= Solution
There are
$$
20^{300}=10^{300\log_{10}20}\simeq2.04\times10^{390}
$$
possible sequences of length 300 over the standard twenty-amino-acid alphabet. Sampling $10^{20}$ sequences would cover only about $4.9\times10^{-371}$ of that space, even before allowing repeated sequences. \b[We cannot conclude that all possible <protein folds> have been explored.]
However, this sequence count is not a count of folds: many sequences can share a fold, and many arbitrary sequences may not form a stable folded <protein>. Evolution also samples sequences non-uniformly. The calculation establishes vastly incomplete sequence-space exploration; proving either exhaustive or non-exhaustive coverage of physically realizable folds needs an additional model relating sequences to structures. The observed structural-cluster count alone supplies no such proof.
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