diff --git a/pkgs/racket-test-core/tests/racket/number.rktl b/pkgs/racket-test-core/tests/racket/number.rktl
index 895ad15b95..7d27ca6ee9 100644
--- a/pkgs/racket-test-core/tests/racket/number.rktl
+++ b/pkgs/racket-test-core/tests/racket/number.rktl
@@ -2736,6 +2736,10 @@
   (test '#(1062645402 3593208522 3838676319 2291995347 179540564 3081399108)
         pseudo-random-generator->vector (current-pseudo-random-generator)))
 
+(test 1110944503
+      random 4294967087 (vector->pseudo-random-generator
+                         '#(2182378604 1199273501 1921976687 2184096762 3398188531 1221198170)))
+
 (test #t = 0 0)
 (test #f = 0 (expt 2 32))
 (test #f = (expt 2 32) 0)
diff --git a/racket/src/ChezScheme/s/5_3.ss b/racket/src/ChezScheme/s/5_3.ss
index 04d8bc5681..fb2a928133 100644
--- a/racket/src/ChezScheme/s/5_3.ss
+++ b/racket/src/ChezScheme/s/5_3.ss
@@ -2777,19 +2777,26 @@
          (random-double s)]
         [(s x)
          (define (random-integer s x)
-           (modulo (let loop ([bits (integer-length x)])
-                     (cond
-                      [(<= bits 0) 0]
-                      [else (bitwise-ior (bitwise-arithmetic-shift-left (loop (- bits 24)) 24)
-                                         (random-int s #xFFFFFF))]))
-                   x))
+           (let ([bits (integer-length x)])
+             (let loop ([shift 0])
+               (cond
+                 [(<= bits shift) 0]
+                 [else
+                  ;; Assuming that a `uptr` is at least 32 bits:
+                  (bitwise-ior (loop (+ shift 32))
+                               (let ([n (bitwise-bit-field x shift (+ shift 32))])
+                                 (if (zero? n)
+                                     0
+                                     (bitwise-arithmetic-shift-left
+                                      (random-int s n)
+                                      shift))))]))))
          (unless (is-pseudo-random-generator? s) ($oops who "not a pseudo-random generator ~s" s))
          (cond
           [(fixnum? x)
            (unless (fxpositive? x) ($oops who "not a positive exact integer ~s" x))
            (meta-cond
             [(<= (constant most-negative-fixnum) 4294967087 (constant most-positive-fixnum))
-             (if (fx< x 4294967087)
+             (if (fx<= x 4294967087)
                  (random-int s x)
                  (random-integer s x))]
             [else