The singularity probability of an n by n random circulant Bernoulli matrix is asymptotically the p-th power sum of binomial probabilities, where p is the smallest prime divisor of n.
Catalan , R´ echerches sur les d´ eterminants, Bulletins de l’Acad´ emie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 1 3 (1846)
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On the singularity probability of random circulant Bernoulli matrices
The singularity probability of an n by n random circulant Bernoulli matrix is asymptotically the p-th power sum of binomial probabilities, where p is the smallest prime divisor of n.