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The largest number that has a commonly-known specific name is a "googleplex", which is a 1 followed by a googol zeros, where a "googol" is 10100 (a 1 followed by 100 zeros).

Obviously the number could be larger if instead of 1 we substitute 1 googol for 1 giving us a googolgoogol or a 1 followed by 100 zeros multiplied by itself 1x10100 times.

Customarily the largest number (by definition) is infinity (usually represented as )

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