Thursday, 28 March 2013

THURSDAY, 28 MARCH 2013

Today is the $87^{th}$ day of the year.

$87 = 3 \times 29$

$2^2 + 3^2 + 5^2 + 7^2 = 4 + 9 + 25 + 49 = 87$ which means that $87$ is the sum of the first four prime numbers squared.

$87$ is a member of the following two primitive Pythagorean triples:
$(87, 416, 425)$
$(87, 3785, 3785)$

According to the Prime Curios website $87^2 + 3^2 + 29^2 = 8,719$ and $87^2 - 3^2 - 29^2 = 6,719$  are both prime.
According to OEIS, $6 \times 87 +1 = 523$ and $6 \times 87 - 1 = 521$ are both primes, see A002822. In fact $521$ and$523$ are twin primes because they differ by two, see A001359 and A006512.