Call 'Euclidean Primes' those of
the form: P = 2.p.q.r...+ 1 or -1 .

Call 'Non-Euclidean
primes' those that in both forms there is at least a factor raised to a
power >1 . Ex. : 127 = 2x3^2x7 + 1 = 2^7 - 1

For this last type of primes I
say that the relation:

**[Numb. of
Non-euclidean ] / [Numb of primes ] is less than N, when N--->
infinite, is = 1/4 .**

Example: There are 9592 primes <
100000 and 2381 Non_Euclidean . 2381/9592 = 0.248

The first Non-Euclidean are:
17,19,53,89,97,127,149,151,163,197,199,233,241,251.

**Q1.- There is
any explanation of that property?**

**Q2.- The
presence of so many twin primes is a mere coincidence?**