Some philosophy about gaps
- Some philosophy about gaps
The fact that the prime numbers are apparently so irregularly
distributed is not at the prime numbers, but because of the question.
The question about gaps implies an additive nature of the prime
numbers, but the prime numbers are only multiplicatively defined. Sieve
of Eratosthenes: As long as there is only multiple of 2, there is no
problem. But now 2+1=3 comes into play, thus the addition, and thus the
next prime number. Each prime number p is the beginning of a sequence
of multiples n*p and result of an addition p=k+1, where k is multiple
of a prime number < p. There is no space for a question about gaps
beyond gap = 1; each prime number is a beginning, as the name says.
There are no gaps between the primes, the primes ARE the gaps the
gaps between the non-primes. Each prime number is a gap in the world
through which the Nothing grins.
Werner D. Sand