ARSE

Mon 23 May 2022

Centred Square Prime Days

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A centred square prime is a centred square number that is prime.

Unlike regular square numbers, which are never prime, quite a few of the centred square numbers are prime.

Centred square numbers are of the form
**n ^{2} + (n - 1)^{2}**

In elementary number theory, a centred square number is a centred figurate number that gives the number of dots in a square with a dot in the centre and all other dots surrounding the centre dot in successive square layers. That is, each centred square number equals the number of dots within a given city block distance of the centre dot on a regular square lattice. While centred square numbers, like figurate numbers in general, have few if any direct practical applications, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties.

The figures for the first four centred square numbers are shown below: