diff --git a/.idea/misc.xml b/.idea/misc.xml
index ce0c400..46ad6d9 100644
--- a/.idea/misc.xml
+++ b/.idea/misc.xml
@@ -1,4 +1,4 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
-  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.9 (UNI_Python)" project-jdk-type="Python SDK" />
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.10.6 WSL (Ubuntu): (/home/janniclas/.virtualenvs/Informationssysteme/bin/python)" project-jdk-type="Python SDK" />
 </project>
\ No newline at end of file
diff --git a/.idea/python.iml b/.idea/python.iml
index b567092..ca820fc 100644
--- a/.idea/python.iml
+++ b/.idea/python.iml
@@ -5,7 +5,7 @@
       <excludeFolder url="file://$MODULE_DIR$/Virtualenv" />
       <excludeFolder url="file://$MODULE_DIR$/venv" />
     </content>
-    <orderEntry type="jdk" jdkName="Python 3.9 (UNI_Python)" jdkType="Python SDK" />
+    <orderEntry type="jdk" jdkName="Python 3.10.6 WSL (Ubuntu): (/home/janniclas/.virtualenvs/Informationssysteme/bin/python)" jdkType="Python SDK" />
     <orderEntry type="sourceFolder" forTests="false" />
   </component>
 </module>
\ No newline at end of file
diff --git a/ha_03/loosen_janniclas_1540907_04.py b/ha_03/loosen_janniclas_1540907_04.py
new file mode 100644
index 0000000..9db67f6
--- /dev/null
+++ b/ha_03/loosen_janniclas_1540907_04.py
@@ -0,0 +1,34 @@
+# Jan-Niclas Loosen
+# 1540907
+
+def sieve_of_eratosthenes(limit):
+    primes = [True] * (limit + 1)
+    primes[0] = primes[1] = False   # 0 and 1 are not primes
+
+    for num in range(2, int(limit ** 0.5) + 1):  # only necessary to the square root of the limit
+        if primes[num]:
+            prime = num
+            for i in range(1,limit):
+                mult = prime * (i + 1)
+                if mult >= len(primes):  # more loops are unnecessary
+                    break
+                primes[mult] = False
+
+    return primes
+
+def prime_factorization(n):
+    primes = sieve_of_eratosthenes(n)
+    factors = []
+    for i in range(2, n + 1):
+        if primes[i] and n % i == 0:
+            while n % i == 0:
+                factors.append(i)
+                n = n // i
+    return factors
+
+# dialog for testing the functions
+num = int(input("insert positive integer: "))
+if num < 0 :
+    print("invalid input")
+else:
+    print(prime_factorization(num))