Chris Caldwell <

caldwell@...> wrote: > It is highly probable that this is a well known fact, but I

> can't find anything on the web (typing in "frequency of

> primes mod3" into Google did not produce anything.

Look up prime number race instead. Indeed it is well known and well studied.

> Whilst the Chebychev bias is well documented, the Twin Prime Race does not appear to be, and here I would appreciate some guidance.

The other day I realised that all the twin primes, excluding, but indirectly including 5 and 7, can be turned into 3 tables of twin primes each headed by very basic calculations from the first three prime numbers, 2, 3 and 5. ( I was quite surprised by this, though I've always believed rightly or wrongly that the secrets of the primes must be discernable from the first few )

The three columns of prime pairs generated under 2, 3 and 5 obviously contains large numbers of non-prime pairs as well, giving biases in one column or another.

Have these biases also been well studied?

Kind regards

Bob

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