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This page contains Roman numeral-related numbers.

List of Roman numeral-related numbers

  • 201 is an odd lucky number. Its Roman numeral (CCI) is used in Googocci.
    • Its prime factorization is 3 × 67.
  • 209 is a natural number following 208 and preceding 210. Its prime factorization is 11 × 19.
  • 299 is an odd unlucky number. Its unofficial Roman numeral (CCIC) is used in Googoccic. The official Roman numeral is CCXCIX.
  • 990 is the 44th triangular number. Its unofficial Roman numeral (XM) is used in Googoxem.[3] Here, an “e” has been inserted for euphonical reasons. The official Roman numeral is CMXC.
    • Its prime factorization is 2 × 32 × 5 × 11.
  • 1,002 is the 22nd partition number. Its Roman numeral (MII) is used in Fibonamij.[4] Here, the second “i” has been spelled “j” for euphonical reasons.
    • Its prime factorization is 2 × 3 × 167.
  • 1,099 is a natural number following 1,098 and preceding 1,100. Its prime factorization is 7 × 157.
    • Its unofficial Roman numeral (MIC) is used in googocciplemic. The official Roman numeral is MXCIX.
    • Sbiis Saibian gives unique names for the first 1099 counting numbers.[5]
  • 1,444 is the smallest positive number with pandigital Roman numeral, namely MCDXLIV.
  • 1,666 is the largest number with pandigital Roman numeral without redundant digits, namely MDCLXVI.
  • The 3,999 undisputed Roman numerals use a total of 2,400 characters with negative value.
  • 3,888 is the number with the longest undisputed Roman numeral, namely MMMDCCCLXXXVIII.
  • 3,999 is the largest number with an undisputed Roman numeral, namely MMMCMXCIX.
    • Its prime factorization is 3 × 31 × 43.
  • In the 3,999 undisputed Roman numerals, the characters "C" and "X" are used 6,000 times each.
  • 7,473 is the largest number whose Roman numeral (namely, MMMMMMMCDLXXIII (or \(\bar{\text{V}} \text{MMCDLXXIII}\) )) has been used in literature (namely, by Voltaire).[6]
  • The 3,999 undisputed Roman numerals use a total of 30,000 characters.
  • The 7,473 Roman numerals used in literature use a total of 68,934 characters.

Approximations of these numbers

For 30,000:

Notation Lower bound Upper bound
Scientific notation \(3\times10^4\)
Arrow notation \(31\uparrow3\) \(2\uparrow15\)
Steinhaus-Moser Notation 5[3] 6[3]
Copy notation 2[5] 3[5]
Chained arrow notation \(31\rightarrow3\) \(2\rightarrow15\)
Taro's multivariable Ackermann function A(3,12) A(3,13)
Pound-Star Notation #*(21)*3 #*(22)*3
PlantStar's Debut Notation [2] [3]
BEAF {31,3} {2,15}
Hyper-E notation 3E4
Bashicu matrix system (0)[173] (0)[174]
Hyperfactorial array notation 7! 8!
Bird's array notation {31,3} {2,15}
Strong array notation s(31,3) s(2,15)
Fast-growing hierarchy \(f_{2}(11)\) \(f_{2}(12)\)
Hardy hierarchy \(H_{\omega^2}(11)\) \(H_{\omega^2}(12)\)
Slow-growing hierarchy \(g_{\omega^4\times 3}(10)\)

Sources

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