2017
 Details

Published on 2017. március 14. kedd, 11:48
A bit late, but this note is about the number 2017 of this year.
Before the list comes observe that 2017 is prime number.
 $[2017\cdot \pi+0.5]$ is a prime;
 $[2017\cdot e+0.5]$ is a prime.
 The sum of all odd primes up to 2017 is a prime number
 The sum of the cube of gap of primes up to 2017 is a prime number. That is $(32)^3 + (53)^3 + (75)^3 + (117)^3 + \dots + (20172011)^3$ is a prime number;
 The prime number before 2017 is $2017+(2017)$, and the prime after 2017 is $2017+(2+0+1+7)$;
 27017, 20717, 20177, 20177 are all primes.
 2017 is still a prime number if read as an octal;
 2017 can be written as a sum of three cubes of primes;
 2017 can be written as a sum of cubes of five distinct integers;
 2017 can be written as $x^2+y^2$, $x^2+2y^2$, $x^2+3y^2$, $x^2+4y^2 x^2+6y^2$, $x^2+7y^2$, $x^2+8y^2$, $x^2+9y^2$, where $x,y$ are positive integers;
 20170123456789 is also a prime
 the 2017th prime number is 17539 and 201717539 is also a prime;
 $(2017+1)/2$ and $(2017+2)/3$ are also prime numbers;
 2017 is the least integer the first ten digits of the decimal expansion of the cubic root of which contains all different digits 09;
 $2^{11}2017$ is just the $11$th prime.
Source:
2017 is not just another prime number
To verify these facts one only has to see the
SageMath
worksheet
by William Stein.