[CJefferson]

Many catalogues of mathematical groups contain things like the monster group, which has 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. That won't fit in a 64 or even 128 bit integer.

It is common to want to ask a database "tell me all groups of size greater than X, with properties A, B and C". Now, if you have arbitrary sized ints, no problem. If your database (or language) doesn't support big ints, you need to figure out how to do "bigger than X", when you are storing big numbers in some other format, probably strings.

[logfromblammo]

Surely if you're storing numeric values as strings, it would be better to use something like base64 encoding to use as much of the available symbol space as possible?

If you can sort a numeric string in base 10, you can sort one in base 16, or base 64, or base 256.

[CJefferson]

I think you could use this method with other bases, although be careful with base 256 -- if your strings are stored in UTF8 or something, then base 256 isn't actually that useful.

However, the important bit (to me) is that you can use your database's sorting function to compare the numbers.

The advantage of base-10 is it's easy to display the number :) Others bases do provide a constant speed improvement of course.

[infogulch]

If we're in a database context you could store the length of the number in another number (64 bit would be plenty, nobody is storing a number with 18 exabytes of digits) then compare/sort by that first then the number itself, bases are irrelevant, besides the space savings of storing it directly in binary.

In fact I'd make an index on (len(N), N), then include len(X) and X in all your comparisons and range queries (wrapping for ergonomics as needed). You can use any base storage (including compact varbinary base256).

[jcwayne]

I'm genuinely curious, does anyone actually want/need to look at numbers larger than will fit in a 128bit int? I understand there are applications that require use and storage of such numbers, but how often is there are real need to display them?

[neunhoef]

In discrete mathematics this happens a lot. Group orders, sizee of conjugacy classes, semigroup orders, numbers of isomorphism classes, character degrees, etc.

[Retra]

"It happens" doesn't imply there's any need for it to happen.