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68 (număr)

Pentru anul 68 al erei noastre, vedeți 68.
← 67 68 69 →
Cardinalșaizeci și opt
Ordinal68-lea
șaizeci și optulea
Factorizare22· 17
Divizori1, 2, 4, 17, 34, 68
Cifre romaneLXVIII
Binar10001002
Ternar21123
Cuaternar10104
Cvinariu2335
Senar1526
Octal1048
Duodecimal5812
Hexazecimal4416
Vigesimal3820
Baza 361W36
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68 (șaizeci și opt) este numărul natural care urmează după 67 și este urmat de 69.

În matematică

  • 68 este un număr compus și are divizorii: 1, 2, 4, 17, 34, 68.
  • Este un număr nontotient.[1][2]
  • Este un număr Perrin.[3]
  • Este cel mai mare număr cunoscut care poate fi scris ca suma a două prime în exact două moduri diferite: 68 = 7 + 61 = 31 + 37.[4] Toate numerele mai mari care au fost studiate pot fi scrise ca suma a trei sau mai multe perechi de prime. Această conjectură este strâns legată de Conjectura lui Goldbach și este încă nedemonstrată.[5]
  • Deoarece poate fi scris factorizat ca 68 = 22 × (222 + 1), se poate construi cu rigla și compasul un poligon regulat cu 68 de laturi.[6]
  • În baza 10 (sub forma 68), este cel mai mare număr format din două cifre care apare pentru prima dată în cifrele zecimale ale numărului pi.[7]
  • Este un număr fericit, adică prin însumarea repetată a pătratelor cifrelor pe care le conține se ajunge la 1:[8][9]
68 → 62 + 82 = 100 → 12 + 02 + 02 = 1.
  • În baza de numerație octală, 6810 se notează 1048, în timp ce 10410 este 6816 în sistemul hexadecimal. Această proprietate se aplică tuturor numerelor de la 64 la 69.

În știință

Astronomie

În alte domenii

Șaizeci și opt se poate referi la:

Note

  1. ^ Coman, Enciclopedia…, p. 54
  2. ^ Șirul A005277 la Enciclopedia electronică a șirurilor de numere întregi (OEIS)
  3. ^ Șirul A001608 la Enciclopedia electronică a șirurilor de numere întregi (OEIS)
  4. ^ Sixty-Eight Arhivat în , la Wayback Machine. Accesat 9 decembrie 20202
  5. ^ „Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways (A000954)”. Enciclopedia electronică a șirurilor de numere întregi. 
  6. ^ „Numbers of edges of polygons constructible with ruler and compass (A003401)”. Enciclopedia electronică a șirurilor de numere întregi. 
  7. ^ Șirul A032510 la Enciclopedia electronică a șirurilor de numere întregi (OEIS)
  8. ^ Coman, Enciclopedia…, p. 34
  9. ^ Șirul A007770 la Enciclopedia electronică a șirurilor de numere întregi (OEIS)
  10. ^ Meija, Juris; Coplen, Tyler B.; Berglund, Michael; Brand, Willi A.; Bièvre, Paul De; Gröning, Manfred; Holden, Norman E.; Irrgeher, Johanna; Loss, Robert D.; Walczyk, Thomas; Prohaska, Thomas (). „Atomic weights of the elements 2013 (IUPAC Technical Report)”. Pure and Applied Chemistry (în engleză). 88 (3): 344–344. doi:10.1515/pac-2015-0305. ISSN 0033-4545. 
  11. ^ en „Telephone and Internet Country Codes in 10 Languages”. LincMad. 

Bibliografie

  • Marius Coman, Enciclopedia matematică a claselor de numere întregi, Columbus, Ohio: Education Publishing, 2013, ISBN: 978-1-59973-243-4

Legături externe

Materiale media legate de 68 la Wikimedia Commons

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