金声玉亮2.0模型评测报告

Complete the following python code:

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""

答案

模型	模型答案	测试结果
金声玉亮2.0	To complete the `prime_fib` function, we need to generate Fibonacci numbers and check whether they are prime. We'll keep doing this until we find the n-th Fibonacci number that is also prime. Here's the completed code: ```python def is_prime(num: int) -> bool: """Check if a number is prime.""" if num <= 1: return False if num == 2: return True if num % 2 == 0: return False for i in range(3, int(num0.5) + 1, 2): if num % i == 0: return False return True def prime_fib(n: int) -> int: """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ fib_a, fib_b = 0, 1 count = 0 while count < n: fib_a, fib_b = fib_b, fib_a + fib_b if is_prime(fib_b): count += 1 return fib_b if __name__ == "__main__": import doctest doctest.testmod() ``` ### Explanation: 1. is_prime Function: - This function checks if a given number is prime. - It returns `False` for numbers less than or equal to 1. - It returns `True` for 2. - It checks if the number is divisible by any number from 3 up to the square root of the number, incrementing by 2 (to skip even numbers). 2. prime_fib Function: - It initializes the first two Fibonacci numbers (`fib_a` and `fib_b`). - It uses a `while` loop to generate Fibonacci numbers and checks if they are prime. - It keeps a `count` of how many prime Fibonacci numbers have been found. - When `count` reaches `n`, it returns the current Fibonacci number (`fib_b`). 3. Testing**: - The `doctest` module is used to verify that the function works as expected based on the provided examples.	passed
deepseekr1	To solve this problem, we need to find the n-th number in the Fibonacci sequence that is also a prime number. The Fibonacci sequence starts with 1 and 1, and each subsequent number is the sum of the previous two. We need to check each Fibonacci number for primality and collect them in order until we reach the n-th prime Fibonacci number. ### Approach 1. Generate Fibonacci Numbers: Start with the first two Fibonacci numbers (1 and 1) and generate subsequent numbers by summing the last two numbers in the sequence. 2. Check for Primality: For each generated Fibonacci number, check if it is a prime number. A number is prime if it is greater than 1 and has no divisors other than 1 and itself. 3. Collect Prime Fibonacci Numbers: Maintain a list of prime Fibonacci numbers. Once this list contains n elements, return the n-th element. ### Solution Code ```python def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ def is_prime(x): if x <= 1: return False if x == 2: return True if x % 2 == 0: return False for i in range(3, int(x0.5) + 1, 2): if x % i == 0: return False return True primes = [] a, b = 1, 1 while True: next_fib = a + b if is_prime(next_fib): primes.append(next_fib) if len(primes) == n: return primes[-1] a, b = b, next_fib ``` ### Explanation 1. Prime Check Function: The `is_prime` function checks if a number is prime by testing divisibility up to the square root of the number. This is efficient for numbers that are not excessively large. 2. Fibonacci Generation: The Fibonacci sequence is generated using two variables `a` and `b` which are updated in each iteration to produce the next Fibonacci number. 3. Collecting Primes**: Each generated Fibonacci number is checked for primality. If it is prime, it is added to the list `primes`. When this list reaches the required length `n`, the function returns the last element of the list, which is the n-th prime Fibonacci number. This approach efficiently generates Fibonacci numbers and checks their primality, ensuring that we find the required n-th prime Fibonacci number in a straightforward manner.	passed
gpto1	To complete the code, you need to define a function that generates Fibonacci numbers and checks if they are prime until it finds the nth prime Fibonacci number. Below is the complete code: ```python def is_prime(n): if n <= 1: return False elif n <= 3: return True elif n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def prime_fib(n: int): count = 0 a, b = 0, 1 # Initialize the first two Fibonacci numbers while True: fib = a + b a, b = b, fib # Move to the next Fibonacci number if is_prime(fib): count += 1 if count == n: return fib ``` This code defines an `is_prime` function to check if a number is prime and then uses it within the `prime_fib` function to find the nth prime Fibonacci number.	passed
