Strange behaviour of prime numbers

[ijabbott]

(05-31-2019 07:07 PM)Gilles Wrote:  I'm not expert of this, but I guess this could be explain by the fact that there are some links between "divisibilty" and digits of a number. The most obvious is that a number is divisible by 3 if the sum of its digits is divisible by 3.

Suppose a prime number composed like this : abc3
Of course, a+b+c+3 is not divisible by 3. Remains 1 or 2

The next number with 3 at the end is : ab(c+1)3 . And there is a probability of 50% that a+b+(c+1)+3 is divisible by 3. So the probability of ab(c+1)3 is a prime number decrease of 50%.

The "gap" between the digits is also important, I imagine

That's why I suggested trying base 8 or base 16, because the base is co-prime with all odd numbers.