The largest Roman numeral which will fit in a Tweet is an "M" plus 279 overbars, which expresses exactly 10^840, as I shall now demonstrate
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M̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
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This is actually significantly larger than the largest Arabic numeral which will fit in a Tweet, which is 280 "9" digits in a row, expressing 10^280 - 1
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However, plenty of Roman numerals for smaller values, such as 10^840 - 1, won't fit at all
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The smallest number whose Roman numeral won't fit in a Tweet is, I believe, 78,888,888,888,887,888,888. Everything up to 78,888,888,888,887,888,887 fits (see next Tweet)
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L̅̅̅̅̅̅X̅̅̅̅̅̅X̅̅̅̅̅̅V̅̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅D̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅L̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅V̅̅̅̅̅M̅̅̅̅M̅̅̅̅M̅̅̅̅D̅̅̅̅C̅̅̅̅C̅̅̅̅C̅̅̅̅L̅̅̅̅X̅̅̅̅X̅̅̅̅X̅̅̅̅V̅̅̅̅M̅̅̅M̅̅̅M̅̅̅D̅̅̅C̅̅̅C̅̅̅C̅̅̅L̅̅̅X̅̅̅X̅̅̅X̅̅̅V̅̅̅M̅̅M̅̅M̅̅D̅̅C̅̅C̅̅C̅̅L̅̅X̅̅X̅̅X̅̅V̅̅M̅M̅D̅C̅C̅C̅L̅X̅X̅X̅V̅MMMDCCCLXXXVII
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Here is some handy code for handling very large Roman numeralshttps://github.com/qntm/big-roman
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Ah! I think my earlier calculation was wrong. The smallest number which has a 281-character Roman numeral is actually 38,888,888,888,887,888,888, not 78,888,888,888,887,888,888. So the answer to the question is 38,888,888,888,887,888,887 (see next Tweet):
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X̅̅̅̅̅̅X̅̅̅̅̅̅X̅̅̅̅̅̅V̅̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅M̅̅̅̅̅D̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅C̅̅̅̅̅L̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅X̅̅̅̅̅V̅̅̅̅̅M̅̅̅̅M̅̅̅̅M̅̅̅̅D̅̅̅̅C̅̅̅̅C̅̅̅̅C̅̅̅̅L̅̅̅̅X̅̅̅̅X̅̅̅̅X̅̅̅̅V̅̅̅̅M̅̅̅M̅̅̅M̅̅̅D̅̅̅C̅̅̅C̅̅̅C̅̅̅L̅̅̅X̅̅̅X̅̅̅X̅̅̅V̅̅̅M̅̅M̅̅M̅̅D̅̅C̅̅C̅̅C̅̅L̅̅X̅̅X̅̅X̅̅V̅̅M̅M̅D̅C̅C̅C̅L̅X̅X̅X̅V̅MMMDCCCLXXXVII
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Here is the code I used to figure this out:https://gist.github.com/qntm/e0daf631d6983d97647ebae841f6aaf1 …
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