GPT-4o	To complete the `prime_fib` function, we need to achieve the following steps: 1. Generate Fibonacci numbers. 2. Check if a number is prime. 3. Collect Fibonacci numbers that are also prime. 4. Return the n-th prime Fibonacci number. Here's the complete implementation: ```python def is_prime(num): """Helper function to check if a number is prime.""" if num <= 1: return False if num <= 3: return True if num % 2 == 0 or num % 3 == 0: return False i = 5 while i * i <= num: if num % i == 0 or num % (i + 2) == 0: return False i += 6 return True def generate_fibonacci(): """Generator to yield Fibonacci numbers.""" a, b = 0, 1 while True: yield b a, b = b, a + b def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ prime_fibs = [] for fib_num in generate_fibonacci(): if is_prime(fib_num): prime_fibs.append(fib_num) if len(prime_fibs) == n: return prime_fibs[-1] # Testing the function if __name__ == "__main__": import doctest doctest.testmod() ``` ### Explanation: 1. `is_prime(num)` function: This function checks if a number is prime. 2. `generate_fibonacci()` function: This is a generator function that yields Fibonacci numbers indefinitely. 3. `prime_fib(n)` function: This function uses the above two helper functions to find the n-th Fibonacci number that is also prime. The `prime_fib` function will iterate through Fibonacci numbers, check if they are prime, and collect them until it reaches the n-th prime Fibonacci number, which it then returns.	passed
llama3.1-70B-Instruct	def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ def is_prime(num: int) -> bool: """ Checks if a number is prime. """ if num < 2: return False for i in range(2, int(num ** 0.5) + 1): if num % i == 0: return False return True def fibonacci() -> int: """ Generates Fibonacci numbers. """ a, b = 0, 1 while True: yield a a, b = b, a + b fib = fibonacci() count = 0 while True: num = next(fib) if is_prime(num): count += 1 if count == n: return num	passed
llama3.1-405B-Instruct	def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ def is_prime(num: int) -> bool: """ Checks if a number is prime. """ if num < 2: return False for i in range(2, int(num**0.5) + 1): if num % i == 0: return False return True def fibonacci() -> int: """ Generates Fibonacci numbers. """ a, b = 0, 1 while True: yield a a,	failed:
DeepSeek-Coder-V2	To complete the `prime_fib` function, we need to generate Fibonacci numbers, check if they are prime, and return the n-th such number. Here's the complete code: ```python def is_prime(num): """Check if a number is prime.""" if num <= 1: return False if num <= 3: return True if num % 2 == 0 or num % 3 == 0: return False i = 5 while i * i <= num: if num % i == 0 or num % (i + 2) == 0: return False i += 6 return True def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ if n <= 0: raise ValueError("n must be a positive integer") a, b = 0, 1 count = 0 while True: if is_prime(b): count += 1 if count == n: return b a, b = b, a + b # Example usage: if __name__ == "__main__": import doctest doctest.testmod() ``` ### Explanation: 1. is_prime function: This helper function checks if a given number is prime. 2. prime_fib function: - It initializes two variables `a` and `b` to 0 and 1, respectively, which are the first two Fibonacci numbers. - It uses a `while True` loop to generate Fibonacci numbers. - For each Fibonacci number `b`, it checks if it is prime using the `is_prime` function. - If `b` is prime, it increments the `count`. - When the `count` equals `n`, it returns the current Fibonacci number `b`. This code will correctly return the n-th Fibonacci number that is also prime.	passed
Qwen2-72B-Instruct	```python from sympy import isprime def prime_fib(n: int): found = 0 fib1, fib2 = 0, 1 while found < n: fib1, fib2 = fib2, fib1 + fib2 if fib2 > 1 and isprime(fib2): found += 1 return fib2 print(prime_fib(1)) # 2 print(prime_fib(2)) # 3 print(prime_fib(3)) # 5 print(prime_fib(4)) # 13 print(prime_fib(5)) # 89 ``` In this code, we generate the Fibonacci sequence using two variables `fib1` and `fib2`. We start with `fib1 = 0` and `fib2 = 1`, and in each iteration of the while loop, we update them to the next two Fibonacci numbers. We check if `fib2` is prime using the `isprime` function from the sympy library. If it is prime, we increment the counter `found`. The loop continues until we have found `n` prime Fibonacci numbers. The function then returns the `n`-th prime Fibonacci number.	passed
baichuan4	To complete the Python code for the `prime_fib` function, we need to generate Fibonacci numbers and check if they are prime. We'll use a generator for the Fibonacci sequence and a simple primality test for demonstration purposes, though more efficient methods exist for large primes. Here's the completed function: ```python def is_prime(num): """Simple primality test.""" if num < 2: return False for i in range(2, int(num**0.5) + 1): if num % i == 0: return False return True def fibonacci_gen(): """Generator for the Fibonacci sequence.""" a, b = 0, 1 while True: yield a a, b = b, a + b def prime_fib(n: int): """ prime_fib returns the n-th number that is a Fibonacci number and it's also prime. """ if n <= 0: raise ValueError("Input must be a positive integer") prime_fib_count = 0 fib_gen = fibonacci_gen() fib_number = next(fib_gen) # Skip the first Fibonacci number since it's 0 (not considered prime) next(fib_gen) while prime_fib_count < n: fib_number = next(fib_gen) if is_prime(fib_number): prime_fib_count += 1 if prime_fib_count == n: return fib_number # Example usage: print(prime_fib(1)) # Output: 2 print(prime_fib(2)) # Output: 3 print(prime_fib(3)) # Output: 5 print(prime_fib(4)) # Output: 13 print(prime_fib(5)) # Output: 89 ``` This code defines a helper function `is_prime` to check the primality of a number, a generator `fibonacci_gen` to produce an infinite sequence of Fibonacci numbers, and the main function `prime_fib` that finds the n-th Fibonacci number that is also prime. The function raises a `ValueError` if the input is not a positive integer, ensuring the precondition is met. Please note that for large values of `n`, the computation can become quite intensive due to the nature of generating large Fibonacci numbers and checking their primality. In practice, more efficient algorithms or precomputed lists of Fibonacci primes would be used for such cases.	passed
doubao	Here's the completed Python code: ```python def is_prime(n: int) -> bool: if n <= 1: return False if n <= 3: return True if n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def fibonacci(n: int) -> int: a, b = 0, 1 for _ in range(n): a, b = b, a + b return a def prime_fib(n: int): count = 0 i = 1 while count < n: fib = fibonacci(i) if is_prime(fib): count += 1 i += 1 return fibonacci(i - 1) ``` ```	passed
minimax	To complete the code, we need to implement the `prime_fib` function that will generate Fibonacci numbers and check if they are prime until we find the `n`-th one that meets both criteria. Here's the complete function: ```python def is_prime(num): """Check if a number is a prime number.""" if num < 2: return False for i in range(2, int(num**0.5) + 1): if num % i == 0: return False return True def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. """ if n <= 0: raise ValueError("n must be a positive integer") prime_count = 0 fib_a, fib_b = 0, 1 while True: fib_a, fib_b = fib_b, fib_a + fib_b if is_prime(fib_a): prime_count += 1 if prime_count == n: return fib_a # Example usage: print(prime_fib(1)) # Output: 2 print(prime_fib(2)) # Output: 3 print(prime_fib(3)) # Output: 5 print(prime_fib(4)) # Output: 13 print(prime_fib(5)) # Output: 89 ``` This code defines a helper function `is_prime` to check if a number is prime. The `prime_fib` function then generates Fibonacci numbers in a loop and uses the `is_prime` function to check if each Fibonacci number is prime. When the `n`-th prime Fibonacci number is found, it is returned. Note that this code may not be the most efficient for large values of `n`, as the Fibonacci sequence grows exponentially and prime checking can be computationally expensive for large numbers. However, it should work fine for small values of `n` as shown in the examples.	passed
kimi	To complete the Python code for the `prime_fib` function, we need to implement a way to generate Fibonacci numbers and check if they are prime. Here's a possible implementation: ```python def is_prime(num: int) -> bool: """Check if a number is a prime number.""" if num <= 1: return False if num <= 3: return True if num % 2 == 0 or num % 3 == 0: return False i = 5 while i * i <= num: if num % i == 0 or num % (i + 2) == 0: return False i += 6 return True def prime_fib(n: int) -> int: """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. """ a, b = 0, 1 count = 0 while True: a, b = b, a + b if is_prime(a): count += 1 if count == n: return a ``` Here's what the code does: 1. `is_prime(num: int) -> bool`: This helper function checks if a given number is prime. It handles the special cases for numbers less than 2, then checks divisibility by 2 and 3, and then checks for factors up to the square root of the number. 2. `prime_fib(n: int) -> int`: This function generates Fibonacci numbers and uses the `is_prime` function to check if they are prime. It keeps track of the count of prime Fibonacci numbers and returns the `n`-th one. The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two. The function `prime_fib` generates these numbers and checks each one to see if it is prime. When it finds the `n`-th prime Fibonacci number, it returns that number. Here's how you can use the function: ```python print(prime_fib(1)) # Output: 2 print(prime_fib(2)) # Output: 3 print(prime_fib(3)) # Output: 5 print(prime_fib(4)) # Output: 13 print(prime_fib(5)) # Output: 89 ``` Keep in mind that this function can be slow for large values of `n`, as it involves checking many Fibonacci numbers for primality.	passed
