Number reference
17 explained.
17: seventeen, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- seventeen
- Classification
- prime
- Factors
- 1, 17
- Prime factorization
- 17
- Square root
- 4.123106
- Cube root
- 2.571282
- Binary
- 10001
- Octal
- 21
- Hexadecimal
- 11
- Roman numeral
- XVII
- Digit sum
- 8
- Digital root
- 8
What makes 17 notable
- Prime. 17 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
17 in everyday use
Seventeen is the atomic number of chlorine and the number of syllables in a haiku, split five-seven-five. Some North American periodical cicadas emerge only every seventeen years, a prime interval thought to make it harder for predators to synchronise with them. In Italy 17 is treated as unlucky rather than 13, because the Roman numeral XVII can be rearranged to VIXI, "I have lived". Seventeen magazine, founded in 1944, named a whole demographic.
Seventeen is the seventh prime and a Fermat prime, 2⁴ + 1, which allowed the nineteen-year-old Gauss to prove in 1796 that a regular seventeen-sided polygon can be drawn with compass and straightedge — a result he wanted engraved on his tombstone. It is the sum of the first four primes, 2 + 3 + 5 + 7. In 2012 a computer search confirmed that seventeen is the smallest number of clues a sudoku can have and still possess a unique solution.
Nearby numbers
How to read this page
Because 17 is prime, the factor list stops at 1 and 17 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 17 in its prime factorisation inherits it from here.
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