Tag Archives: Prime Numbers

p+np# – a formula for the primes?


Take virtually any prime number as a start, and add any multiple of the next, smaller, prime number and you will create a set of integers that contains every prime…….provided one takes into account the structure of the primes as … Continue reading

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Introduction


Prime Number distribution has been a source of fascination to both professional and amateur mathematicians for many years. The distribution is easy to explain, and conceptually easy to understand, once explained, but almost impossible to see if one looks just at the prime … Continue reading

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Prime Number Symmetry


Most texts on Prime Numbers (and even a professor of Maths at Oxford University?) don’t seem to explain the patterns and order in the primes and instead prefer to use words such as “random”, “unruly or “mysterious”. There is no doubt their … Continue reading

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The balance of the primes – conjecture


Primes align. This first becomes apparent with the bases 5 and 7; all subsequent primes can be stated as multiples of 3#, adding a base of either 5 or 7. The next alignment occurs using the eight bases 11, 13, … Continue reading

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The interdependence of Primes


David Wells’ book on Prime Numbers notes the parallels between lucky numbers and primes, suggesting the role of the sieve (p147/8 under “random” primes). Imagine what the effect would be if one prime was no longer considered to be prime. … Continue reading

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Counting the Primes


Counting the primes: once one realises that Eratosthenes sieve removes composite numbers in repeatable patterns it is a relatively straightforward job of estimating how many integers are left as prime; however since these patterns only start being effective after p … Continue reading

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The gaps in the prime number distribution


Considering the prime number distribution is disjointed by a sequence of steps it is possible to explain, in part, some of the longest gaps in the prime number distribution: The first gap of 4 (between 7 and 11) is between … Continue reading

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