hello, There is this puzzling property of the B(4n+2), I consider here only the fractional part, easily computable with the Von-Staudt-Clausen formula. Also, the B(4n+2) are all positives. Property ; the fractional part of the positive Bernoulli Numbers is almost never : 1/6 < {Bernoulli(4*n+2)} < 2/3. ... except for 2 cases (so far), which is {B(2072070)} = .666443506838622... and {B(6216210)} = .6588649656359250... Now, is this known? , my fist thought was that no Bernoulli(4n+2) has a fractional part between 1/6 and 2/3 , so far only 2 cases. I saw no references on this subject. The behaviour of {B(2*n)} when negative is well distributed mod 1 but the positive cases are NOT well distributed at all. Here is a graph of the succ. fractional part of Bernoulli's plotted on a circle, that is x in [-1,1] -> exp(2*Pi*x) a line is drafted between values x(0), x(1), ... http://www.lacim.uqam.ca/~plouffe/SuccFracBernoulli5000points.jpg Does someone has any reference on this? Simon Plouffe