Certainly! To write a test case generator for the problem "Expression Mining," we need to produce random expressions conforming to the specified grammar and a target value `n` for the expressions. Here is a Python function to generate such test cases:

```python
import random

def generate_expression(max_length, depth=0):
    if depth > 1000 or random.random() < 0.2 and max_length > 1:
        # Base case to prevent too deep recursion or to end early
        return str(random.randint(1, 9))

    length = random.randint(1, max_length)
    expr = []
    while length > 0:
        if random.random() < 0.5:
            # Add a single digit
            expr.append(str(random.randint(1, 9)))
            length -= 1
        else:
            # Add a sub-expression
            if length > 2:
                sub_length = random.randint(1, length - 2)
                sub_expr = generate_expression(sub_length, depth + 1)
                expr.append(f'({sub_expr})')
                length -= (sub_length + 2)
            else:
                expr.append(str(random.randint(1, 9)))
                length -= 1

        if length > 0:
            # Add an operator
            expr.append(random.choice(['+', '*']))
            length -= 1

    # Remove trailing operator if exists
    if expr[-1] in ['+', '*']:
        expr.pop()

    return ''.join(expr)

def tcgen():
    datasets = []
    total_length = 0
    while total_length < 5 * 10**6:
        n = random.randint(1, 10**9)
        remaining_length = min(2 * 10**6, 5 * 10**6 - total_length)
        expr_length = random.randint(1, remaining_length)
        s = generate_expression(expr_length)
        datasets.append((n, s))
        total_length += len(s)

    datasets.append((0, ""))
    return datasets

# Example usage
test_cases = tcgen()
for n, s in test_cases:
    if n == 0:
        print(n)
    else:
        print(n)
        print(s)
```

### Explanation of the Code

1. **`generate_expression` Function**: This function recursively generates a random arithmetic expression conforming to the specified grammar. It ensures the nesting depth of parentheses is limited to 1000, and balances the generation of digits and sub-expressions.

2. **`tcgen` Function**: This main function generates multiple datasets, each consisting of a target value `n` and an arithmetic expression `s`. It ensures the total length of all strings does not exceed 5 million characters. The function adds a line containing a single zero at the end to indicate the termination of input, as specified in the problem statement.

### Output
The generated test cases can be printed or written to a file for use in testing a solution to the "Expression Mining" problem. The provided example usage demonstrates how to print the test cases.