Primzahlenmuster

Es werden gleich lange Reihen von natürlichen Zahlen gebildet.

Primzahlen werden durch O, Nichtprimzahlen durch + dargestellt.

Wenn die Zeilenbreite ein Vielfaches der Produkte von 2, 3 und 5 ist, ergibt sich ein scheinbar besonders regelmäßiges Muster.

   Zeilenbreite 30,  Zahlen von 1 bis 1200

  +OO+O+O+++O+O+++O+O+++O+++++O+

  O+++++O+++O+O+++O+++++O+++++O+

  O+++++O+++O+O+++++O+++O+++++O+

  ++++++O+++O+O+++O+O+++O+++++++

  ++++++O+++O+++++O+O+++++++++O+

  O+++++O+++++O+++O+++++O+++++O+

  O+++++++++O+O+++O+O+++++++++++

  O+++++++++++O+++O+O+++O+++++O+

  O+++++++++O+++++O+++++O+++++O+

  O+++++O+++O+O+++++++++O+++++++

  ++++++O+++O+O+++O+++++++++++++

  O+++++O+++++++++O+O+++O+++++O+

  ++++++O+++++O+++++O+++O+++++O+

  ++++++O+++O+++++++O+++++++++O+

  O+++++++++O+O+++++O+++O+++++O+

  ++++++O+++O+O+++O+++++++++++O+

  ++++++O+++O+++++++O+++O+++++O+

  ++++++++++O+O+++++++++++++++++

  O+++++O+++++++++O+++++O+++++O+

  O+++++O+++++++++O+++++O+++++O+

  O+++++O+++++O+++O+O+++++++++++

  O+++++++++O+O+++O+++++O+++++O+

  O+++++++++++O+++O+++++O+++++++

  O+++++++++O+++++++O+++++++++O+

  ++++++O+++++O+++++O+++O+++++++

  O+++++O+++O+++++++O+++O+++++++

  ++++++O+++++++++O+++++++++++O+

  O+++++++++O+O+++O+O+++++++++O+

  ++++++++++++O+++O+O+++O+++++++

  ++++++O+++O+O+++O+++++++++++++

  ++++++O+++O+++++++O+++++++++O+

  ++++++O+++O+++++O+++++O+++++++

  ++++++O+++O+++++O+++++O+++++++

  O+++++O+++++++++++O+++O+++++O+

  O+++++++++O+O+++++O+++++++++O+

  O+++++++++O+O+++++O+++++++++++

  ++++++O+++O+O+++O+++++O+++++O+

  ++++++O+++++O+++++O+++++++++++

  ++++++++++O+O+++++++++O+++++++

  O+++++++++O+++++O+++++O+++++++

  Primzahlen insgesamt:  196

   Zeilenbreite 30,  1200 Zahlen von 99 991  bis 101 190

  O+++++++++++O+++++++++++++++O+

  ++++++++++++++++++++++O+++++O+

  ++++++O+++++++++++O+++++++++++

  ++++++++++++++++++++++O+++++O+

  ++++++++++++++++++O+++++++++++

  ++++++++++O+O+++++++++++++++O+

  ++++++++++++O+++++O+++O+++++++

  ++++++O+++++O+++++++++++++++++

  ++++++O+++++++++++++++++++++++

  ++++++O+++O+++++++O+++++++++++

  O+++++O+++++++++++++++O+++++++

  ++++++++++++O+++++++++O+++++++

  ++++++O+++O+O+++++++++++++++O+

  ++++++++++O+O+++++++++O+++++++

  O+++++O+++++++++++++++++++++++

  ++++++O+++++++++++O+++++++++O+

  ++++++++++++O+++++++++O+++++++

  O+++++++++O+++++O+O+++O+++++++

  ++++++O+++++++++O+O+++++++++O+

  ++++++++++++++++++++++++++++++

  O+++++++++++++++++O+++O+++++++

  O+++++++++++++++++++++++++++O+

  ++++++++++++++++++O+++O+++++++

  ++++++++++++O+++++O+++O+++++++

  ++++++++++++++++++++++O+++++++

  O+++++O+++++++++++++++++++++O+

  ++++++++++++++++O+++++++++++O+

  O+++++++++O+++++++++++O+++++O+

  ++++++++++++++++O+++++O+++++++

  ++++++++++++++++++++++++++++++

  ++++++++++++++++O+++++O+++++++

  ++++++O+++O+++++O+++++O+++++++

  ++++++O+++++++++++++++++++++++

  O+++++O+++++++++++O+++++++++O+

  ++++++++++O+++++O+++++++++++++

  ++++++++++O+++++++++++O+++++++

  ++++++++++O+++++++O+++++++++++

  ++++++O+++O+O+++O+O+++++++++++

  ++++++++++O+++++++O+++++++++O+

  O+++++++++++O+++++++++O+++++++

 Primzahlen insgesamt:  100

Bereits aus der Primzahlanzahlfunktion ergibt sich, dass die Anzahl der Primzahlen in gleich breiten Intervallen mit zunehmender Größe abnimmt.

