1722 (number)
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| Cardinal | one thousand seven hundred twenty-two | |||
| Ordinal | 1722nd (one thousand seven hundred twenty-second) | |||
| Factorization | 2 × 3 × 7 × 41 | |||
| Divisors | 1, 2, 1722 | |||
| Greek numeral | ,ΑΨΚΒ´ | |||
| Roman numeral | MDCCXXII, mdccxxii | |||
| Binary | 110101110102 | |||
| Ternary | 21002103 | |||
| Senary | 115506 | |||
| Octal | 32728 | |||
| Duodecimal | BB612 | |||
| Hexadecimal | 6BA16 | |||
1722 (one thousand seven hundred [and] twenty-two) is the natural number following 1721 and preceding 1723.[1]
In mathematics
[edit]1722 is an even composite number that is a pronic number,[1] the product of exactly four distinct primes,[2] a 4-digit term in the continued fraction for pi,[3] and the least possible number of diagonals of simple convex polyhedron with 46 face.[4]
It is the number of 8-node graphs that are not determined by their spectrum,[5] and the number of strings of length 4 over a 7-letter alphabet that do not begin with a palindrome
1722 is most notable for being a Giuga number, specifically the third one,[6][7][8] since it is a composite number whose prime factors , 2, 3, 7, and 41, divides . This can be expressed as:
- .[9]
References
[edit]- 1 2 Vanovschi, Vitalii. "Properties of the number 1722". www.numberempire.com. Retrieved 2026-09-27.
- ↑ Sloane, N. J. A. (ed.). "Sequence A046386 (Products of exactly four distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Pi Continued Fraction". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-27.
- ↑ Sloane, N. J. A. (ed.). "Sequence A279019 (Least possible number of diagonals of simple convex polyhedron with n faces)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Determined by Spectrum". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-27.
- ↑ Koninck, Jean-Marie De (2009). Those Fascinating Numbers. American Mathematical Soc. p. 135. ISBN 978-0-8218-4807-4.
- ↑ Burns, Jamaris; Casey, Katherine; Gichimu, Duncan; Stinson, Kerrek (2017). "Giuga's Primality Conjecture for Number Fields". Rose-Hulman Undergraduate Mathematics Journal. 18 (1) 5. Retrieved 2026-09-27.
- 1 2 Weisstein, Eric W. "Giuga Number". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-27.
- ↑ Borwein, D.; Borwein, J. M.; Borwein, P. B.; Girgensohn, R. (1996). "Giuga's Conjecture on Primality" (PDF). American Mathematical Monthly. 103 (1): 40–50. doi:10.2307/2975213. JSTOR 2975213. Zbl 0860.11003. Archived from the original (PDF) on 2005-05-31. Retrieved 2026-09-27.
- ↑ Grau, José María; Oller-Marcén, Antonio M. (2011-03-17). "Generalizing Giuga's conjecture". arXiv.org. Retrieved 2026-09-27.
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