As described in JDK-8146153, the constructor BigInteger(int numBits, Random rnd) generates BigIntegers which are highly skewed toward the upper end of the half-open interval [0, 2^numBits). A simple change is suggested in the aforementioned issue which would likely greatly reduce although not entirely alleviate the lack of uniformity in the distribution of BigIntegers which this constructor produces. This change should be evaluated and considered if testing shows a significant improvement.