wenxinyiyan	To complete the `prime_fib` function, we need to implement two helper functions: one to generate Fibonacci numbers and another to check if a number is prime. Then, we can iterate through the Fibonacci numbers, checking each one to see if it's prime, until we find the n-th prime Fibonacci number. Here's the completed code: ```python def is_prime(num: int) -> bool: """ Helper function to check if a number is prime. """ if num < 2: return False for i in range(2, int(num ** 0.5) + 1): if num % i == 0: return False return True def fibonacci_generator(): """ Helper function to generate Fibonacci numbers. """ a, b = 0, 1 while True: yield a a, b = b, a + b def prime_fib(n: int): """ prime_fib returns the n-th number that is both a Fibonacci number and prime. """ fib_gen = fibonacci_generator() prime_fib_count = 0 while True: fib_num = next(fib_gen) if is_prime(fib_num): prime_fib_count += 1 if prime_fib_count == n: return fib_num ``` Now, if you call `prime_fib(n)` with any positive integer `n`, it will return the n-th prime Fibonacci number.	passed
zhipu	Certainly! Below is the complete Python code for the `prime_fib` function. This function calculates Fibonacci numbers and checks if they are prime, returning the n-th such number. ```python def is_prime(num): """Check if a number is prime.""" if num <= 1: return False if num <= 3: return True if num % 2 == 0 or num % 3 == 0: return False i = 5 while i * i <= num: if num % i == 0 or num % (i + 2) == 0: return False i += 6 return True def prime_fib(n: int): """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ if n <= 0: raise ValueError("n must be a positive integer") count = 0 a, b = 0, 1 while True: if is_prime(b): count += 1 if count == n: return b a, b = b, a + b # Example usage: if __name__ == "__main__": import doctest doctest.testmod() ``` ### Explanation: 1. is_prime function: This helper function checks if a given number is prime. It uses a more efficient algorithm that checks divisibility up to the square root of the number. 2. prime_fib function: - It initializes `count` to keep track of how many prime Fibonacci numbers have been found. - It uses a tuple swap (`a, b = b, a + b`) to generate Fibonacci numbers. - It checks each Fibonacci number for primality and increments the count when a prime is found. - When the count matches `n`, it returns the current Fibonacci number. 3. doctest: The `if __name__ == "__main__":` block allows for running the doctests to verify the correctness of the function. This code should work efficiently for small to moderately large values of `n`. For very large `n`, optimizations or different algorithms might be necessary to handle performance and memory constraints.	passed
gpto1	To complete the code, you need to define a function that generates Fibonacci numbers and checks if they are prime until it finds the nth prime Fibonacci number. Below is the complete code: ```python def is_prime(n): if n <= 1: return False elif n <= 3: return True elif n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def prime_fib(n: int): count = 0 a, b = 0, 1 # Initialize the first two Fibonacci numbers while True: fib = a + b a, b = b, fib # Move to the next Fibonacci number if is_prime(fib): count += 1 if count == n: return fib ``` This code defines an `is_prime` function to check if a number is prime and then uses it within the `prime_fib` function to find the nth prime Fibonacci number.	passed
deepseekv3	To complete the `prime_fib` function, we need to generate Fibonacci numbers and check if they are prime. We'll continue generating Fibonacci numbers until we find the nth prime Fibonacci number. Here's the implementation: ```python def is_prime(num: int) -> bool: """Check if a number is prime.""" if num < 2: return False for i in range(2, int(num0.5) + 1): if num % i == 0: return False return True def prime_fib(n: int) -> int: """ prime_fib returns n-th number that is a Fibonacci number and it's also prime. >>> prime_fib(1) 2 >>> prime_fib(2) 3 >>> prime_fib(3) 5 >>> prime_fib(4) 13 >>> prime_fib(5) 89 """ count = 0 a, b = 1, 1 while True: a, b = b, a + b if is_prime(a): count += 1 if count == n: return a # Test cases print(prime_fib(1)) # Output: 2 print(prime_fib(2)) # Output: 3 print(prime_fib(3)) # Output: 5 print(prime_fib(4)) # Output: 13 print(prime_fib(5)) # Output: 89 ``` ### Explanation: 1. is_prime Function: This function checks if a number is prime by testing divisibility from 2 up to the square root of the number. 2. prime_fib Function**: - We initialize two variables `a` and `b` to 1, representing the first two Fibonacci numbers. - We enter an infinite loop where we generate the next Fibonacci number by updating `a` and `b`. - For each Fibonacci number `a`, we check if it is prime using the `is_prime` function. - If `a` is prime, we increment the count of prime Fibonacci numbers found. - When the count matches `n`, we return the current Fibonacci number `a`. ### Test Cases: The test cases provided in the docstring are included at the end of the code to verify the correctness of the implementation.	passed

