A variable name must start with a letter or an underscore. From perldata:

The rest of the name tells you the particular value to
which it refers.  Most often, it consists of a single
identifier, that is, a string beginning with a letter
or underscore, and containing letters, underscores, and
digits.
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However, a hash *key* can quite well consist only of digits; so as you allude to in the title, what you probably need here is a multidimensional data structure. I don't know what you're planning to store in addition to the bad sequence... presumably something for which you needed a hash in the first place. But anyway:

my %bad = (
    '12598' => {},   # data about bad sequence
    '19203' => {},   # data about other bad sequence
)
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and so on. Each bad sequence string maps in the hash to an anonymous hash that you can use just as you planned to use your original hash, %12598. Instead of saying

$12598{'foo'} = 'bar';   # wrong and illegal
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now you'd say

$bad{'12598'}{'foo'} = 'bar';
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Make sense?