how to speed up 404 recognition?

[serenoo]

6 weeks ago I removed a backlink purchased by me with the goal to come out from Penguin, but google still keeps such page on its index.
Is there a way to speed up the process to remove 404 pages from Google index?
The backlink was on a website I cannot control and that kindly removed the page. I contacted such webmaster and he said he has not a google webmaster tool account.

[netmeg]

I got phantom pages I've been waiting three years for Google to get rid of.

[serenoo]

I do not want to wait all that time. If I add a link to the 404 page, then will that help google to understand it has to remove that page?

[legaleagle]

You could try displaying these pages as a 410 header as google then may see it as a clearer signal that the page has been dropped

[serenoo]

These pages are not under my control. I cannot displaying them in any way.

[lucy24]

OK, now I'm confused. Is it the page or the link that's on your own site? You've got to have control over one or the other. If g### has started penalizing Site A because of activity involving only Sites B and C, I do not want to hear about it.

If it's a page, it doesn't need to exist physically. You can still serve up a 410 in your config or htaccess.

[serenoo]

The page is on external website.
The page does not exist because it returns 404 (it has been removed).
The page is still on google index.
The page that is on external website and that does not exist contains a purchased backlink to my website.

[Robert Charlton]

The backlink was on a website I cannot control and that kindly removed the page.

Google will keep references to a page returning a 404 and will check for the page periodically... as has been noted, often for years. It's normal for a search engine to do that. As Google's JohnMu explains, in this Google support discussion [google.com...]

[Removed pages] will show up as crawl errors in Webmaster Tools, but that's fine -- they're supposed to. They won't negatively affect the rest of your site's crawling, indexing or ranking. Having pages that return 404 is fine and to be expected.

Google understands that a 404 means the page doesn't exist. Why are you assuming that Google thinks the link that was on the removed page is still linking to you?

[serenoo]

because when I search on Google for a sentence that was on that page, then google displays the page on the results.