What are examples of open problems with at most one unknown solution and some known solutions?
Some examples:
There is at most one more Idoneal number.
CLASS NUMBER TWO FOR REAL QUADRATIC FIELDS OF RICHAUD-DEGERT TYPE: The following are equivalent (a) $h_\Delta=2$ (b) $\Delta$ s one of the following values, with one GRH-ruled-out exception: {85, 165, 221, 285, ...
Trying the make the question well defined the problems shouldn't be artificially constructed.
Preferably the missing solution shouldn't be ruled out by some plausible conjecture.
