There is no common criterion for a number being "large". In practice, numbers that are larger than any considered for practical purposes by non-specialists are clearly large. The intent of this category is to use large in that sense.

The (annual) GNP of the US is trillions of dollars, the total of GNPs is tens of trillions of dollars, and the GNP of Japan is trillions of dollars and hundreds of trillions of yen. In English, a quadrillion and anything larger is undoubtedly a large integer. (It may be that the Japanese-language press discusses the quadrillions of yen in the "world gross product"; if, so it can be argued that the Japanese-language equivalent of "large integer" requires something larger than a quadrillion.)

This category is intended to embrace both:

• the integers, larger than 10¹², used as approximations of really large numbers needed in chemistry, physics, astronomy, perhaps geology, and especially number theory, and
• various sequences of integers, often starting with small or moderate integers, that are used for dealing with such integers.