27424 is a product of a power of 2 and a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 32^2 + 100^2.

27424 is a member of OEIS A192087: potential magic constants of a 10 X 10 magic square composed of consecutive primes. The initial members are:

2862, 3092, 3500, 4222, 4780, 5608, 7124, 10126, 10198, 11212, 11426, 12140, 12212, 12284, 12356, 12428, 12714, 12854, 12924, 15270, 16252, 16476, 18594, 18672, 18750, 18828, 19214, 20764, 21150, 23752, 24214, 24598, 24828, 27180, 27342, 27424, 27916, 28666, 29406, 29568

27424 forms part of a trio with 27423 and 27425. See blog post Divisibility Sequences.

27424 is an untouchable and iban number.

27424 can be expressed as a digit equation as follows:

2 ^ (7 - 4) = 2 * 4

27424 stabilises after about 235 generations of Conway's Game of Life to a single glider, a single traffic light oscillator and an assortment of still life shapes.