 Zeilenbreite 43,  Zahlen von 1 bis 1978

  +OO+O+O+++O+O+++O+O+++O+++++O+O+++++O+++O+O

  +++O+++++O+++++O+O+++++O+++O+O+++++O+++O+++

  ++O+++++++O+++O+O+++O+O+++O+++++++++++++O++

  +O+++++O+O+++++++++O+O+++++O+++++O+++O+++++

  O+++++O+O+++++++++O+O+++O+O+++++++++++O++++

  +++++++O+++O+O+++O+++++O+O+++++++++O+++++O+

  ++++O+++++O+O+++++O+++O+O+++++++++O++++++++

  +++++O+++O+O+++O+++++++++++++O+++++O+++++++

  ++O+O+++O+++++O+++++++O+++++O+++++O+++O++++

  +O+++++++O+++O+++++++O+++++++++O+O+++++++++

  O+O+++++O+++O+++++O+++++++O+++O+O+++O++++++

  +++++O+++++++O+++O+++++++O+++O+++++O+++++++

  ++++O+O+++++++++++++++++O+++++O+++++++++O++

  +++O+++++O+O+++++O+++++++++O+++++O+++++O+O+

  ++++O+++++O+++O+O+++++++++++O+++++++++O+O++

  +O+++++O+++++O+O+++++++++++O+++O+++++O+++++

  ++O+++++++++O+++++++O+++++++++O+++++++O++++

  +O+++++O+++O+++++++O+++++O+++O+++++++O+++O+

  ++++++++++++O+++++++++O+++++++++++O+O++++++

  +++O+O+++O+O+++++++++O+++++++++++++O+++O+O+

  ++O+++++++++++++O+++O+O+++O++++++++++++++++

  +++O+++O+++++++O+++++++++O+++++++O+++O+++++

  O+++++O+++++++++++++O+++O+++++O+++++O++++++

  +O+++++O+++++++++++O+++O+++++O+O+++++++++O+

  O+++++O+++++++++O+O+++++++++O+O+++++O++++++

  +++++++++++O+++O+O+++O+++++O+++++O+++++++O+

  ++++O+++++O+++++++++++++++++++++O+O++++++++

  +O+++++++O+++++++++O+++++O+++++O+++++++O+++

  ++++++++O+++O+++++O+++++O+O+++++O++++++++++

  +O+++++++++O+++++++++++++++++O+O+++O+++++O+

  O+++++O+++O+O+++O+++++++++++O+O+++++O++++++

  +++++++++++++++++++++++++++O+++++O+++++O+++

  ++++O+++++++++++++++++O+++++++++O++++++++++

  +++O+++O+O+++O+++++O+++++++O+++O+O+++++O+++

  ++++++++O+++++++++O+O+++O+O+++O+++++O++++++

  +++++O+++++++++++O+++++++O+++++++++++O+++++

  O+++O+++++O+++++++O+++O+++++++O+++O++++++++

  +++++O+++O+++++O+O+++O+++++O+O+++++O+++++++

  ++O+++++++++++++++++++O+++++O+++O+O++++++++

  +++++++++++++++O+++O+O+++++++++O+++++++++++

  O+O+++++++++O+++++++O+++++O+++++O+++++O++++

  +++++++++++++O+++++O+++O+O+++++++++++O+++++

  ++++O+++++++++++O+++++++O+++++++++++++++O++

  +++++++++++O+++++O+++O+O+++O+O+++++++++O+++

  ++++++++O+++++O+++++O+++++++++++++++++O+O++

  +++++++++++++O+O+++++++++++++++++++++O+++++

  Zeilenbreite 55,  Zahlen von 1 bis 2970

  +OO+O+O+++O+O+++O+O+++O+++++O+O+++++O+++O+O+++O+++++O++

  +++O+O+++++O+++O+O+++++O+++O+++++O+++++++O+++O+O+++O+O+

  ++O+++++++++++++O+++O+++++O+O+++++++++O+O+++++O+++++O++

  +O+++++O+++++O+O+++++++++O+O+++O+O+++++++++++O+++++++++

  ++O+++O+O+++O+++++O+O+++++++++O+++++O+++++O+++++O+O++++

  +O+++O+O+++++++++O+++++++++++++O+++O+O+++O+++++++++++++

  O+++++O+++++++++O+O+++O+++++O+++++++O+++++O+++++O+++O++

  +++O+++++++O+++O+++++++O+++++++++O+O+++++++++O+O+++++O+

  ++O+++++O+++++++O+++O+O+++O+++++++++++O+++++++O+++O++++

  +++O+++O+++++O+++++++++++O+O+++++++++++++++++O+++++O+++

  ++++++O+++++O+++++O+O+++++O+++++++++O+++++O+++++O+O++++

  +O+++++O+++O+O+++++++++++O+++++++++O+O+++O+++++O+++++O+

