diff --git a/packages/next/build/index.ts b/packages/next/build/index.ts
index ff02753bb52e0..1780e579c01d8 100644
--- a/packages/next/build/index.ts
+++ b/packages/next/build/index.ts
@@ -676,7 +676,7 @@ export default async function build(
       const nonStaticErrorPageSpan = staticCheckSpan.traceChild(
         'check-static-error-page'
       )
-      const nonStaticErrorPagePromise = nonStaticErrorPageSpan.traceAsyncFn(
+      const errorPageHasCustomGetInitialProps = nonStaticErrorPageSpan.traceAsyncFn(
         async () =>
           hasCustomErrorPage &&
           (await staticCheckWorkers.hasCustomGetInitialProps(
@@ -687,6 +687,20 @@ export default async function build(
             false
           ))
       )
+
+      const errorPageStaticResult = nonStaticErrorPageSpan.traceAsyncFn(
+        async () =>
+          hasCustomErrorPage &&
+          staticCheckWorkers.isPageStatic(
+            '/_error',
+            distDir,
+            isLikeServerless,
+            runtimeEnvConfig,
+            config.i18n?.locales,
+            config.i18n?.defaultLocale
+          )
+      )
+
       // we don't output _app in serverless mode so use _app export
       // from _error instead
       const appPageToCheck = isLikeServerless ? '/_error' : '/_app'
@@ -847,12 +861,18 @@ export default async function build(
           })
         })
       )
+
+      const errorPageResult = await errorPageStaticResult
+      const nonStaticErrorPage =
+        (await errorPageHasCustomGetInitialProps) ||
+        (errorPageResult && errorPageResult.hasServerProps)
+
       const returnValue = {
         customAppGetInitialProps: await customAppGetInitialPropsPromise,
         namedExports: await namedExportsPromise,
         isNextImageImported,
         hasSsrAmpPages,
-        hasNonStaticErrorPage: await nonStaticErrorPagePromise,
+        hasNonStaticErrorPage: nonStaticErrorPage,
       }
 
       staticCheckWorkers.end()
@@ -989,13 +1009,15 @@ export default async function build(
         mappedPages[page] && mappedPages[page].startsWith('private-next-pages')
     )
     usedStaticStatusPages.forEach((page) => {
-      if (!ssgPages.has(page)) {
+      if (!ssgPages.has(page) && !customAppGetInitialProps) {
         staticPages.add(page)
       }
     })
 
     const hasPages500 = usedStaticStatusPages.includes('/500')
-    const useDefaultStatic500 = !hasPages500 && !hasNonStaticErrorPage
+    const useDefaultStatic500 =
+      !hasPages500 && !hasNonStaticErrorPage && !customAppGetInitialProps
+
     const combinedPages = [...staticPages, ...ssgPages]
 
     if (combinedPages.length > 0 || useStatic404 || useDefaultStatic500) {
diff --git a/packages/next/next-server/server/next-server.ts b/packages/next/next-server/server/next-server.ts
index d1f38c8ae60e8..885937ea74b58 100644
--- a/packages/next/next-server/server/next-server.ts
+++ b/packages/next/next-server/server/next-server.ts
@@ -1439,6 +1439,7 @@ export default class Server {
     opts: RenderOptsPartial
   ): Promise<string | null> {
     const is404Page = pathname === '/404'
+    const is500Page = pathname === '/500'
 
     const isLikeServerless =
       typeof components.Component === 'object' &&
@@ -1560,7 +1561,7 @@ export default class Server {
               : resolvedUrlPathname
           }${query.amp ? '.amp' : ''}`
 
-    if (is404Page && isSSG) {
+    if ((is404Page || is500Page) && isSSG) {
       ssgCacheKey = `${locale ? `/${locale}` : ''}${pathname}${
         query.amp ? '.amp' : ''
       }`
diff --git a/test/integration/500-page/test/index.test.js b/test/integration/500-page/test/index.test.js
index 01ade2663d05f..eb512749a9723 100644
--- a/test/integration/500-page/test/index.test.js
+++ b/test/integration/500-page/test/index.test.js
@@ -111,7 +111,7 @@ describe('500 Page Support', () => {
     runTests('serverless')
   })
 
