• Introduction
  • Introduction
  • Disclaimer
  • Version control
• Double primorial sieve
  • PDF: The (double) Primorial sieve
  • Definition of the primorial
  • Third Primorial Sieve
  • Wheel factorization size 30
  • Last digit gap of successive primes
• Numeral systems
  • PDF: Base 10^m   numeral system
• Prime spirals
  • Ulam spiral unraveled
    • PDF: The Ulam spiral unraveled
    • PDF: Prime patterns in the Ulam spiral
    • Using a Cartesian coordinate system
    • The eight families of functions
    • Exclusion lines definition
    • Exclusion lines in the Ulam spiral
    • Coordinates of natural numbers
    • Tracking the 59th SE diagonal
    • Tracking the 41th SW diagonal
    • Ulam spiral functions (mod 210)
    • Building a spiral
  • Segmented prime spirals
    • PDF: Segmented prime spirals
    • PDF: Modulo primality test
    • Prime spiral with four segments
    • Prime spiral with three segments
    • Prime spiral with two segments
    • Prime spiral with one segment
    • Analyzing segmented prime spirals
    • Prime spiral with more segments
• Miscellaneous
  • PDF: Guestbook
  • PDF: Prime number projects for students
  • Q1 spiral  in coordinate system
  • Prime pyramid  in coordinate system
  • TXT: Prime number list < 800,000
  • Links

The counterclockwise Ulam spiral (1963) with startvalue  0  is defined by  eight  families of functions.
These  eight  families of functions where discovered by placing the counterclockwise  Ulam spiral  with startvalue  0  in a Cartesian coordinate system.
Note: when using a different startvalue, this startvalue is added to each element.

The find made it possible to use  Excel  to further examine  the Ulam spiral.pdf,  while  (large) computer programs  can use the same principles.


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