The problem is that all the programs start their search at 1 (except tinhorn2's, which starts at 9). If 1 is composite, then it's a counterexample, because it cannot be expressed as a prime plus twice a square. (In fact, 1 is neither prime nor composite.)

Fortunately, they're all easy to fix. The stream-based programs can use (integers-starting-with 3) instead of integers or (stream-iota); the sequence-based programs can use (in-naturals 3); and the loop program can use (let ((n 3)) ...).