Here are some unsolved mathematical problems:
- Goldbach’s conjecture: Can every even integer greater than 2 be written as a sum of two primes?
- Twin Prime Conjecture: A twin prime is a pair of primes with difference 2, such as 11 and 13. Are there infinitely many twin primes?
- Does the Fibonacci sequence contain an of primes?
- Are there infinitely many perfect numbers?
- Are there any odd perfect numbers?
The Clay Mathematics Institute posted seven unresolved problems in 2000; they also offer a prize of $1.000.000 for each solution. One of the problems has been solved (Poincaré Conjecture – solved by Grigoriy Perelman, 2002-3); the six remaining problems are described in simple terms in sub-pages here.