I have a trouble solving this problem. Let's define $I$ as a set of those $i \in N$ such that $\varphi_i$ is an injective total recursive function and its range consists of all primes. Are $I$ and its complement $I^C$ recursively enumerable? Thank you in advance for your help.
2026-03-28 07:43:29.1774683809
Numbering of prime enumerating functions
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