Author Archives: primepatterns

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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Counting the primes


One of the key missing elements of the prime number sequence is the ability to identify the i th  term in the sequence. That works two ways – can we calculate the  i th  term and if we have a prime number … 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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Start here…..Composite arrays or more strictly helices


Arrays of composite numbers associated with each prime number 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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