prime number
We know there is infinitely many primes, but are there infinitely many twin primes? 

In issue No 1 we introduced GIMPS, the Great Internet Mersenne Prime Search. Well, on Sunday 24th August 1997 they did it again. 
Every even number greater than 4 can be written as the sum of two odd primes  a simple statement, but still unproven today. 
You may think that searching for new prime numbers is a job for supercomputers. However, on 13th November 1996, Frenchman Joel Armengaud discovered a new one using his humble PC. 
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