diff --git a/package.json b/package.json
index f8aff70..9405b91 100644
--- a/package.json
+++ b/package.json
@@ -42,6 +42,7 @@
     "pretest": "npm run compile",
     "posttest": "npm run lint",
     "test": "vitest",
+    "fuzz": "FUZZ=1 vitest",
     "compile-legacy": "tsc -p tsconfig-legacy.json",
     "prebench": "npm run compile && npm run compile-legacy",
     "bench": "vitest bench",
diff --git a/src/__tests__/index.spec.ts b/src/__tests__/index.spec.ts
index ac6e836..f34bd7e 100644
--- a/src/__tests__/index.spec.ts
+++ b/src/__tests__/index.spec.ts
@@ -24,6 +24,8 @@ import {
   wilsonHeight,
 } from '../index';
 
+const FUZZ = 'FUZZ' in process.env;
+
 describe('Array equality tester', () => {
   it('works on integer arrays', () => {
     expect(arraysEqual([1, 2, 3], [1, 2, 3])).toBeTruthy();
@@ -600,7 +602,7 @@ describe('Wilson complexity measure', () => {
     expect(wilsonHeight(fraction)).toBe(height);
   });
 
-  it.skip('fuzzes the fraction property', () => {
+  it.runIf(FUZZ)('fuzzes the fraction property', () => {
     for (let i = 0; i < 100; ++i) {
       const n = Math.floor(Math.random() * 1073741823);
       const d = Math.floor(Math.random() * 1073741822) + 1;
@@ -609,7 +611,7 @@ describe('Wilson complexity measure', () => {
     }
   });
 
-  it.skip('fuzzes the multiplicative property', () => {
+  it.runIf(FUZZ)('fuzzes the multiplicative property', () => {
     for (let i = 0; i < 10000; ++i) {
       const x = Math.floor(Math.random() * 32768);
       const y = Math.floor(Math.random() * 32768);
diff --git a/src/__tests__/monzo.spec.ts b/src/__tests__/monzo.spec.ts
index 8bbf796..6ab2b2f 100644
--- a/src/__tests__/monzo.spec.ts
+++ b/src/__tests__/monzo.spec.ts
@@ -10,6 +10,8 @@ import {
 } from '../monzo';
 import {isPrime} from '../primes';
 
+const FUZZ = 'FUZZ' in process.env;
+
 function toMonzoAndResidual11(n: number): [number[], number] {
   const result = [0, 0, 0, 0, 0];
   if (!n) {
@@ -442,6 +444,7 @@ describe('Sparse monzos', () => {
     17719 * 21909,
     15812 * 27083,
     21097 * 29468,
+    30038 * 7605,
   ])('works on a tough case %s found during fuzzing', n => {
     const exponentByPrime = primeFactorize(n);
     let m = 1;
@@ -452,7 +455,7 @@ describe('Sparse monzos', () => {
     expect(m).toBe(n);
   });
 
-  it.skip('fuzzes for more broken cases', () => {
+  it.runIf(FUZZ)('fuzzes for more broken cases', () => {
     for (let i = 0; i < 100; ++i) {
       const n = Math.floor(Math.random() * 62837328) + 1;
       const exponentByPrime = primeFactorize(n);
diff --git a/src/monzo.ts b/src/monzo.ts
index 5279c3a..175a186 100644
--- a/src/monzo.ts
+++ b/src/monzo.ts
@@ -694,16 +694,28 @@ export function primeFactorize(value: FractionValue): Map<number, number> {
     result.set(-1, 1);
     value = -value;
   }
-  if (value > 1073741823) {
-    throw new Error('Factorization not implemented above 1073741823.');
+  if (value > Number.MAX_SAFE_INTEGER) {
+    throw new Error(
+      `Factorization not implemented above ${Number.MAX_SAFE_INTEGER}.`
+    );
   }
   let [monzo, residual] = intToMonzo7(value);
+  if (residual > 1073741823) {
+    throw new Error(
+      'Factorization not implemented when 7-limit residual > 1073741823.'
+    );
+  }
   for (let i = 0; i < monzo.length; ++i) {
     if (monzo[i]) {
       result.set(PRIMES[i], monzo[i]);
     }
   }
-  // This is entirely ad. hoc. with holes patched as they came up during fuzzing.
+  // Skip cascade for known primes.
+  if (PRIMES.includes(residual)) {
+    result.set(residual, 1);
+    return result;
+  }
+  // This is entirely ad hoc with holes patched as they came up during fuzzing.
   while (residual !== 1) {
     let factor = rhoCascade(residual);
     residual /= factor;