Cracking hash knowing password length?

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I do know the password length is 24.

I also do know the search space: lower case, upper case and digits.

The combinations should be (26+26+10)^24 = 62^24, right?

I've tried with hashcat to set the charset and the mask

-1 ?l?u?d filename_to_crack ?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1?1 

but it won't start because of an integer overflow error due to a huge keyspace; I guess the mask is too large!

Someone can suggest another solution? I was thinking maybe I could write a script that generate a file of random (24 length) strings and then using this to perform a dictionary attack.

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Your idea to pre-generate random strings to get around the integer overflow would work. It's not really a dictionary attack at that point, more a rainbow table approach. It's going to take up a lot of space too.

I might suggest trying a dictionary attack of 24 character passwords before generating your brute force list. Perhaps with the lists from https://crackstation.net/ or somewhere else, filtered for length 24, of course. If you want to get creative/more thorough, you could add rules to the passwords from these lists, like l33tspeak substitutions.