diff --git a/src/sage/functions/orthogonal_polys.py b/src/sage/functions/orthogonal_polys.py
index 2a5ed971550..9a1078049b4 100644
--- a/src/sage/functions/orthogonal_polys.py
+++ b/src/sage/functions/orthogonal_polys.py
@@ -2083,9 +2083,7 @@ class Func_ultraspherical(GinacFunction):
         32*t^3 - 12*t
         sage: _ = var('x')
         sage: for N in range(100):
-        ....:     n = ZZ.random_element().abs() + 5
-        ....:     if n > 5000:  # avoid timeouts
-        ....:         continue
+        ....:     n = ZZ.random_element(5, 5001)
         ....:     a = QQ.random_element().abs() + 5
         ....:     assert ((n+1)*ultraspherical(n+1,a,x) - 2*x*(n+a)*ultraspherical(n,a,x) + (n+2*a-1)*ultraspherical(n-1,a,x)).expand().is_zero()
         sage: ultraspherical(5,9/10,3.1416)