I am a beginner to python. I would like to write a program to find the first till 10th prime number.

Below is my code. For some reason the loop part in the function find_10th_prime doesn’t work. If I type find_10th_prime(100), the output is [2,1]. So the loop stops after the 1st prime is found.

def prime_check(primeNum,testNum):
if len(primeNum)==0:
return True
elif len(primeNum) ==1 and testNum % primeNum[0] !=0:
return True
elif testNum % primeNum[0] != 0 and testNum % primeNum[-1] != 0:
prime_check(primeNum[1:-1],testNum)
else: return False
def find_10th_prime(max):
counter=0
primeNum=[2]
for testNum in range(1,max+1):
if counter>=10:
print (counter)
break
elif prime_check (primeNum,testNum) == True:
counter=counter +1
print ("prime found")
primeNum.append(testNum)
print (primeNum,counter)

If “elif testNum % primeNum[0] != 0 and testNum % primeNum[-1] != 0:” is true, it will take out the first number and the last number from the prime number list and run the prime_check function based on the new prime number list.

I have test as below. The result is correct.
prime_check([1,2,3,5],11)

sorry, it looks there is also a problem with the prime_check function.
I have corrected the elseif condition as below:

def prime_check(primeNum,testNum):

if len(primeNum)==0:
return True
elif len(primeNum) ==1 and testNum % primeNum[0] !=0:
return True
else: return testNum % primeNum[0] != 0 and testNum % primeNum[-1] != 0 and prime_check(primeNum[1:-1],testNum)
#divide test number by first prime number and the last prime number, if both yield a remainder, continue the prime check
#by creating a new prime list (excl. the first prime and last prime from the prime list) & run the prime_check function again
#based on the new prime list

However, I still don’t understand why this code doesn’t work.
elif testNum % primeNum[0] != 0 and testNum % primeNum[-1] != 0:
prime_check(primeNum[1:-1],testNum)

This time the previous elif runs instead, returning True. However:

# Stepping back out:
elif testNum % primeNum[0] != 0 and testNum % primeNum[-1] != 0:
prime_check(primeNum[1:-1],testNum)

The recursive prime_check call returns True, but you don’t do anything with it. The function finishes without reaching an explicit return statement, so the final return value is None.

I think you should throw out this code and start again with a better algorithm for checking for prime numbers.

And better names for your variables would also help. Why do you have a list of primes called “primeNum” as if it was a single prime number?

There is no good reason to use recursion here (except maybe to prove it can be done, or to deliberately write an inefficient, obfuscated version). Recursion is a very unnatural way to do prime detection, especially since you are making multiple copies of the “primeNum” list of primes. You only need one copy of it.

primes = [2] # Initial list of primes.
def is_prime(num):
"""Return True if num is prime."""
for p in primes:
if num % p == 0:
return False
return True
def find_10th_prime():
# Skip 1, which we know is not a prime,
# and 2, which we know is.
candidate = 3
while len(primes) < 10:
if is_prime(candidate):
print(candidate, "is prime")
primes.append(candidate)
else:
print(candidate, "is not prime")
candidate += 1
assert len(primes) == 10
print("The tenth prime is", primes[-1])

If you think about which candidates are tested, you should realise that this does twice as much work as needed. You can halve the amount of candidates tested with a simple, one line change. Can you find it?

You are right! I assume it’s stupid mistake for veterans. the prime_check function simply runs the loop, but no input is stored for the caller as no return expression is used in the prime-check function