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def filter_predicate_by_primary_keys(predicate, primary_keys):
    """
    Filter out predicates that are not related to primary key fields.
    """
    from pypaimon.api import Predicate

    if predicate is None or primary_keys is None:
        return predicate

    py_predicate = predicate.py_predicate

    if py_predicate.method in ['and', 'or']:
        filtered_literals = []
        for literal in py_predicate.literals:
            filtered = filter_predicate_by_primary_keys(literal, primary_keys)
            if filtered is not None:
                filtered_literals.append(filtered)

        if not filtered_literals:
            return None

        if len(filtered_literals) == 1:
            return filtered_literals[0]

        return Predicate(Predicate(
            method=py_predicate.method,
            index=py_predicate.index,
            field=py_predicate.field,
            literals=filtered_literals
        ), None)

    if py_predicate.field in primary_keys:
        return predicate
    else:
        return None