模型

模型答案

测试结果

金声玉亮2.0

To complete the `prime_fib` function, we need to generate Fibonacci numbers and check whether they are prime. We'll keep doing this until we find the n-th Fibonacci number that is also prime.

Here's the completed code:

```python
def is_prime(num: int) -> bool:
"""Check if a number is prime."""
if num <= 1:
return False
if num == 2:
return True
if num % 2 == 0:
return False
for i in range(3, int(num**0.5) + 1, 2):
if num % i == 0:
return False
return True

def prime_fib(n: int) -> int:
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
fib_a, fib_b = 0, 1
count = 0

while count < n:
fib_a, fib_b = fib_b, fib_a + fib_b
if is_prime(fib_b):
count += 1

return fib_b

if __name__ == "__main__":
import doctest
doctest.testmod()
```

### Explanation:

1. **is_prime Function**:
- This function checks if a given number is prime.
- It returns `False` for numbers less than or equal to 1.
- It returns `True` for 2.
- It checks if the number is divisible by any number from 3 up to the square root of the number, incrementing by 2 (to skip even numbers).

2. **prime_fib Function**:
- It initializes the first two Fibonacci numbers (`fib_a` and `fib_b`).
- It uses a `while` loop to generate Fibonacci numbers and checks if they are prime.
- It keeps a `count` of how many prime Fibonacci numbers have been found.
- When `count` reaches `n`, it returns the current Fibonacci number (`fib_b`).

3. **Testing**:
- The `doctest` module is used to verify that the function works as expected based on the provided examples.

passed

deepseekr1

To solve this problem, we need to find the n-th number in the Fibonacci sequence that is also a prime number. The Fibonacci sequence starts with 1 and 1, and each subsequent number is the sum of the previous two. We need to check each Fibonacci number for primality and collect them in order until we reach the n-th prime Fibonacci number.

### Approach
1. **Generate Fibonacci Numbers**: Start with the first two Fibonacci numbers (1 and 1) and generate subsequent numbers by summing the last two numbers in the sequence.
2. **Check for Primality**: For each generated Fibonacci number, check if it is a prime number. A number is prime if it is greater than 1 and has no divisors other than 1 and itself.
3. **Collect Prime Fibonacci Numbers**: Maintain a list of prime Fibonacci numbers. Once this list contains n elements, return the n-th element.

### Solution Code
```python
def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
def is_prime(x):
if x <= 1:
return False
if x == 2:
return True
if x % 2 == 0:
return False
for i in range(3, int(x**0.5) + 1, 2):
if x % i == 0:
return False
return True

primes = []
a, b = 1, 1
while True:
next_fib = a + b
if is_prime(next_fib):
primes.append(next_fib)
if len(primes) == n:
return primes[-1]
a, b = b, next_fib
```

### Explanation
1. **Prime Check Function**: The `is_prime` function checks if a number is prime by testing divisibility up to the square root of the number. This is efficient for numbers that are not excessively large.
2. **Fibonacci Generation**: The Fibonacci sequence is generated using two variables `a` and `b` which are updated in each iteration to produce the next Fibonacci number.
3. **Collecting Primes**: Each generated Fibonacci number is checked for primality. If it is prime, it is added to the list `primes`. When this list reaches the required length `n`, the function returns the last element of the list, which is the n-th prime Fibonacci number.

This approach efficiently generates Fibonacci numbers and checks their primality, ensuring that we find the required n-th prime Fibonacci number in a straightforward manner.

passed

gpto1

To complete the code, you need to define a function that generates Fibonacci numbers and checks if they are prime until it finds the nth prime Fibonacci number. Below is the complete code:

```python
def is_prime(n):
if n <= 1:
return False
elif n <= 3:
return True
elif n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
if n % i == 0 or n % (i + 2) == 0:
return False
i += 6
return True

def prime_fib(n: int):
count = 0
a, b = 0, 1 # Initialize the first two Fibonacci numbers
while True:
fib = a + b
a, b = b, fib # Move to the next Fibonacci number
if is_prime(fib):
count += 1
if count == n:
return fib
```

This code defines an `is_prime` function to check if a number is prime and then uses it within the `prime_fib` function to find the nth prime Fibonacci number.

passed

GPT-4o

To complete the `prime_fib` function, we need to achieve the following steps:

1. Generate Fibonacci numbers.
2. Check if a number is prime.
3. Collect Fibonacci numbers that are also prime.
4. Return the n-th prime Fibonacci number.

