Okay - there are a few really large interesting numbers - at least - interesting in the sense that they were used in a proof and have been given names - so largest named numbers:
For a while, Skewe's number was the record holder 10^(10^(10^963)) - an early upper bound for another number now known to be somewhere between 10^14 and 10^317. Skewes' number, also Skewes' Numbers - Large Numbers
Then there's Graham's number, too large to notate using powers (even e.g. a power tower with as many numbers in it as there are particles in the known observable universe would be far too small).
Graham's number
Again - the interesting thing is - used in a proof as an upper bound - though the number it's an upper bound for is believed to be quite small. The lower bound is 13.
(see also These are the biggest numbers in the universe).
Those though are just upper bounce, not especially interesting in their own right, more interesting, because used in proofs of other things.
It's very easy to make far larger numbers than these. But these I think are good candidates for "meaningful" because used in famous proofs and because they have been given names.
As for numbers interesting in their own right, perhaps the Mersenne primes are largest?
These are the largest known prime numbers. See Mersenne prime
Largest currently I think is
M57885161
which has 17,425,170 digits in decimal notation
The Largest Known prime by Year: A Brief History
For a while, Skewe's number was the record holder 10^(10^(10^963)) - an early upper bound for another number now known to be somewhere between 10^14 and 10^317. Skewes' number, also Skewes' Numbers - Large Numbers
Then there's Graham's number, too large to notate using powers (even e.g. a power tower with as many numbers in it as there are particles in the known observable universe would be far too small).
Graham's number
Again - the interesting thing is - used in a proof as an upper bound - though the number it's an upper bound for is believed to be quite small. The lower bound is 13.
(see also These are the biggest numbers in the universe).
Those though are just upper bounce, not especially interesting in their own right, more interesting, because used in proofs of other things.
It's very easy to make far larger numbers than these. But these I think are good candidates for "meaningful" because used in famous proofs and because they have been given names.
As for numbers interesting in their own right, perhaps the Mersenne primes are largest?
These are the largest known prime numbers. See Mersenne prime
Largest currently I think is
M57885161
which has 17,425,170 digits in decimal notation
The Largest Known prime by Year: A Brief History
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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