How to Find Twin Primes with a Simple Recursive Sieve in Python and Java

After reading the book *The Loneliness of Prime Numbers*, the author wanted to explore twin prime distribution and implemented a simple algorithm to generate primes and detect twin prime pairs.

The algorithm creates a list of integers starting from 2, then iteratively removes any number divisible by the current base number, effectively implementing a sieve. In Java, elements can be removed from the list during iteration by adjusting the loop index (i--) to avoid index errors; Python does not support in‑loop deletions, so elements are collected and removed after the traversal.

#!/usr/bin/python3

class Test():
    def __init__(self):
        print("fan")
    def get(self, lst, st):
        n = lst[st]
        a = []
        for i in range(st+1, len(lst)):
            if lst[i] % n == 0:
                a.append(lst[i])
        for x in a:
            lst.remove(x)
        if len(lst) > st+1:
            self.get(lst, st+1)

if __name__ == "__main__":
    test = Test()
    lst = [i for i in range(2, 5000)]
    test.get(lst, 0)
    for i in range(len(lst)-1):
        a = lst[i]
        b = lst[i+1]
        if b - a == 2:
            print("Twin primes: " + str(a) + "----" + str(b))

The program then scans the resulting prime list for consecutive primes whose difference is exactly 2 and prints each twin prime pair.

Note: Python limits recursion depth to prevent memory overflow, so attempting to process numbers up to 10,000 may raise a RecursionError: maximum recursion depth exceeded in comparison . Increasing the recursion limit or switching to an iterative approach is required for larger ranges.