We know from Gödel's First Incompleteness Theorem that there are true statements in the natural numbers that have no proof. Obviously we know of many that do ("theorems").

Are results known about the relative sparsity of these two sets? For instance, perhaps one could order statements by the number of characters N, and look at true statements. Do we know if "most" true statements are theorems, or the opposite, and does the fraction depend on N? Are Gödel's examples rare jury-rigged freaks, or do they actually become the rule?

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