, exists also for isolated primes.This shows that the distribution of primes is biased towards nonsquarefreenumbers, a phenomenon most likely previously unknown. For twins, this leads tononsquarefree numbers gaining an excess of $1.2\%$ of the total number oftwins. In the case of isolated primes, this excess for nonsquarefree numbersamounts to $0.4\%$ of the total number of such primes. The above numbers arefor the first $10^{10}$ primes, with the bias showing a tendency to grow, atleast for isolated primes.

Statistical Bias in the Distribution of Prime Pairs and Isolated Primes