  O+++++++++++O+++O+++++O+++++++O+++++++++O+++++++O++++++

  +++O+++++++O+++++O+++++O+++O+++++++O+++++O+++O+++++++O+

  ++O+++++++++++++O+++++++++O+++++++++++O+O+++++++++O+O++

  +O+O+++++++++O+++++++++++++O+++O+O+++O+++++++++++++O+++

  O+O+++O+++++++++++++++++++O+++O+++++++O+++++++++O++++++

  +O+++O+++++O+++++O+++++++++++++O+++O+++++O+++++O+++++++

  O+++++O+++++++++++O+++O+++++O+O+++++++++O+O+++++O++++++

  +++O+O+++++++++O+O+++++O+++++++++++++++++O+++O+O+++O+++

  ++O+++++O+++++++O+++++O+++++O+++++++++++++++++++++O+O++

  +++++++O+++++++O+++++++++O+++++O+++++O+++++++O+++++++++

  ++O+++O+++++O+++++O+O+++++O+++++++++++O+++++++++O++++++

  +++++++++++O+O+++O+++++O+O+++++O+++O+O+++O+++++++++++O+

  O+++++O+++++++++++++++++++++++++++++++++O+++++O+++++O++

  +++++O+++++++++++++++++O+++++++++O+++++++++++++O+++O+O+

  ++O+++++O+++++++O+++O+O+++++O+++++++++++O+++++++++O+O++

  +O+O+++O+++++O+++++++++++O+++++++++++O+++++++O+++++++++

  ++O+++++O+++O+++++O+++++++O+++O+++++++O+++O++++++++++++

  +O+++O+++++O+O+++O+++++O+O+++++O+++++++++O+++++++++++++

  ++++++O+++++O+++O+O+++++++++++++++++++++++O+++O+O++++++

  +++O+++++++++++O+O+++++++++O+++++++O+++++O+++++O+++++O+

  ++++++++++++++++O+++++O+++O+O+++++++++++O+++++++++O++++

  +++++++O+++++++O+++++++++++++++O+++++++++++++O+++++O+++

  O+O+++O+O+++++++++O+++++++++++O+++++O+++++O++++++++++++

  +++++O+O+++++++++++++++O+O+++++++++++++++++++++O+++++O+

  ++++++O+++++O+++O+O+++O+++++++O+++++O+++++++++O+O++++++

  +++O+++++++++++++O+++++++++O+++++O+++++++++++O+O+++O+O+

  ++++++++O+++++++++++O+O+++++++++++++++O+O+++++O+++O+O++

  +++++++O+++++++O+++++++++++++++++O+++++++++++++++++++++

  ++O+++O+++++O+++++++O+++++++++++++++O+O+++O+++++++O++++

  +++++++++++O+O+++O+++++++O+++++O+++++O+++O+++++++++++O+

  O+++++++++++++++++++++O+++++O+O+++++O+++O+++++O++++++++

  +++++O+++++O+++O+O+++++O+++O+++++O+++++++++++O+++++O+++

  ++O+++++++++++++O+++O+++++O+++++++++++O+++++++O+++++O++

  +O+++++++++++++++++++++++++O+++++++++++++++++O+++++++++

  O+++++++O+++O+++++O+O+++++O+++++++++++++++++++++O++++++

  +++++O+O+++++++++++++++O+++++++O+++O+++++++++++O+++++++

  ++++++O+++++++++O+O+++O+++++++O+++++O+++++O+++O+O+++O++

  +++O+++++++O+++O+O+++++O+++++++++O+O+++++++++O+++++++O+

  ++O+++++++++++++O+++++++++O+++++++++++O+O+++++O+++O+O++

  +++++++++++++O+++++++++++++O+++O+++++O+++++++O+++++O+++

  O+++++++++++++++++O+++++++O+++++++++O+++++O+++++O++++++

  +O+++++++++O+++++++++++O+++++++++++++O+++O+++++O+++++O+

Es wird vermutet, dass es unendlich viele Primzahlzwillinge, gibt, das sind Primzahlen, die die Differenz 2  haben.

Andererseits kann der Abstand zwischen zwei aufeinanderfolgenden Primzahlen beliebig groß werden.

Wie zufällig ist nun die Anzahl der Primzahlen pro Zeile im „Zahlenteppich“ mit einer vorgegebenen Zeilenbreite?

Weiterführende Internetseiten:

http://www.hp-gramatke.de/primes/german/page0050.htm

http://de.wikipedia.org/wiki/Primzahlzwilling