Hey,
I was just wondering if there was any result which shows you can always find a prime of length k for any k. From the prime number theorem its clear that if you randomly (with a uniform distribution) select numbers of length k then after a given number of selections you can estimate the probability of finding a prime (and so show that there is a high likelihood of finding primes of length k). I don't really know enough number theory so this may be a pretty trivial problem. (Also I'm pretty sure I was reading something about this recently but can't remember where, any ideas?)
Thanks.

ok, this is what I was looking at: http://michaelnielsen.org/polymath1/index.php?title=Finding_primes but its about finding a polynomial time deterministic algorithm for a prime of at least length k.

Yeah, it's always possible. You can use Bertrand's postulate for example: there's always a prime between and . I can't really think of anything more elementary, I doubt you can really find much easier because in essence both this and Bertrand's postulate say more or less the same thing.

Thanks, I think I'll go and check that out in 'Proofs from the Book'.