How to make Vigenere unbreakable

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If you use multiple keys whose lengths are relatively prime, your effective Vigenere key length is the product of the lengths of all the keys.  Imagine using keys with relatively prime lengths 9, 10, and 11.  Your effective key length would be 1,320 characters long!  Using an easily-remembered phrase that you can break up until lengths of perhaps 29, 30, and 31, you're practically using a one-time pad 26,970 letters long that you can store in your head!

Is there any way to crack such a ciphertext if it's shorter than the effective key length?

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