None, there is nothing on an actual computer that allows you to store an ininitelly large integer on any computer language known today. And I doubt that will ever exist.
now lets do an experiment.
lets assume your computer and OS and your program can run with 1 GB
your computer RAM has 4 GB, and your hard drive has 1TB
and lets assume this means 1028 Gb of memory in total but you used 1 for the program so that will be 1027 GB that is 1027 * 1024 * 1024 * 1024 * 8 in bits.
that is rather big number right? even that number is just 8821862825984. (quite long but not infinite and that is the number of bits your entire computer can have, with the hardware i said, the rest it needs it to run the program to set this large integer).
so now lets see using ALL that memory what is the max integer you can hold from 0 clearly.
and it is quite easy it is just 2^8821862825984
yes you can have ANY number from 0 to that amount.
which is equivalent on decimal (more or less) to 10^3^882186282599 (rounding up)
which in term is 10^2646558847797
so the MAX number from 0 as an integer you can hold with the ENTIRE memory+drive of that computer is no more than 10^2646558847797
clearly is a very big number but it is not even near from infinite than 0.
even so if you consider things in scale and we compare that the minimal scale is a neutrino
an electroni is in the scale of 10^−18 (of meter) and the neutrino is said to be millons of time smaller, so lets assume 10^-27 (not saying this values are ok).
now lets see the size of the observable universe.
8.8 × 10^26, so no more than 10^27
why i am calculating this because, if we say our “unit” of measure is a neutrino.
means the longest number we will ever need to measure ANYTHING on the observable universe, should be about 10^27/10^-27 (wonder why this values give the same exponent) and that is 10^54
so you can hold a number a lot of times bigger (and a lot really) than the size of the observable universe measured in neutrino, why you will need such a big number for?
and clearly you cannot do anything with it as, you do not have enough space to store a different one.
so as you see is not possible