Here's the complete implementation:

```python
def is_prime(num):
"""Helper function to check if a number is prime."""
if num <= 1:
return False
if num <= 3:
return True
if num % 2 == 0 or num % 3 == 0:
return False
i = 5
while i * i <= num:
if num % i == 0 or num % (i + 2) == 0:
return False
i += 6
return True

def generate_fibonacci():
"""Generator to yield Fibonacci numbers."""
a, b = 0, 1
while True:
yield b
a, b = b, a + b

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
prime_fibs = []
for fib_num in generate_fibonacci():
if is_prime(fib_num):
prime_fibs.append(fib_num)
if len(prime_fibs) == n:
return prime_fibs[-1]

# Testing the function
if __name__ == "__main__":
import doctest
doctest.testmod()
```

### Explanation:
1. **`is_prime(num)` function**: This function checks if a number is prime.
2. **`generate_fibonacci()` function**: This is a generator function that yields Fibonacci numbers indefinitely.
3. **`prime_fib(n)` function**: This function uses the above two helper functions to find the n-th Fibonacci number that is also prime.

The `prime_fib` function will iterate through Fibonacci numbers, check if they are prime, and collect them until it reaches the n-th prime Fibonacci number, which it then returns.

passed

llama3.1-70B-Instruct

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
def is_prime(num: int) -> bool:
"""
Checks if a number is prime.
"""
if num < 2:
return False
for i in range(2, int(num ** 0.5) + 1):
if num % i == 0:
return False
return True

def fibonacci() -> int:
"""
Generates Fibonacci numbers.
"""
a, b = 0, 1
while True:
yield a
a, b = b, a + b

fib = fibonacci()
count = 0
while True:
num = next(fib)
if is_prime(num):
count += 1
if count == n:
return num

passed

llama3.1-405B-Instruct

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
def is_prime(num: int) -> bool:
"""
Checks if a number is prime.
"""
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True

def fibonacci() -> int:
"""
Generates Fibonacci numbers.
"""
a, b = 0, 1
while True:
yield a
a,

failed:

DeepSeek-Coder-V2

To complete the `prime_fib` function, we need to generate Fibonacci numbers, check if they are prime, and return the n-th such number. Here's the complete code:

```python
def is_prime(num):
"""Check if a number is prime."""
if num <= 1:
return False
if num <= 3:
return True
if num % 2 == 0 or num % 3 == 0:
return False
i = 5
while i * i <= num:
if num % i == 0 or num % (i + 2) == 0:
return False
i += 6
return True

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
if n <= 0:
raise ValueError("n must be a positive integer")

a, b = 0, 1
count = 0
while True:
if is_prime(b):
count += 1
if count == n:
return b
a, b = b, a + b

# Example usage:
if __name__ == "__main__":
import doctest
doctest.testmod()
```

### Explanation:
1. **is_prime function**: This helper function checks if a given number is prime.
2. **prime_fib function**:
- It initializes two variables `a` and `b` to 0 and 1, respectively, which are the first two Fibonacci numbers.
- It uses a `while True` loop to generate Fibonacci numbers.
- For each Fibonacci number `b`, it checks if it is prime using the `is_prime` function.
- If `b` is prime, it increments the `count`.
- When the `count` equals `n`, it returns the current Fibonacci number `b`.

This code will correctly return the n-th Fibonacci number that is also prime.

passed

Qwen2-72B-Instruct

```python
from sympy import isprime

def prime_fib(n: int):
found = 0
fib1, fib2 = 0, 1
while found < n:
fib1, fib2 = fib2, fib1 + fib2
if fib2 > 1 and isprime(fib2):
found += 1
return fib2

print(prime_fib(1)) # 2
print(prime_fib(2)) # 3
print(prime_fib(3)) # 5
print(prime_fib(4)) # 13
print(prime_fib(5)) # 89
```

In this code, we generate the Fibonacci sequence using two variables `fib1` and `fib2`. We start with `fib1 = 0` and `fib2 = 1`, and in each iteration of the while loop, we update them to the next two Fibonacci numbers.

We check if `fib2` is prime using the `isprime` function from the sympy library. If it is prime, we increment the counter `found`. The loop continues until we have found `n` prime Fibonacci numbers. The function then returns the `n`-th prime Fibonacci number.

passed

baichuan4

To complete the Python code for the `prime_fib` function, we need to generate Fibonacci numbers and check if they are prime. We'll use a generator for the Fibonacci sequence and a simple primality test for demonstration purposes, though more efficient methods exist for large primes.

