Strange behaviour of prime numbers

[ijabbott]

(05-27-2019 08:38 AM)fred_76 Wrote:  If we write [nm] to identify a couple of primes, the first ending by n followed by the second ending by m then :
- least frequent are the "double ending" 11, 33, 77, 99 with a % of occurence in the range of 17%.
- most frequent is 91 with an occurence of a bit less than 33%
- then 17, 13, 39 and 79 with about 30%
- and 19, 31, 37, 71, 73, 93, 97 between about 21% and 28%

The table for the 10 first million primes is as follows. It shows the proportion of primes ending by n, followed by a prime ending by m, to the number of primes ending by n :

Code:


nm    %
11    17.9%
13    30.2%
17    30.8%
19    21.1%
    
31    23.7%
33    16.9%
37    28.6%
39    30.8%
    
71    25.6%
73    27.3%
77    16.9%
79    30.3%
    
91    32.8%
93    25.6%
97    23.7%
99    17.8%

I wonder how much the results are perturbed by the larger gap between 3 and 7 (due to the missing digit 5)? It would be interesting to repeat the test for base 8 or base 16 where there are no gaps in candidate odd number last digit.