A previously unnoticed property of prime numbers
The results are particularly striking in base 11 - looking at primes below 100 million, only 4.3% of primes ending in 2 are followed by another prime ending in 2 (compared to the 9.1% you would naively expect) with similar numbers for other pairs.<p>A prime ending in 2 (in base 11) is also unlikely to be following by a prime ending in 5, 7 or 9, whereas it is particularly likely to be following by a prime ending in 4 or 8.<p>It would be interesting to know what structure there is (if any) in this NxN &quot;transition matrix&quot; for various bases.<p><pre><code>   1: ( 1,  4.3%) ( 2, 13.0%) ( 3, 14.3%) ( 4,  7.7%) ( 5, 11.5%) ( 6,  6.3%) ( 7, 18.0%) ( 8,  9.0%) ( 9, 10.7%) (10,  5.2%) 
   2: ( 1, 10.0%) ( 2,  3.7%) ( 3, 11.3%) ( 4, 14.1%) ( 5,  7.5%) ( 6, 12.1%) ( 7,  5.3%) ( 8, 17.5%) ( 9,  7.8%) (10, 10.7%) 
   3: ( 1,  6.1%) ( 2, 10.3%) ( 3,  3.7%) ( 4, 12.5%) ( 5, 14.0%) ( 6,  9.2%) ( 7, 12.1%) ( 8,  5.6%) ( 9, 17.5%) (10,  9.0%) 
   4: ( 1, 11.1%) ( 2,  6.1%) ( 3,  9.9%) ( 4,  4.1%) ( 5, 11.5%) ( 6, 14.5%) ( 7,  7.7%) ( 8, 12.0%) ( 9,  5.3%) (10, 18.0%) 
   5: ( 1,  9.6%) ( 2, 12.7%) ( 3,  6.3%) ( 4, 11.5%) ( 5,  4.0%) ( 6, 13.6%) ( 7, 14.5%) ( 8,  9.2%) ( 9, 12.1%) (10,  6.4%) 
   6: ( 1, 17.9%) ( 2,  8.5%) ( 3, 10.6%) ( 4,  5.0%) ( 5,  9.6%) ( 6,  4.0%) ( 7, 11.4%) ( 8, 14.0%) ( 9,  7.5%) (10, 11.5%) 
   7: ( 1,  6.0%) ( 2, 19.1%) ( 3,  8.8%) ( 4, 11.1%) ( 5,  5.1%) ( 6, 11.6%) ( 7,  4.1%) ( 8, 12.5%) ( 9, 14.1%) (10,  7.7%) 
   8: ( 1, 12.0%) ( 2,  5.5%) ( 3, 17.5%) ( 4,  8.8%) ( 5, 10.6%) ( 6,  6.3%) ( 7,  9.9%) ( 8,  3.7%) ( 9, 11.3%) (10, 14.3%) 
   9: ( 1,  8.8%) ( 2, 12.4%) ( 3,  5.5%) ( 4, 19.1%) ( 5,  8.6%) ( 6, 12.7%) ( 7,  6.0%) ( 8, 10.3%) ( 9,  3.7%) (10, 13.0%) 
  10: ( 1, 14.3%) ( 2,  8.8%) ( 3, 12.0%) ( 4,  6.0%) ( 5, 17.8%) ( 6,  9.6%) ( 7, 11.1%) ( 8,  6.1%) ( 9, 10.0%) (10,  4.3%)</code></pre>