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Fix a number field k with its adele ring A. Let G=O(n+3) be an orthogonalgroup of k-rank 1 and H=O(n+2) a k-anisotropic subgroup. We have previously[arXiv:0908.3521] described how to factor the global period of a sphericalEisenstein series of G against a cuspform F of H into an Euler product. Here,we describe how to evaluate the factors at even primes. When the local field isunramified, we carry out the computation in all cases. We show also concreteexamples of the complete period when k=Q. The results are consistent with theGross-Prasad conjecture.

Compact periods of Eisenstein series of orthogonal groups of rank one at even primes