0.5714285714285714285...

This number is neither prime nor composite.

                                         0. 5714285714 2857142857 1428571428
5714285714 2857142857 1428571428 5714285714 2857142857 1428571428 5714285714

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The number of primes p < N = 2^n for which r (arbitrarily placed) digits in the binary expansion of p are specified is, when n large enough, equal to r < c(n/log n)^(4/7). [Post]