Facts about 2017

10 interesting facts about 2017

$2017$ is a prime $\big($ the $306^\text{th}\big).$

$2017 ^ 2 - 2017 + 1$ is also a prime.

$2017 = 1009^2 - 1008^2$ is the only way to express it as the difference of 2 squares.

$2017 = 44^2 + 9^2 = 37^2 + 2 \times 18^2 = 17^2 + 3 \times 24^2 = 9^2 + 4 \times 22^2$ . It cannot be written in the form $n^2 + 5 \times m^2$ .

$2017 = 11^3 + 7^3 + 7^3 = 15 ^3 - 3^3 - 11^3$ .

With 63 straight cuts on a circular pizza, each cut going through 2 points on the circumference, we get a maximum of 2017 pieces.

$\sqrt[3]{2017} = 12.63480759\ldots$ , and 2017 is the first positive integer the first 10 digits of whose cube root are the distinct digits 0 to 9.

$2017 = \frac{ 63 \times 64 } { 2} + 1$ is a central polygonal number.

There are 2017 ways to place the integers from 1 to 16 in a $4 \times 4$ grid so that each row, column, and both diagonals are increasing.

2 and 3 are quadratic residues mod 2017: $986^2 \equiv 2 \pmod{2017}$ and $258^2 \equiv 3 \pmod {2017}.$

Additional facts about 2017

$\phi(2017) = \phi (2016) + \phi (2015)$ , so 2017 is a Fibonacci number.
$2017, \frac{ 2017 + 1 } { 2} , \frac{ 2017 + 2 }{ 3}$ are all primes.
$2017$ in bases 31 and 32 are each a palindrome: $2017_{10} = 232_{31} = 1v1_{32}$ .
$2017= 29^2 + 6 \times 14^2 = 15^2 + 7 \times 16^2 = 37^2 + 8 \times 9^2 = 44^2 + 9 \times 3^2$ .
$2017 = 2^{11} - (11^{\text{th}} \text{ prime})$ .
$2017 =2^{11} - 2^5 + 1$ is a Solinas prime.
$2017\pi$ rounded to the nearest integer is a prime.
$2017e$ rounded to the nearest integer is a prime.
The sum of all primes till 2017 is a prime number.
The sum of the cubes of the differences between adjacent primes till 2017 is prime: i.e. $(3-2)^3 + (5-3)^3 + (7-5)^3 + \cdots$ is prime.
The prime before 2017 is $2017+(2-0-1-7)$ making it a sexy prime, and the prime after 2017 is $2017+(2+0+1+7)$ .
Inserting 7 between any two adjacent digits in 2017 results in a prime number: i.e. 20177, 20717, 27017 are all primes.
$2017_8$ is a prime number.
$2017 = 12^3 + 6^3 + 4^3 + 2^3 + 1^3$ .
20170123456789 is a prime number.
The 2017 $^\text{th}$ prime is 17359, and 201717359 is a prime.
$2017 = 44^2 + 3^4$ .
$\phi (2017) = 2 \times \phi(2018)$ . This is equivalent to the fact that both $2017$ and $\frac{2017+1}{2}$ are prime.
$2017 = 11111100001_2 = 100000000000_2 - 100000_2 +1.$
$2017 = 19\cdot 22 + 22\cdot 39 + 39\cdot 19$ . In a form of $2017 = xy+yz+zx$ , the minimum sum of positive integers $x+y+z = 19+22+39=80$ .