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If we use an infinite basis for counting, each integer is represented by a single symbol. Thus, very large numbers are not different ones. There would be no quantitative difference between the number "23" and a number "first great".
The quest of large numbers, especially of large prime numbers, is motivated by the fact that the numbers are increasing in physical size as and when they list. We feel that a number is "great" because it is "long". But this length is only due to the use of a finite basis.
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