A line of thought that occurs to me to advance the cuase for the truth of TPC is this.

The number of primes of the form 6n-1 and 6n-1 tends to be equal in the long run.

It the TPC is not true, then beyond that n which constitutes the largest higher twin 6n+1, then every prime of the form 6n-1 demands that the next gap will be at least 6. This creates a bias towards primes 6n+7, 6n+13, 6n+19,...... for all n greater than the maximum n referred to, and away from 6n+1 which is no longer permissible.

Thus the form 6n+1 would seem to have to compensate somehow by a process unknown, or covered by the word infinitesmally, which as in the delta y and delta x in differential calculus is conveniently disregarded with no harm to the calculus itself, so we are assured as the dy/dx is a limit to the ratio of delta y and delta x.

How does the form 6n+1 "catch up" if the TPC be not true? That is my question.

I hope the question is not too spooky.

John

> --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@> wrote:

> >

> > --- On Thu, 5/30/13, Maximilian Hasler <maximilian.hasler@> wrote:

> > > But of course the number 2 is the ultimate challenge, it is special in

> > > several ways, which partially may be, but aren't necessarily directly, a

> > > consequence of the fact that its the smallest possible gap.

> >

> > Just thinking about it, falsity of the TPC would be deeply disturbing.

> > Just imagine the concept of being given a prime, and then being able to instantly determine the primality a different number without knowing

> > any of its factors (in particular, knowing that it's composite). That's even spookier than magnets.

> >

> > Does anyone seriously doubt the TPC's truth?

> >

> > Phil

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