You seem to be defining "current languages" to mean "languages that have recently originated" rather than "languages that are currently used". But the languages that are heavily used currently - C, C++, C#, and Java - while they have bignum packages available, the integers within the languages themselves are not arbitrary-precision.
It isn't just recent languages that have this. One of the confusions of many folks starting to use most lisps is actually that they typically have very solid number libraries. Such that it is sometimes confusing to see 1/3 as the number you are holding, instead of an approximation.
