There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems include
1. The Goldbach conjecture.
2. The Riemann hypothesis.
3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4.
4. The twin prime conjecture .
5. Determination of whether NP-problems are actually P-problems.
6. The Collatz problem.
7. Proof that the 196-algorithm does not terminate when applied to the number 196.
8. Proof that 10 is a solitary number.
9. Finding a formula for the probability that two elements chosen at random generate the symmetric group .
10. Solving the happy end problem for arbitrary .
11. Finding an Euler brick whose space diagonal is also an integer.
12. Proving which numbers can be represented as a sum of three or four cubic numbers.
13. Lehmers Mahler measure problem and Lehmers totient problem on the existence of composite numbers such that , where is the totient function.
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