diff --git a/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt b/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
index 685b42af..64a479bd 100644
--- a/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
+++ b/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
@@ -1902,6 +1902,15 @@
 [nan? (make-pred-ty (list -Real) B -InexactRealNan)]
 
 [infinite? (make-pred-ty (list -Real) B (Un -PosInfinity -NegInfinity))]
+[positive-integer? (asym-pred Univ B (-PS (-is-type 0 (Un -PosInt -PosFlonum -PosSingleFlonum))
+                                          (-not-type 0 -PosInt)))]
+[negative-integer? (asym-pred Univ B (-PS (-is-type 0 (Un -NegInt -NegFlonum -NegSingleFlonum))
+                                          (-not-type 0 -NegInt)))]
+[nonpositive-integer? (asym-pred Univ B (-PS (-is-type 0 (Un -NonPosInt -NonPosFlonum -NonPosSingleFlonum))
+                                             (-not-type 0 -NonPosInt)))]
+[nonnegative-integer? (asym-pred Univ B (-PS (-is-type 0 (Un -Nat -NonNegFlonum -NonNegSingleFlonum))
+                                             (-not-type 0 -Nat)))]
+[natural? (make-pred-ty -Nat)]
 
 ;; racket/fixnum
 [fx+ (fx+-type)]
diff --git a/typed-racket-test/unit-tests/typecheck-tests.rkt b/typed-racket-test/unit-tests/typecheck-tests.rkt
index 8170614e..11b0a7cf 100644
--- a/typed-racket-test/unit-tests/typecheck-tests.rkt
+++ b/typed-racket-test/unit-tests/typecheck-tests.rkt
@@ -4374,6 +4374,54 @@
           (void))
         #:ret (ret -Void #f #f)
         #:msg #rx"type mismatch"]
+
+        ;; pr615 : positive-integer?
+        [tc-e/t (let: ([x : Exact-Rational 3/2])
+                  (if (positive-integer? x) x 0))
+               -Nat]
+        [tc-e/t (let: ([x : Flonum 1.0])
+                  (if (positive-integer? x) x 2.0))
+               -PosFlonum]
+        [tc-e/t (let: ([x : (Un Flonum Positive-Integer) 1.0])
+                  (if (not (positive-integer? x)) x 1.0))
+               -Flonum]
+        ;; pr615 : negative-integer?
+        [tc-e/t (let: ([x : Exact-Rational -3/2])
+                  (if (negative-integer? x) x -5))
+               -NegInt]
+        [tc-e/t (let: ([x : Flonum 1.0])
+                  (if (negative-integer? x) x -2.0))
+               -NegFlonum]
+        [tc-e/t (let: ([x : (Un Flonum Negative-Integer) -1.0])
+                  (if (not (negative-integer? x)) x -1.0))
+               -Flonum]
+        ;; pr615 : nonpositive-integer?
+        [tc-e/t (let: ([x : Exact-Rational -3/2])
+                  (if (nonpositive-integer? x) x 0))
+               -NonPosInt]
+        [tc-e/t (let: ([x : Flonum -1.0])
+                  (if (nonpositive-integer? x) x 0.0))
+               -NonPosFlonum]
+        [tc-e/t (let: ([x : (Un Flonum Negative-Integer) -1.0])
+                  (if (not (nonpositive-integer? x)) x -1.0))
+               -Flonum]
+        ;; pr615 : nonnegative-integer?
+        [tc-e/t (let: ([x : Exact-Rational 3/2])
+                  (if (nonnegative-integer? x) x 0))
+               -Nat]
+        [tc-e/t (let: ([x : Flonum 1.0])
+                  (if (nonnegative-integer? x) x 2.0))
+               -NonNegFlonum]
+        [tc-e/t (let: ([x : (Un Flonum Natural) 1.0])
+                  (if (not (nonnegative-integer? x)) x 1.0))
+               -Flonum]
+        ;; pr615 : natural?
+        [tc-e/t (let: ([x : Real 1])
+                  (if (natural? x) x 1))
+               -Nat]
+        [tc-e/t (let: ([x : (Un Flonum Natural) 0.0])
+                  (if (not (natural? x)) x 1.0))
+               -Flonum]
        )
 
   (test-suite