algorythm for representing a larg group of numbers

Hi,
i have no background in math, my problem is related to software development and is as follows:
i am looking for an algorythm that can take a large (3000) 4 digits numbers and represent them as one number not of about 30-40 digits then i need a way when given a number to determine if it was used when building the numbers list
in computer terms it would be somthing like(pseudo code)
function hashList(listOfNumbers)
{
ll = somemath(listOfNumbers)
}
function wasNumInList(num)
{
if num in ll return true
else return false
}
so hashList(1312,4445,4648,7676,...n)
would give :
ll = 43653244669232323 or somthing like this
and when
wasNumInList(1312) will return true
and will work with 43653244669232323

can it be done?

thanks

Shay.
.