561 (number)
| ||||
|---|---|---|---|---|
| Cardinal | five hundred sixty-one | |||
| Ordinal | 561st (five hundred sixty-first) | |||
| Factorization | 3 × 11 × 17 | |||
| Divisors | 1, 3, 11, 17, 33, 51, 187, 561 | |||
| Greek numeral | ΦΞΑ´ | |||
| Roman numeral | DLXI, dlxi | |||
| Binary | 10001100012 | |||
| Ternary | 2022103 | |||
| Senary | 23336 | |||
| Octal | 10618 | |||
| Duodecimal | 3A912 | |||
| Hexadecimal | 23116 | |||
561 (five hundred [and] sixty-one) is the natural number following 560 and preceding 562.[1]
In mathematics
[edit]561 is a Fermat pseudoprime to base 2,[2] a centered icosahedral number,[3] the 33rd triangular number, and the 17th hexagonal number. It is a composite number, with the divisors being 1, 3, 11, 17, 33, 51, 187, and 561. Its prime factorization is 3 * 11 * 17.[1]
Carmichael number
[edit]561 is most notable for being the first, and smallest Carmichael number.[4][5][6] 561 is considered one since it satisfies the Korselt’s Criterion. A number satisfies the criterion if the number is an odd number, consists of a product of distinct primes, and satisfies (p − 1) | (n − 1) for every prime p dividing the number.[7] It was first discovered by Václav Šimerka along with six more other numbers.[a][6]
Notes
[edit]- ↑ The seven Carmichael numbers that Václav Šimerka discovered are 561, 1105, 1729, 2465, 2821, 6601, and 8911.[8]
References
[edit]- 1 2 Vanovschi, Vitalii. "Properties of the number 561". www.numberempire.com. Retrieved 2026-08-15.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-08-15.
- ↑ Sloane, N. J. A. (ed.). "Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-08-15.
- ↑ Friedman, Erich. "What's Special About This Number?". Retrieved 2026-08-09.
- ↑ Koninck, J. M. de (2009). Those fascinating numbers. Internet Archive. Providence, R.I. : American Mathematical Society. p. 93. ISBN 978-0-8218-4807-4.
- 1 2 Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-08-15.
- ↑ Riemer, Emily (2016-05-03). Pseudoprimes and Carmichael Numbers (PDF). Retrieved 2026-08-15.
- ↑ Webster, Jonathan (2025). Carmichael Numbers: A Computational Perspective. UNIVERSITY OF CALGARY. Retrieved 2026-08-15.
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