Here's the completed function:

```python
def is_prime(num):
"""Simple primality test."""
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True

def fibonacci_gen():
"""Generator for the Fibonacci sequence."""
a, b = 0, 1
while True:
yield a
a, b = b, a + b

def prime_fib(n: int):
"""
prime_fib returns the n-th number that is a Fibonacci number and it's also prime.
"""
if n <= 0:
raise ValueError("Input must be a positive integer")

prime_fib_count = 0
fib_gen = fibonacci_gen()
fib_number = next(fib_gen)

# Skip the first Fibonacci number since it's 0 (not considered prime)
next(fib_gen)

while prime_fib_count < n:
fib_number = next(fib_gen)
if is_prime(fib_number):
prime_fib_count += 1
if prime_fib_count == n:
return fib_number

# Example usage:
print(prime_fib(1)) # Output: 2
print(prime_fib(2)) # Output: 3
print(prime_fib(3)) # Output: 5
print(prime_fib(4)) # Output: 13
print(prime_fib(5)) # Output: 89
```

This code defines a helper function `is_prime` to check the primality of a number, a generator `fibonacci_gen` to produce an infinite sequence of Fibonacci numbers, and the main function `prime_fib` that finds the n-th Fibonacci number that is also prime. The function raises a `ValueError` if the input is not a positive integer, ensuring the precondition is met.

Please note that for large values of `n`, the computation can become quite intensive due to the nature of generating large Fibonacci numbers and checking their primality. In practice, more efficient algorithms or precomputed lists of Fibonacci primes would be used for such cases.

passed

doubao

Here's the completed Python code:

```python
def is_prime(n: int) -> bool:
if n <= 1:
return False
if n <= 3:
return True
if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
if n % i == 0 or n % (i + 2) == 0:
return False
i += 6
return True

def fibonacci(n: int) -> int:
a, b = 0, 1
for _ in range(n):
a, b = b, a + b
return a

def prime_fib(n: int):
count = 0
i = 1
while count < n:
fib = fibonacci(i)
if is_prime(fib):
count += 1
i += 1
return fibonacci(i - 1)
```
```

passed

minimax

To complete the code, we need to implement the `prime_fib` function that will generate Fibonacci numbers and check if they are prime until we find the `n`-th one that meets both criteria. Here's the complete function:

```python
def is_prime(num):
"""Check if a number is a prime number."""
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
"""
if n <= 0:
raise ValueError("n must be a positive integer")

prime_count = 0
fib_a, fib_b = 0, 1
while True:
fib_a, fib_b = fib_b, fib_a + fib_b
if is_prime(fib_a):
prime_count += 1
if prime_count == n:
return fib_a

# Example usage:
print(prime_fib(1)) # Output: 2
print(prime_fib(2)) # Output: 3
print(prime_fib(3)) # Output: 5
print(prime_fib(4)) # Output: 13
print(prime_fib(5)) # Output: 89
```

This code defines a helper function `is_prime` to check if a number is prime. The `prime_fib` function then generates Fibonacci numbers in a loop and uses the `is_prime` function to check if each Fibonacci number is prime. When the `n`-th prime Fibonacci number is found, it is returned.

Note that this code may not be the most efficient for large values of `n`, as the Fibonacci sequence grows exponentially and prime checking can be computationally expensive for large numbers. However, it should work fine for small values of `n` as shown in the examples.

passed

kimi

To complete the Python code for the `prime_fib` function, we need to implement a way to generate Fibonacci numbers and check if they are prime. Here's a possible implementation:

```python
def is_prime(num: int) -> bool:
"""Check if a number is a prime number."""
if num <= 1:
return False
if num <= 3:
return True
if num % 2 == 0 or num % 3 == 0:
return False
i = 5
while i * i <= num:
if num % i == 0 or num % (i + 2) == 0:
return False
i += 6
return True

def prime_fib(n: int) -> int:
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
"""
a, b = 0, 1
count = 0
while True:
a, b = b, a + b
if is_prime(a):
count += 1
if count == n:
return a
```

Here's what the code does:

1. `is_prime(num: int) -> bool`: This helper function checks if a given number is prime. It handles the special cases for numbers less than 2, then checks divisibility by 2 and 3, and then checks for factors up to the square root of the number.

2. `prime_fib(n: int) -> int`: This function generates Fibonacci numbers and uses the `is_prime` function to check if they are prime. It keeps track of the count of prime Fibonacci numbers and returns the `n`-th one.

The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two. The function `prime_fib` generates these numbers and checks each one to see if it is prime. When it finds the `n`-th prime Fibonacci number, it returns that number.

Here's how you can use the function:

