pi(x) is the number of primes not larger than x x pi(x) ---- ----------------------------- 2^1 : 1 2^2 : 2 2^3 : 4 2^4 : 6 2^5 : 11 2^6 : 18 2^7 : 31 2^8 : 54 2^9 : 97 2^10 : 172 2^11 : 309 2^12 : 564 2^13 : 1.028 2^14 : 1.900 2^15 : 3.512 2^16 : 6.542 2^17 : 12.251 2^18 : 23.000 2^19 : 43.390 2^20 : 82.025 2^21 : 155.611 2^22 : 295.947 2^23 : 564.163 2^24 : 1.077.871 2^25 : 2.063.689 2^26 : 3.957.809 2^27 : 7.603.553 2^28 : 14.630.843 2^29 : 28.192.750 2^30 : 54.400.028 2^31 : 105.097.565 2^32 : 203.280.221 2^33 : 393.615.806 2^34 : 762.939.111 2^35 : 1.480.206.279 2^36 : 2.874.398.515 2^37 : 5.586.502.348 2^38 : 10.866.266.172 2^39 : 21.151.907.950 2^40 : 41.203.088.796 2^41 : 80.316.571.436 2^42 : 156.661.034.233 2^43 : 305.761.713.237 2^44 : 597.116.381.732 2^45 : 1.166.746.786.182 2^46 : 2.280.998.753.949 2^47 : 4.461.632.979.717 2^48 : 8.731.188.863.470 2^49 : 17.094.432.576.778 2^50 : 33.483.379.603.407 2^51 : 65.612.899.915.304 2^52 : 128.625.503.610.475 2^53 : 252.252.704.148.404 2^54 : 494.890.204.904.784 2^55 : 971.269.945.245.201 2^56 : 1.906.879.381.028.850 2^57 : 3.745.011.184.713.964 2^58 : 7.357.400.267.843.990 2^59 : 14.458.792.895.301.660 2^60 : 28.423.094.496.953.330 2^61 : 55.890.484.045.084.135 2^62 : 109.932.807.585.469.973 2^63 : 216.289.611.853.439.384 2^64 : 425.656.284.035.217.743 2^65 : 837.903.145.466.607.212 2^66 : 1.649.819.700.464.785.589 2^67 : 3.249.254.387.052.557.215 2^68 : 6.400.771.597.544.937.806 2^69 : 12.611.864.618.760.352.880 2^70 : 24.855.455.363.362.685.793 2^71 : 48.995.571.600.129.458.363 2^72 : 96.601.075.195.075.186.855 2^73 : 190.499.823.401.327.905.601 2^74 : 375.744.164.937.699.609.596 2^75 : 741.263.521.140.740.113.483 2^76 : 1.462.626.667.154.509.638.735 The table is from Tomas Oliveira e Silva : http://sweet.ua.pt/tos/primes.html |
