Why should I switch to Python? - Infinity of Primes

[Christian Bau]

In article <38EAC8C4.ADC25640 at cosc.canterbury.ac.nz>, Greg Ewing
<greg at cosc.canterbury.ac.nz> wrote:

> "David C. Ullrich" wrote:
> > 
> >     There's nothing non-constructive about the traditional
> > proof of the infinitude of the sequence of primes - given
> > a sequence of primes it _constructs_ a prime not on the
> > list.
> 
> Um, no it doesn't - it constructs a number which is
> *either* prime *or* divisible by some other prime bigger
> than the one you started with.
> 
> If someone actually came up with a formula for constructing
> primes, it would be rather large news -- isn't that one of
> the Big Unsolved Problems?

Take any non-empty set S of prime numbers, calculate their product, add
one, and take the smallest factor that is not equal to one. That factor is
a prime number that is not in the set S.