```python
print(prime_fib(1)) # Output: 2
print(prime_fib(2)) # Output: 3
print(prime_fib(3)) # Output: 5
print(prime_fib(4)) # Output: 13
print(prime_fib(5)) # Output: 89
```

Keep in mind that this function can be slow for large values of `n`, as it involves checking many Fibonacci numbers for primality.

passed

wenxinyiyan

To complete the `prime_fib` function, we need to implement two helper functions: one to generate Fibonacci numbers and another to check if a number is prime. Then, we can iterate through the Fibonacci numbers, checking each one to see if it's prime, until we find the n-th prime Fibonacci number.

Here's the completed code:

```python
def is_prime(num: int) -> bool:
"""
Helper function to check if a number is prime.
"""
if num < 2:
return False
for i in range(2, int(num ** 0.5) + 1):
if num % i == 0:
return False
return True

def fibonacci_generator():
"""
Helper function to generate Fibonacci numbers.
"""
a, b = 0, 1
while True:
yield a
a, b = b, a + b

def prime_fib(n: int):
"""
prime_fib returns the n-th number that is both a Fibonacci number and prime.
"""
fib_gen = fibonacci_generator()
prime_fib_count = 0
while True:
fib_num = next(fib_gen)
if is_prime(fib_num):
prime_fib_count += 1
if prime_fib_count == n:
return fib_num
```
Now, if you call `prime_fib(n)` with any positive integer `n`, it will return the n-th prime Fibonacci number.

passed

zhipu

Certainly! Below is the complete Python code for the `prime_fib` function. This function calculates Fibonacci numbers and checks if they are prime, returning the n-th such number.

```python
def is_prime(num):
"""Check if a number is prime."""
if num <= 1:
return False
if num <= 3:
return True
if num % 2 == 0 or num % 3 == 0:
return False
i = 5
while i * i <= num:
if num % i == 0 or num % (i + 2) == 0:
return False
i += 6
return True

def prime_fib(n: int):
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
if n <= 0:
raise ValueError("n must be a positive integer")

count = 0
a, b = 0, 1
while True:
if is_prime(b):
count += 1
if count == n:
return b
a, b = b, a + b

# Example usage:
if __name__ == "__main__":
import doctest
doctest.testmod()
```

### Explanation:
1. **is_prime function**: This helper function checks if a given number is prime. It uses a more efficient algorithm that checks divisibility up to the square root of the number.
2. **prime_fib function**:
- It initializes `count` to keep track of how many prime Fibonacci numbers have been found.
- It uses a tuple swap (`a, b = b, a + b`) to generate Fibonacci numbers.
- It checks each Fibonacci number for primality and increments the count when a prime is found.
- When the count matches `n`, it returns the current Fibonacci number.
3. **doctest**: The `if __name__ == "__main__":` block allows for running the doctests to verify the correctness of the function.

This code should work efficiently for small to moderately large values of `n`. For very large `n`, optimizations or different algorithms might be necessary to handle performance and memory constraints.

passed

gpto1

passed

deepseekv3

To complete the `prime_fib` function, we need to generate Fibonacci numbers and check if they are prime. We'll continue generating Fibonacci numbers until we find the nth prime Fibonacci number. Here's the implementation:

```python
def is_prime(num: int) -> bool:
"""Check if a number is prime."""
if num < 2:
return False
for i in range(2, int(num**0.5) + 1):
if num % i == 0:
return False
return True

def prime_fib(n: int) -> int:
"""
prime_fib returns n-th number that is a Fibonacci number and it's also prime.
>>> prime_fib(1)
2
>>> prime_fib(2)
3
>>> prime_fib(3)
5
>>> prime_fib(4)
13
>>> prime_fib(5)
89
"""
count = 0
a, b = 1, 1
while True:
a, b = b, a + b
if is_prime(a):
count += 1
if count == n:
return a

# Test cases
print(prime_fib(1)) # Output: 2
print(prime_fib(2)) # Output: 3
print(prime_fib(3)) # Output: 5
print(prime_fib(4)) # Output: 13
print(prime_fib(5)) # Output: 89
```

### Explanation:
1. **is_prime Function**: This function checks if a number is prime by testing divisibility from 2 up to the square root of the number.
2. **prime_fib Function**:
- We initialize two variables `a` and `b` to 1, representing the first two Fibonacci numbers.
- We enter an infinite loop where we generate the next Fibonacci number by updating `a` and `b`.
- For each Fibonacci number `a`, we check if it is prime using the `is_prime` function.
- If `a` is prime, we increment the count of prime Fibonacci numbers found.
- When the count matches `n`, we return the current Fibonacci number `a`.

### Test Cases:
The test cases provided in the docstring are included at the end of the code to verify the correctness of the implementation.

passed

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