diff --git a/src/Parser.js b/src/Parser.js
index 31f51e5..82d0777 100644
--- a/src/Parser.js
+++ b/src/Parser.js
@@ -343,6 +343,9 @@ Parser.prototype.parseAtom = function() {
             subscript = this.handleSupSubscript("subscript");
         } else if (lex.text === "'") {
             // We got a prime
+            if (superscript) {
+                throw new ParseError("Double superscript", lex);
+            }
             const prime = new ParseNode("textord", "\\prime", this.mode);
 
             // Many primes can be grouped together, so we handle this here
@@ -354,7 +357,12 @@ Parser.prototype.parseAtom = function() {
                 primes.push(prime);
                 this.consume();
             }
-            // Put them into an ordgroup as the superscript
+            // If there's a superscript following the primes, combine that
+            // superscript in with the primes.
+            if (this.nextToken.text === "^") {
+                primes.push(this.handleSupSubscript("superscript"));
+            }
+            // Put everything into an ordgroup as the superscript
             superscript = new ParseNode("ordgroup", primes, this.mode);
         } else {
             // If it wasn't ^, _, or ', stop parsing super/subscripts
diff --git a/test/errors-spec.js b/test/errors-spec.js
index 641863c..190e75c 100644
--- a/test/errors-spec.js
+++ b/test/errors-spec.js
@@ -106,6 +106,16 @@ describe("Parser:", function() {
             expect("1^{2+3}_4^5").toFailWithParseError(
                    "Double superscript at position 10: 1^{2+3}_4^̲5");
         });
+        it("rejects double superscripts involving primes", function() {
+            expect("1'_2^3").toFailWithParseError(
+                   "Double superscript at position 5: 1'_2^̲3");
+            expect("1^2'").toFailWithParseError(
+                   "Double superscript at position 4: 1^2'̲");
+            expect("1^2_3'").toFailWithParseError(
+                   "Double superscript at position 6: 1^2_3'̲");
+            expect("1'_2'").toFailWithParseError(
+                   "Double superscript at position 5: 1'_2'̲");
+        });
         it("rejects double subscripts", function() {
             expect("1_2_3").toFailWithParseError(
                    "Double subscript at position 4: 1_2_̲3");
diff --git a/test/katex-spec.js b/test/katex-spec.js
index 15012f7..36dd5f5 100644
--- a/test/katex-spec.js
+++ b/test/katex-spec.js
@@ -1260,7 +1260,6 @@ describe("A TeX-compliant parser", function() {
         expect("x''''").toParse();
         expect("x_2''").toParse();
         expect("x''_2").toParse();
-        expect("x'_2'").toParse();
     });
 
     it("should fail when sup/subscripts are interspersed with arguments", function() {
diff --git a/test/screenshotter/images/PrimeSuper-chrome.png b/test/screenshotter/images/PrimeSuper-chrome.png
new file mode 100644
index 0000000..4a4c689
Binary files /dev/null and b/test/screenshotter/images/PrimeSuper-chrome.png differ
diff --git a/test/screenshotter/images/PrimeSuper-firefox.png b/test/screenshotter/images/PrimeSuper-firefox.png
new file mode 100644
index 0000000..41352b3
Binary files /dev/null and b/test/screenshotter/images/PrimeSuper-firefox.png differ
diff --git a/test/screenshotter/ss_data.yaml b/test/screenshotter/ss_data.yaml
index bef0d7b..8838e48 100644
--- a/test/screenshotter/ss_data.yaml
+++ b/test/screenshotter/ss_data.yaml
@@ -124,6 +124,7 @@ OpLimits: |
 OverUnderline: x\underline{x}\underline{\underline{x}}\underline{x_{x_{x_x}}}\underline{x^{x^{x^x}}}\overline{x}\overline{x}\overline{x^{x^{x^x}}} \blue{\overline{\underline{x}}\underline{\overline{x}}}
 Phantom: \dfrac{1+\phantom{x^{\blue{2}}} = x}{1+x^{\blue{2}} = x}
 PrimeSpacing: f'+f_2'+f^{f'}
+PrimeSuper: x'^2+x'''^2+x'^2_3+x_3'^2
 RlapBug: \frac{\rlap{x}}{2}
 Rule: \rule{1em}{0.5em}\rule{1ex}{2ex}\rule{1em}{1ex}\rule{1em}{0.431ex}
 SizingBaseline: