A lecture on prime numbers

Here is a very accessible lecture for a general audience, on prime numbers, by a very bright young mathematician.
   http://www.youtube.com/watch?v=PtsrAw1LR3E

In the beginning of the video observe the description of his profile.

The key result of his that he talks about is the following:
"Primes contain arbitrarily long arithmetic progressions"

Examples:
   3,5,7 are primes. These are an arithmetic progression of 3 prime numbers spaced 2 apart.
5,11,17,23 are an arithmetic progression of 4 prime numbers with common difference 6.
7,157,307,457,607,757 are an arithmetic progression of 7 prime numbers (the common difference is 150).

The result he proved in 2004 says that among primes, there are arbitrarily long arithmetic progressions. The longest found so far contain 23 prime numbers:
56211383760397 + 44546738095*n  ( n = 0, 1, ... , 22)

I am sure most of you will agree that understanding the result is easy. Notice, in the lecture, that he mentions that there can be arithmetic progressions millions of prime numbers long; no one knows how to find them!!  The best we have got is 23 primes sequence.

 Also, visit his blog http://terrytao.wordpress.com/ and check out the "Career Advice" section for something you may find useful.