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323 (number)

From Wikipedia, the free encyclopedia

323 (three hundred [and] twenty-three) is thenatural number following322 and preceding324.

Natural number
← 322323 324 →
Cardinalthree hundred twenty three
Ordinal323d(three hundred twenty-third)
Factorization17 × 19
Divisors1, 17, 19, 323
Greek numeralΤΚΓ´
Roman numeralCCCXXIII
Binary1010000112
Ternary1022223
Senary12556
Octal5038
Duodecimal22B12
Hexadecimal14316

In mathematics

[edit]
  • 323 is asemiprime, 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 eighthMotzkin number,M8{\displaystyle M_{8}}, meaning there are 323 ways to draw non-intersecting chords between eight points on a circle.[1]
  • 323 is the firstLucas pseudoprime with parameters (P, Q) defined bySelfridge's method.[2][3]
  • 323 is the firstFibonacci pseudoprime (Lucas pseudoprime with P = 1 and Q = -1).[4]

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A001006 (Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Sloane, N. J. A. (ed.)."Sequence A217120 (Lucas pseudoprimes.)".TheOn-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.)."Sequence A081264 (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).)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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