Valid private keys on curve25519
The private keys are integers $x$ with $2^{254} \leq x &lt; 2^{255}$ and $x \equiv 0 \pmod 8$, or just $x \in 2^{254} + 8\{0,1,2,\dots,2^{251} - 1\}$, so there are exactly $2^{254}/8 = 2^{251}$ of them.