  We present fast Rydberg-mediated entanglement involving nuclear spins of
divalent atoms with $^{171}$Yb as an example. First, we show a nuclear-spin
controlled phase gate of an arbitrary phase realizable either with two laser
pulses when assisted by Stark shifts, or with three pulses. Second, we propose
to create a state $(\lvert\text{cc}\rangle_{\text{e}} \otimes
\lvert\Phi\rangle_{\text{n}} + \lvert\Phi\rangle_{\text{e}} \otimes
\lvert\Psi\rangle_{\text{n}} )/\sqrt{2}$ entangled between the electrons~(e)
and nuclear spins~(n) of two atoms, where $\lvert\Phi\rangle$ and
$\lvert\Psi\rangle$ are two orthogonal Bell states and $\lvert
\text{c}\rangle_{\text{e}}$ denotes the clock state. For want of a better term,
it is called a Super Bell State for it mimics a ``large'' Bell state
incorporating three ``smaller'' Bell states. Third, we show a protocol to
create a three-atom state $(\sqrt{3}\lvert\text{ccc}\rangle_{\text{e}} \otimes
\lvert\Lambda\rangle_{\text{n}} + \lvert \text{W}\rangle_{\text{e}} \otimes
\lvert \text{GHZ}\rangle_{\text{n}} )/2$, where
$\lvert\Lambda\rangle_{\text{n}}$ is a nuclear-spin state, $\lvert
\text{W}\rangle_{\text{e}}$ is a W state in the ground-clock state space, and
$\lvert \text{GHZ}\rangle_{\text{n}}$ is the Greenberger-Horne-Zeilinger~(GHZ)
state in the nuclear-spin state space. The four protocols possess high
intrinsic fidelities, do not require single-site Rydberg addressing, and can be
executed with large $\Omega_{\text{m}}$ in a weak, Gauss-scale magnetic field
for they involve Rydberg excitation of both nuclear-spin qubit states in each
atom. The latter two protocols can enable measurement-based preparation of
Bell, hyperentangled, and GHZ states.