-  it('still builds 500 statically with getInitialProps in _app', async () => {
+  it('does not build 500 statically with getInitialProps in _app', async () => {
     await fs.writeFile(
       pagesApp,
       `
@@ -127,8 +127,71 @@ describe('500 Page Support', () => {
       stderr: true,
       stdout: true,
     })
+
     await fs.remove(pagesApp)
 
+    expect(stderr).not.toMatch(gip500Err)
+    expect(buildStdout).not.toContain('rendered 500')
+    expect(code).toBe(0)
+    expect(
+      await fs.pathExists(join(appDir, '.next/server/pages/500.html'))
+    ).toBe(false)
+
+    let appStdout = ''
+    const appPort = await findPort()
+    const app = await nextStart(appDir, appPort, {
+      onStdout(msg) {
+        appStdout += msg || ''
+      },
+      onStderr(msg) {
+        appStdout += msg || ''
+      },
+    })
+
+    await renderViaHTTP(appPort, '/err')
+    await killApp(app)
+
+    expect(appStdout).toContain('rendered 500')
+  })
+
+  it('does build 500 statically with getInitialProps in _app and getStaticProps in pages/500', async () => {
+    await fs.writeFile(
+      pagesApp,
+      `
+      import App from 'next/app'
+
+      const page = ({ Component, pageProps }) => <Component {...pageProps} />
+      page.getInitialProps = (ctx) => App.getInitialProps(ctx)
+      export default page
+    `
+    )
+    await fs.rename(pages500, `${pages500}.bak`)
+    await fs.writeFile(
+      pages500,
+      `
+      const page = () => {
+        console.log('rendered 500')
+        return 'custom 500 page'
+      }
+      export default page
+
+      export const getStaticProps = () => {
+        return {
+          props: {}
+        }
+      }
+    `
+    )
+    await fs.remove(join(appDir, '.next'))
+    const { stderr, stdout: buildStdout, code } = await nextBuild(appDir, [], {
+      stderr: true,
+      stdout: true,
+    })
+
+    await fs.remove(pagesApp)
+    await fs.remove(pages500)
+    await fs.rename(`${pages500}.bak`, pages500)
+
     expect(stderr).not.toMatch(gip500Err)
     expect(buildStdout).toContain('rendered 500')
     expect(code).toBe(0)
@@ -139,6 +202,9 @@ describe('500 Page Support', () => {
     let appStdout = ''
     const appPort = await findPort()
     const app = await nextStart(appDir, appPort, {
+      onStdout(msg) {
+        appStdout += msg || ''
+      },
       onStderr(msg) {
         appStdout += msg || ''
       },
@@ -270,6 +336,59 @@ describe('500 Page Support', () => {
     expect(appStderr).toContain('called _error.getInitialProps')
   })
 
+  it('does not build 500 statically with no pages/500 and getServerSideProps in _error', async () => {
+    await fs.rename(pages500, `${pages500}.bak`)
+    await fs.writeFile(
+      pagesError,
+      `
+        function Error({ statusCode }) {
+          return <p>Error status: {statusCode}</p>
+        }
+
+        export const getServerSideProps = ({ req, res, err }) => {
+          console.error('called _error getServerSideProps')
+
+          if (req.url === '/500') {
+            throw new Error('should not export /500')
+          }
+
+          return {
+            props: {
+              statusCode: res && res.statusCode ? res.statusCode : err ? err.statusCode : 404
+            }
+          }
+        }
+
+        export default Error
+      `
+    )
+    await fs.remove(join(appDir, '.next'))
+    const { stderr: buildStderr, code } = await nextBuild(appDir, [], {
+      stderr: true,
+    })
+    await fs.rename(`${pages500}.bak`, pages500)
+    await fs.remove(pagesError)
+    console.log(buildStderr)
+    expect(buildStderr).not.toMatch(gip500Err)
+    expect(code).toBe(0)
+    expect(
+      await fs.pathExists(join(appDir, '.next/server/pages/500.html'))
+    ).toBe(false)
+
+    let appStderr = ''
+    const appPort = await findPort()
+    const app = await nextStart(appDir, appPort, {
+      onStderr(msg) {
+        appStderr += msg || ''
+      },
+    })
+
+    await renderViaHTTP(appPort, '/err')
+    await killApp(app)
+
+    expect(appStderr).toContain('called _error getServerSideProps')
+  })
+
   it('does not build 500 statically with no pages/500 and custom getInitialProps in _error and _app', async () => {
     await fs.rename(pages500, `${pages500}.bak`)
     await fs.writeFile(