323 (number)

323 (three hundred [and] twenty-three) is the natural number following 322 and preceding 324.

← 322 323 324 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	three hundred twenty three
Ordinal	323d (three hundred twenty-third)
Factorization	17 × 19
Divisors	1, 17, 19, 323
Greek numeral	ΤΚΓ´
Roman numeral	CCCXXIII
Binary	1010000112
Ternary	1022223
Senary	12556
Octal	5038
Duodecimal	22B12
Hexadecimal	14316

In mathematics

• 323 is a semiprime, and the product of two consecutive prime numbers (17 × 19).
• 323 is the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53) and the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47)
• 323 is the eighth Motzkin number, ${\displaystyle M_{8}}$, meaning there are 323 ways to draw non-intersecting chords between eight points on a circle. ^[1]
• 323 is the first Lucas pseudoprime with parameters (P, Q) defined by Selfridge's method. ^{[2] [3]}
• 323 is the first Fibonacci pseudoprime (Lucas pseudoprime with P = 1 and Q = -1). ^[4]

References

1. Sloane, N. J. A. (ed.). "SequenceA001006(Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA217120(Lucas pseudoprimes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Baillie, Robert; Wagstaff, Samuel S. (1980). "Lucas pseudoprimes". Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. ISSN   0025-5718.
4. Sloane, N. J. A. (ed.). "SequenceA081264(Odd Fibonacci pseudoprimes: odd composite numbers k such that either (1) k divides Fibonacci(k-1) if k == +-1 (mod 5) or (2) k divides Fibonacci(k+1) if k == +-2 (mod 5).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.