diff --git a/pkgs/racket-test/tests/racket/contract/random-generate.rkt b/pkgs/racket-test/tests/racket/contract/random-generate.rkt
index 7799eda374..2b1d98b077 100644
--- a/pkgs/racket-test/tests/racket/contract/random-generate.rkt
+++ b/pkgs/racket-test/tests/racket/contract/random-generate.rkt
@@ -3,6 +3,7 @@
 (require racket/contract
          racket/contract/private/generate-base
          rackunit
+         racket/math
          (for-syntax racket/base))
 
 ;; this is expected to never have a generator.
@@ -41,6 +42,8 @@
 (check-not-exn (λ () (test-contract-generation (listof number?))))
 
 (check-not-exn (λ () (test-contract-generation (integer-in 0 100))))
+(check-not-exn (λ () (test-contract-generation exact-nonnegative-integer?)))
+(check-not-exn (λ () (test-contract-generation natural?)))
 (check-not-exn (λ () (test-contract-generation (integer-in 0 (expt 2 1000)))))
 (check-not-exn (λ () (test-contract-generation (char-in #\a #\z))))
 (check-not-exn (λ () (test-contract-generation #\a)))
diff --git a/racket/collects/racket/contract/private/generate-base.rkt b/racket/collects/racket/contract/private/generate-base.rkt
index e09c19e042..843837a730 100644
--- a/racket/collects/racket/contract/private/generate-base.rkt
+++ b/racket/collects/racket/contract/private/generate-base.rkt
@@ -1,5 +1,6 @@
 #lang racket/base
-(require "rand.rkt")
+(require "rand.rkt"
+         "../../private/math-predicates.rkt")
 
 (provide
   contract-random-generate-fail
@@ -71,6 +72,9 @@
    exact-integer?
    exact-integer-gen
    
+   natural?
+   exact-nonnegative-integer-gen
+
    exact-nonnegative-integer?
    exact-nonnegative-integer-gen
    
diff --git a/racket/collects/racket/math.rkt b/racket/collects/racket/math.rkt
index df28590218..0bf7b5ad7b 100644
--- a/racket/collects/racket/math.rkt
+++ b/racket/collects/racket/math.rkt
@@ -5,7 +5,8 @@
 #lang racket/base
 
 (require "unsafe/ops.rkt"
-         "performance-hint.rkt")
+         "performance-hint.rkt"
+         "private/math-predicates.rkt")
 
 (provide pi pi.f
          nan? infinite?
@@ -26,30 +27,6 @@
 
 (begin-encourage-inline
 
-  ;; real predicates
-  (define (nan? x)
-    (unless (real? x) (raise-argument-error 'nan? "real?" x))
-    (or (eqv? x +nan.0) (eqv? x +nan.f)))
-
-  (define (infinite? x)
-    (unless (real? x) (raise-argument-error 'infinite? "real?" x))
-    (or (= x +inf.0) (= x -inf.0)))
-
-  (define (positive-integer? x)
-    (and (integer? x) (positive? x)))
-
-  (define (negative-integer? x)
-    (and (integer? x) (negative? x)))
-
-  (define (nonpositive-integer? x)
-    (and (integer? x) (not (positive? x))))
-
-  (define (nonnegative-integer? x)
-    (and (integer? x) (not (negative? x))))
-
-  (define (natural? x)
-    (exact-nonnegative-integer? x))
-
   ;; z^2
   (define (sqr z)
     (unless (number? z) (raise-argument-error 'sqr "number?" z))
diff --git a/racket/collects/racket/private/math-predicates.rkt b/racket/collects/racket/private/math-predicates.rkt
new file mode 100644
index 0000000000..c188157e14
--- /dev/null
+++ b/racket/collects/racket/private/math-predicates.rkt
@@ -0,0 +1,38 @@
+#lang racket/base
+(require "performance-hint.rkt")
+(provide nan?
+         infinite?
+         positive-integer?
+         negative-integer?
+         nonpositive-integer?
+         nonnegative-integer?
+         natural?)
+
+;; these are broken out from racket/math
+;; so that racket/contract can depend on them
+
+(begin-encourage-inline
+
+  ;; real predicates
+  (define (nan? x)
+    (unless (real? x) (raise-argument-error 'nan? "real?" x))
+    (or (eqv? x +nan.0) (eqv? x +nan.f)))
+
+  (define (infinite? x)
+    (unless (real? x) (raise-argument-error 'infinite? "real?" x))
+    (or (= x +inf.0) (= x -inf.0)))
+
+  (define (positive-integer? x)
+    (and (integer? x) (positive? x)))
+
+  (define (negative-integer? x)
+    (and (integer? x) (negative? x)))
+
+  (define (nonpositive-integer? x)
+    (and (integer? x) (not (positive? x))))
+
+  (define (nonnegative-integer? x)
+    (and (integer? x) (not (negative? x))))
+
+  (define (natural? x)
+    (exact-nonnegative-integer? x)))
\ No newline at end of file