The ABC or Masser--Oesterle' Conjecture in Number Theory
Sites related to the Catalan Conjecture, that 8 and 9 are the only consecutive powers.
The Collatz, Syracuse or 3x+1 problem
Goldbach conjectured that every even number is the sum of two primes.
Numbers not known to yield a palindrome under repeated applications of the reverse-decimal-digits--then--add map.