Problems & Puzzles: Puzzles

Puzzle 984. Happy new year 2020-II. 1. Emmanuel Vantieghem sent the following prime-arithmetic expression and curio for the integer 2020: 2020 = 17^2+19^2+23^2+29^2 2. Carlos Rivera produced the following expressions and curio: 2020 = = {[(2222-22)*22]/(2+2)+22-2}/(2+2+2) = {[(3333-33)*33]/(3+3)+33-3}/(3+3+3) = {[(5555-55)*55]/(5+5)+55-5}/(5+5+5) = {[(7777-77)*77]/(7+7)+77-7}/(7+7+7) Q. Send more interesting arithmetic curio expressions for 2020; if using only primes, the better.

---

Contributions came, along the week 4-10, 2019, from Fausto Morales, Emmanuel Vantieghem.

***

Fausto wrote:

Using only Fermat primes: 2020 = 65537 - (5!/3)^3 + 257 + 3^5 - 17

***

Emmnuel wrote:

As difference of two primes composed only of prime-digits: 2020 = 2357-337

***