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Abstract :

The distribution of the non-prime numbers and prime numbers can be described in a graphical way with a simple Wave-Model (or Interference Model): see Table 2

There are clear rules which define the distribution and the existence of prime numbers. But not the prime numbers define these rules !

The non-prime numbers between the prime numbers are the defining elements of these rules !

In principle there are two basic number sequences which play a major role in the prime number distribution.

The first Number Sequence ( SQ1 ) contains all prime numbers of the form 6n+5 and the second Number Sequence ( SQ2 ) contains all prime numbers of the form 6n+1.

All existing prime numbers are contained in these two number sequences except of the prime numbers 2 and 3.

Another key role in the distribution of the prime number plays the number 5 and its periodic occurrence in the two number sequences SQ1 & SQ2.

All non-prime numbers in SQ1 & SQ2 are caused by recurrences of these two number sequences with increasing wave-lengths in themselves, in a similar fashion

as “Overtones” ( harmonics ) or “Undertones” derive from a fundamental frequency.

On the contrary prime numbers represent “silent spots” in these two basic Number Sequences SQ1 & SQ2 where there is no interference caused by these recurring number sequences.

here the complete image of the Wave-Model for the prime number distribution :