17 (number)
17 (seventeen) is the natural number following 16 and preceding 18.
| Template:Numbers 10s | |
| Cardinal | 17 seventeen |
| Ordinal | 17th seventeenth |
| Factorization | prime |
| Divisors | 1, 17 |
| Roman numeral | XVII |
| Binary | 10001 |
| Hexadecimal | 11 |
In mathematics
Seventeen is the 7th smallest prime number, and is a Fermat prime. The next prime is nineteen, with which it comprises a twin prime. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071.
There are exactly seventeen two-dimensional space (plane symmetry) groups. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.
Like 41, the number 17 is a prime that yields primes in the polynomial n2 + n + p, for all positive n < p - 1.
Consider a sequence of real numbers between 0 and 1 such that the first two lie in different halves of this interval, the first three in different thirds, and so forth. The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).
Since 17 is a Fermat prime, heptadecagons can be drawn with compass and ruler. This was proved by Karl Friedrich Gauss.
In Science
- The atomic number of chlorine.
- The Brodmann area defining the primary visual processing area of mammallian brains.
In human affairs: Age 17
- In the United States, the age at which one may donate blood and join the military voluntarily.
- In the United States, the age at which one may view R-rated movies without a parent's accompaniment according to MPAA standards.
In other fields
Seventeen is:
- Described at MIT as `the least random number', according to hacker's lore.
- The number of guns in a gun salute to U.S. Army, Air Force and Marine Corps Generals, and Navy and Coast Guard Admirals.
- A swear word in Swedish. The origin is debated, and is commonly used as "sjutton också!" ("seventeen, too!"). It is of course also used for the number 17.
- The maximum number of strokes of a Chinese radical.
- The number of syllables in a haiku.
- In the Nordic countries the seventeenth day of the year is considered the heart and/or the back of winter.
- The designation of United States Interstate 17, a freeway in Arizona.
- The title of At Seventeen, a famous song by Janis Ian.
- The title of Seventeen, a magazine.
- The number of trees Dostoevsky could see out of the window of his cell while he was in prison.
- The number of little porcelain pigs seized by police from the window ledge of Nancy Bennett of Leicester, Britain, on May 25, 1998; since she lived on the street with a big mosque, worshippers there had complained.
- The number of special significance to the Yellow Pig Day.
- Historical years: 17 A.D., 17 B.C., or 1917
- A number of great significance to horror-core band Insane Clown Posse
- The number of surat al-Isra in the Qur'an
References
Berlekamp, E. R. and Graham, R. L., Irregularities in the distributions of finite sequences, J. Number Theory 2 (1970), 152–161.