Árpád Kurusa
mathematician, associate professor
Department of Geometry
Bolyai Institute
Faculty of Science
University of Szeged


Árpád Kurusa

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2017

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 $(3-2)^3 + (5-3)^3 + (7-5)^3 + (11-7)^3 + \dots + (2017-2011)^3$ is a prime number;
  • The prime number before 2017 is $2017+(2-0-1-7)$, 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 0-9;
  • $2^{11}-2017$ 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.


© 2020 Árpád Kurusa