I crudely piped a prime generator into a Wilson tester. Typical output: 9429 1*22287829 18832 4*22292549 13353 2*22297841 40999 8*52931741 65432 1*1079779313 meaning the number N=9429 is represented as 1*P-floor(sqrt(1*P))^2 where P is a prime of form 4m+1, namely P=22287829. And so on: 18832=4*22292549 - 9442^2, etc. Result: After 7 minutes of printing it had found Wilson/Smith representations for every N={1,2,3,...,65536} in the form N = 2^k * P - c^2 where c = floor(sqrt(2^k * P)) and P=prime of form 4m+1 and k in {0,1,2,3}. Note, previous post I had erroneously said k in {0,1,2} forgetting 3. So this confirms Wilson "yes" conjectured answer out to 2^16, and only primes P below about 2^31 were needed to do it. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)