Prime Ratios

  Lists of prime ranges, number of primes, and the ratio of primes to
non-primes. The charts were made using primegen by D. J. Bernstein (see
http://cr.yp.to/).

Primes from 1-N:

  N, n, (R)

  For example, there are four primes (2, 3, 5, 7) from 1-10; thus, N is
10, n is 4, and R is 0.4.


1. Powers of 10.

              10,          4 (0.400000)
             100,         25 (0.250000)
            1000,        168 (0.168000)
           10000,       1229 (0.122900)
          100000,       9592 (0.095920)
         1000000,      78498 (0.078498)
        10000000,     664579 (0.066458)
       100000000,    5761455 (0.057615)
      1000000000,   50847534 (0.050848)

2. Powers of 9.

               9,          4 (0.444444)
              81,         22 (0.271605)
             729,        129 (0.176955)
            6561,        847 (0.129096)
           59049,       5968 (0.101069)
          531441,      43934 (0.082670)
         4782969,     334349 (0.069904)
        43046721,    2607165 (0.060566)
       387420489,   20700806 (0.053432)

3. Powers of 8.

               8,          4 (0.500000)
              64,         18 (0.281250)
             512,         97 (0.189453)
            4096,        564 (0.137695)
           32768,       3512 (0.107178)
          262144,      23000 (0.087738)
         2097152,     155611 (0.074201)
        16777216,    1077871 (0.064246)
       134217728,    7603553 (0.056651)

4. Powers of 7.

               7,          4 (0.571429)
              49,         15 (0.306122)
             343,         68 (0.198251)
            2401,        357 (0.148688)
           16807,       1939 (0.115369)
          117649,      11098 (0.094331)
          823543,      65685 (0.079759)
         5764801,     397764 (0.068999)
        40353607,    2453911 (0.060810)
       282475249,   15353323 (0.054353)

5. Powers of 6.

               6,          3 (0.500000)
              36,         11 (0.305556)
             216,         47 (0.217593)
            1296,        210 (0.162037)
            7776,        985 (0.126672)
           46656,       4821 (0.103331)
          279936,      24427 (0.087259)
         1679616,     126726 (0.075449)
        10077696,     669432 (0.066427)
        60466176,    3588148 (0.059341)

6. Powers of 5.

               5,          3 (0.600000)
              25,          9 (0.360000)
             125,         30 (0.240000)
             625,        114 (0.182400)
            3125,        445 (0.142400)
           15625,       1821 (0.116544)
           78125,       7671 (0.098189)
          390625,      33118 (0.084782)
         1953125,     145713 (0.074605)
         9765625,     650133 (0.066574)
        48828125,    2934858 (0.060106)

7. Powers of 4.

               4,          2 (0.500000)
              16,          6 (0.375000)
              64,         18 (0.281250)
             256,         54 (0.210938)
            1024,        172 (0.167969)
            4096,        564 (0.137695)
           16384,       1900 (0.115967)
           65536,       6542 (0.099823)
          262144,      23000 (0.087738)
         1048576,      82025 (0.078225)
         4194304,     295947 (0.070559)
        16777216,    1077871 (0.064246)

8. Powers of 3.

               3,          2 (0.666667)
               9,          4 (0.444444)
              27,          9 (0.333333)
              81,         22 (0.271605)
             243,         53 (0.218107)
             729,        129 (0.176955)
            2187,        327 (0.149520)
            6561,        847 (0.129096)
           19683,       2227 (0.113143)
           59049,       5968 (0.101069)
          177147,      16097 (0.090868)
          531441,      43934 (0.082670)
         1594323,     120739 (0.075731)
         4782969,     334349 (0.069904)
        14348907,     931260 (0.064901)
        43046721,    2607165 (0.060566)
       129140163,    7332159 (0.056777)
       387420489,   20700806 (0.053432)

9. Powers of 2.

               2,          1 (0.500000)
               4,          2 (0.500000)
               8,          4 (0.500000)
              16,          6 (0.375000)
              32,         11 (0.343750)
              64,         18 (0.281250)
             128,         31 (0.242188)
             256,         54 (0.210938)
             512,         97 (0.189453)
            1024,        172 (0.167969)
            2048,        309 (0.150879)
            4096,        564 (0.137695)
            8192,       1028 (0.125488)
           16384,       1900 (0.115967)
           32768,       3512 (0.107178)
           65536,       6542 (0.099823)
          131072,      12251 (0.093468)
          262144,      23000 (0.087738)
          524288,      43390 (0.082760)
         1048576,      82025 (0.078225)
         2097152,     155611 (0.074201)
         4194304,     295947 (0.070559)
         8388608,     564163 (0.067253)
        16777216,    1077871 (0.064246)
        33554432,    2063689 (0.061503)
        67108864,    3957809 (0.058976)
       134217728,    7603553 (0.056651)
       268435456,   14630843 (0.054504)
       536870912,   28192750 (0.052513)
      1073741824,   54400028 (0.050664)