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, 17, 19, 23, 29, 31, 37. All subsequent primes can be stated as multiples of 5#, adding one of these 8 bases.

Subsequent alignments are based on larger numbers of bases as each p# is considered. At the next the number of bases becomes 48 and the interval 7# or 210.

The question arises are primes balanced between bases? Are there as many primes based on 5 as 7? Over short lengths of primes this is not the case; but over longer runs there seems to be some balance.

Similarly, the 8 bases listed above, there seems to be some sort of balance, but it is anticipated there will be fluctuations but possibly no long term bias?

A nice project for some student?

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2 Responses to The balance of the primes – conjecture

  1. Ernie says:

    This referenced paper may help in providing a related prime number helix concept of distribution.
    http://www.wseas.us/e-library/transactions/mathematics/2010/89-420.pdf

    Like

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