Category Archives: Prime Number Distribution

Euler’s phi function 2,8,48, 480, 5760


It doesn’t take too much delving around with the primes to come across the appearance of Euler’s totient or phi function. It oozes out of the primes in a variety of locations. Firstly the composite helices and thus the prime … Continue reading

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Let’s start at the beginning…..


Composites & Primes – their relationship Continue reading

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What’s the problem?


We want to define the prime numbers as a logical sequence with a workable formula for the nth term and a means of establishing what n is when we have a given integer. As such we should then be able … Continue reading

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Secondary arrays


This element needs to be read after that titled “Composite arrays“. A secondary array of integers (a mix of primes and composites) emerges by dividing the associated composite array by Pn  i.e. by the prime number “associated” with that composite … Continue reading

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Counting the prime pairs


Is there an infinite number of prime pairs? How frequent are prime pairs? Why are their prime pairs? Intriguing questions best examined from the composites: why do they exist for starters? Look at the role of prime factors 2 and … Continue reading

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Prime and Composite


Integers are either Prime or Composite. Think of the composites as a wood block with pattern encrypted and the Primes as the resulting print. However, you can stare at a block of wood for a long timer without seeing the … Continue reading

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Prime or Composite?


Is an integer Prime or Composite? Is there any proof an integer being Prime, other than it not being Composite i.e. it has no prime factors? Lists of potentially prime numbers or pseudo primes http://en.wikipedia.org/wiki/Pseudoprime have been identified using a variety of … Continue reading

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