diff --git a/code/python/src/algorithms/pollard_rho/algorithms.py b/code/python/src/algorithms/pollard_rho/algorithms.py
index 0067ca7..493d9ca 100644
--- a/code/python/src/algorithms/pollard_rho/algorithms.py
+++ b/code/python/src/algorithms/pollard_rho/algorithms.py
@@ -30,24 +30,37 @@ def pollard_rho_algorithm(
     x_init: int = 2,
     verbose: bool = False,
 ):
-    d = 1;
-    x = y = x_init;
     steps = [];
-    steps.append(Step(x=x, y=y));
     success = False;
     f = lambda _: fct(_, n=n);
+
+    d = 1;
+    x = y = x_init;
+    steps.append(Step(x=x));
+    k = 0;
+    k_next = 1;
+
     while True:
+        # aktualisiere x: x = f(x_prev):
         x = f(x);
-        y = f(f(y));
+        # aktualisiere y, wenn k = 2^j: y = x[j] = f(y_prev):
+        if k == k_next:
+            k_next = 2*k_next;
+            y = f(y);
+
+        # ggT berechnen:
         d = math.gcd(abs(x-y), n);
         steps.append(Step(x=x, y=y, d=d));
-        if d == 1:
+
+        # Abbruchkriterien prüfen:
+        if d == 1: # weitermachen, solange d == 1
+            k += 1;
             continue;
-        elif d < n:
-            success = True;
+        elif d == n: # versagt
+            success = False;
             break;
         else:
-            success = False;
+            success = True;
             break;
 
     if verbose:
diff --git a/code/python/src/algorithms/pollard_rho/display.py b/code/python/src/algorithms/pollard_rho/display.py
index 7528211..6ff792e 100644
--- a/code/python/src/algorithms/pollard_rho/display.py
+++ b/code/python/src/algorithms/pollard_rho/display.py
@@ -27,14 +27,14 @@ def display_table(steps: List[Step]) -> str:
     table = pd.DataFrame({
         'i':  [i for i in range(len(steps))],
         'x':  [step.x for step in steps],
-        'y':  [step.y for step in steps],
+        'y':  [step.y or '-' for step in steps],
         'd':  [step.d or '-' for step in steps],
     }) \
     .reset_index(drop=True);
     # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
     repr = tabulate(
         table,
-        headers=['i', 'x[i]', 'y[i] = x[2i]', 'gcd(|x - y|,n)'],
+        headers=['i', 'x(i)', 'y(i) = x([log₂(i)])', 'gcd(|x - y|,n)'],
         showindex=False,
         colalign=('right', 'right', 'right', 'center'),
         tablefmt='simple',
diff --git a/code/python/src/models/pollard_rho/logging.py b/code/python/src/models/pollard_rho/logging.py
index 8819c56..0bc4463 100644
--- a/code/python/src/models/pollard_rho/logging.py
+++ b/code/python/src/models/pollard_rho/logging.py
@@ -22,5 +22,5 @@ __all__ = [
 @dataclass
 class Step():
     x: int = field();
-    y: int = field();
+    y: Optional[int] = field(default=None);
     d: Optional[int] = field(default=None);