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# Open problems with at most one unknown solution and some known solutions

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.