%I #7 May 14 2017 02:58:33

%S 257,353,409,521,569,809,857,953,1129,1153,1201,1217,1249,1657,2113,

%T 2137,2153,2273,2377,2521,2617,2633,2657,2729,2833,3209,3217,3761,

%U 3769,4481,4993,5569,5801,5897,6217,6329,6449,6529,7177,7193

%N Primes p with class number h(-p) divisible by 16.

%C These are a proper subset of the primes of the form x^2+32y^2 whose class numbers are divisible by 8.

%D Cohn, H. Introduction to the construction of class fields, Cambridge, 1985, pp. 147-151

%H Philip A. Leonard and Kenneth S. Williams, <a href="http://dx.doi.org/10.4153/CMB-1982-027-0">On the divisibility of the class numbers of Q(sqrt(-p)) and Q(sqrt(-2p)) by 16</a>, Canadian Math Bulletin,v.25 (1982), pp. 200-6.

%e h(-257)=16: binary quadratic forms of discriminant -4(257) are x^2+257y^2, 2x^2+2xy+129y^2, 3x^2+-2xy+86y^2, 6x^2+-2xy+43y^2,9x^2+-4xy+29y^2, 7x^2+-6xy+38y^2, 14x^2+-6xy+19y^2, 13x^2+-8xy+21y^2, 17x^2+-14xy+18y^2 for 16 forms (the +- forms count twice)

%K nonn

%O 1,1

%A _John L. Drost_, Apr 30 2005