diff --git a/rand_distr/src/binomial.rs b/rand_distr/src/binomial.rs
index 0f49806aba..4cd21fd817 100644
--- a/rand_distr/src/binomial.rs
+++ b/rand_distr/src/binomial.rs
@@ -110,20 +110,34 @@ impl Distribution<u64> for Binomial {
         // Threshold for preferring the BINV algorithm. The paper suggests 10,
         // Ranlib uses 30, and GSL uses 14.
         const BINV_THRESHOLD: f64 = 10.;
+        
+        // Same value as in GSL.
+        // It is possible for BINV to get stuck, so we break if x > BINV_MAX_X and try again.
+        // It would be safer to set BINV_MAX_X to self.n, but it is extremely unlikely to be relevant.
+        // When n*p < 10, so is n*p*q which is the variance, so a result > 110 would be 100 / sqrt(10) = 31 standard deviations away.
+        const BINV_MAX_X : u64 = 110;
 
         if (self.n as f64) * p < BINV_THRESHOLD && self.n <= (core::i32::MAX as u64) {
             // Use the BINV algorithm.
             let s = p / q;
             let a = ((self.n + 1) as f64) * s;
-            let mut r = q.powi(self.n as i32);
-            let mut u: f64 = rng.gen();
-            let mut x = 0;
-            while u > r as f64 {
-                u -= r;
-                x += 1;
-                r *= a / (x as f64) - s;
+            
+            result = 'outer: loop {
+                let mut r = q.powi(self.n as i32);
+                let mut u: f64 = rng.gen();
+                let mut x = 0;
+
+                while u > r as f64 {
+                    u -= r;
+                    x += 1;
+                    if x > BINV_MAX_X {
+                        continue 'outer;
+                    }
+                    r *= a / (x as f64) - s;
+                }
+                break x;
+            
             }
-            result = x;
         } else {
             // Use the BTPE algorithm.
 
@@ -352,4 +366,15 @@ mod test {
     fn binomial_distributions_can_be_compared() {
         assert_eq!(Binomial::new(1, 1.0), Binomial::new(1, 1.0));
     }
+    
+    #[test]
+    fn binomial_avoid_infinite_loop() {
+        let dist = Binomial::new(16000000, 3.1444753148558566e-10).unwrap();
+        let mut sum: u64 = 0;
+        let mut rng = crate::test::rng(742);
+        for _ in 0..100_000 {
+            sum = sum.wrapping_add(dist.sample(&mut rng));
+        }
+        assert_ne!(sum, 0);
+    }
 }