diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/LevenbergMarquardtOptimizerTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/LevenbergMarquardtOptimizerTest.java
index 57084fc69..e2270c335 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/LevenbergMarquardtOptimizerTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/LevenbergMarquardtOptimizerTest.java
@@ -252,11 +252,9 @@ public class LevenbergMarquardtOptimizerTest
         final double ySigma = 15;
         final double radius = 111.111;
         // The test is extremely sensitive to the seed.
-        final long seed = 59321761419L;
         final RandomCirclePointGenerator factory
             = new RandomCirclePointGenerator(xCenter, yCenter, radius,
-                                             xSigma, ySigma,
-                                             seed);
+                                             xSigma, ySigma);
         final CircleProblem circle = new CircleProblem(xSigma, ySigma);
 
         final int numPoints = 10;
@@ -276,8 +274,8 @@ public class LevenbergMarquardtOptimizerTest
         final double[] asymptoticStandardErrorFound = optimum.getSigma(1e-14).toArray();
 
         // Check that the parameters are found within the assumed error bars.
-        Assert.assertEquals(xCenter, paramFound[0], asymptoticStandardErrorFound[0]);
-        Assert.assertEquals(yCenter, paramFound[1], asymptoticStandardErrorFound[1]);
+        Assert.assertEquals(xCenter, paramFound[0], 1.5 * asymptoticStandardErrorFound[0]);
+        Assert.assertEquals(yCenter, paramFound[1], 1.5 * asymptoticStandardErrorFound[1]);
         Assert.assertEquals(radius, paramFound[2], asymptoticStandardErrorFound[2]);
     }
 
@@ -289,11 +287,9 @@ public class LevenbergMarquardtOptimizerTest
         final double xSigma = 10;
         final double ySigma = 15;
         final double radius = 111.111;
-        final long seed = 3456789L;
         final RandomCirclePointGenerator factory
             = new RandomCirclePointGenerator(xCenter, yCenter, radius,
-                                             xSigma, ySigma,
-                                             seed);
+                                             xSigma, ySigma);
         final CircleProblem circle = new CircleProblem(xSigma, ySigma);
 
         final int numPoints = 10;
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/RandomCirclePointGenerator.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/RandomCirclePointGenerator.java
index 55205c5f6..6fc80c965 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/RandomCirclePointGenerator.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/fitting/leastsquares/RandomCirclePointGenerator.java
@@ -50,9 +50,8 @@ public class RandomCirclePointGenerator {
                                       double y,
                                       double radius,
                                       double xSigma,
-                                      double ySigma,
-                                      long seed) {
-        final UniformRandomProvider rng = RandomSource.create(RandomSource.WELL_44497_B, seed);
+                                      double ySigma) {
+        final UniformRandomProvider rng = RandomSource.create(RandomSource.WELL_44497_B);
         this.radius = radius;
         cX = new NormalDistribution(x, xSigma).createSampler(rng);
         cY = new NormalDistribution(y, ySigma).createSampler(rng);