问题描述:
Write a function to find the nth newman–shanks–williams prime number.

测试用例:
['assert newman_prime(3) == 7 ', 'assert newman_prime(4) == 17', 'assert newman_prime(5) == 41']

生成的代码:
def newman_prime(n):
    if n < 1:
        return None

    # Initialize the first three Newman–Shanks–Williams primes
    nsw_primes = [2, 3, 5]
    
    # Generate NSW primes until we have at least n
    while len(nsw_primes) < n:
        next_prime = 0
        for i in range(len(nsw_primes)):
            for j in range(i, len(nsw_primes)):
                candidate = nsw_primes[i] * nsw_primes[j] + 1
                if candidate > next_prime:
                    next_prime = candidate
        
        # Check if next_prime is prime
        def is_prime(num):
            if num < 2:
                return False
            for i in range(2, int(num**0.5) + 1):
                if num % i == 0:
                    return False
            return True
        
        if is_prime(next_prime):
            nsw_primes.append(next_prime)

    return nsw_primes[n - 1]

# Test cases
assert newman_prime(3) == 7 
assert newman_prime(4) == 17 
assert newman_prime(5) == 41