Of course Gauss did not state that he was improving Legendre's result but rather claimed the result for himself since his was the first completely rigorous proof. Legendre later wrote (see):
Ng mga kurso gauss hindi estado na siya ay ang pagpapabuti Legendre's resulta kundi inaangkin ang mga resulta para sa kanyang sarili dahil sa kanyang ay ang unang ganap na mahigpit na katibayan. Legendre mamaya wrote (makita):