k=1000: 17762.0
k=1200: 36983.8
k=1400: 61446.5
k=1600: 91151.5
k=1800: 126099.6
k=2000: 166291.7
k=2200: 211728.3
k=2400: 262409.9

sweep [900,2439]: 0 non-positive 
endpoints: crit(900)=10116.0, crit(2439)=272903.9
VERDICT: ALL POSITIVE — range [900,2439] certified; joins [2440,inf)