193 (number)

← 192 193 194 →
← 190 191 192 193 194 195 196 197 198 199 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred ninety-three
Ordinal	193rd; (one hundred ninety-third)
Factorization	prime
Prime	44th
Divisors	1, 193
Greek numeral	ΡϞΓ´
Roman numeral	CXCIII
Binary	110000012
Ternary	210113
Senary	5216
Octal	3018
Duodecimal	14112
Hexadecimal	C116

193 (one hundred [and] ninety-three) is the natural number following 192 and preceding 194.

In mathematics

193 is a prime number, and a Pierpont prime, implying that a 193-gon can be constructed using a compass, straightedge, and angle trisector.^[1] It is the only odd prime $p$ known for which 2 is not a primitive root of $4p^{2}+1$ .^[2] It is the number of compositions of 14 into distinct parts.^[3] It is also part of the prime quadruplet (191, 193, 197, 199).

References

^ Sloane, N. J. A. (ed.). "Sequence A005109 (Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ E. Friedman, "What's Special About This Number Archived 2018-02-23 at the Wayback Machine" Accessed 2 January 2006 and again 15 August 2007.
^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.

[1] Sloane, N. J. A. (ed.). "Sequence A005109 (Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[2] E. Friedman, "What's Special About This Number Archived 2018-02-23 at the Wayback Machine" Accessed 2 January 2006 and again 15 August 2007.

[3] Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.

[1]

[2]

[3]

In mathematics

See also

References