Wednesday, June 17, 2015

Special properties of number 17 (Today’s Date)

1. 17 is a prime number.
2. 17 is the sum of the first 4 prime numbers: 17 = 2 + 3 + 5 + 7
3. 17 is a palindromic number in binary system (10001).
4. 17 is a Leyland number, 17 = 3^2 + 2^3(In number theory, a Leyland number is a number of the form x^y + y^x where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are
8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124…
5. 17 is the 7th prime number and the only prime of the form p^q + q^p, where p and q are prime: 17 = 2^3 + 3^2
6. 17 is the lowest possible number of givens for a Sudoku puzzle with a unique solution (this was proven in 2012 by Gary McGuire, Bastian Tugemann, and Gilles Civario).
7. No odd Fibonacci Number is divisible by 17.
8. abcdefghabcdefgh is divisible by 17 (replace each letter with a digit. E.g. 1234567812345678). The reason is that any number of that form is a multiple of 100,000,001 - which is divisible by 17.
9. A regular 17-gon can be constructed by using rule and compasses only.
10. There are exactly 17 ways to express 17 as the sum of 1 or more primes i.e. 17 is the only integer which is equal to the number of prime partitions of itself.

11. The famous problem of the 17 camels: a sheik has 3 children and owns 17 camels. His will stipulates that the eldest is to receive half his property; the second son is to receive the third of his property; and the third one, the ninth of his property. On his death, how would the sons share out the inheritance? Solution: They borrow a camel, share out, and give back the camel: (17+1)/2 + (17+1)/3 + (17+1)/9 = 17 camels.

12. The Chemical Element Chlorine has an atomic number of 17.
13. There are 17 muscles in the Human tongue.
14. A day on Uranus lasts for 17 hours.

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