prime pyramid

A prime pyramid is a triangular arrangement of numbers in which each row $n$ has the integers from 1 to $n$ but in an order such that the sum of any two consecutive terms in a row is a prime number. The first number must be 1, and the last number is usually required to be $n$, all the numbers in between are in whatever order fulfills the requirement for prime sums. Unlike other triangular arrangements of numbers like Pascal’s triangle or Losanitsch’s triangle, the contents of a given row are not determined by those of the previous row. However, if it happens that one has calculated row $n-1$ and that $2n-1$ is a prime number, one could just copy the previous row and add $n$ at the end. Here is a prime pyramid reckoned that way:

Often row 1 just contains an asterisk or some other non-numerical symbol, but since the idea of adding two numbers in row 1 is moot, here row 1 just contains a 1 per analogy to the following rows and to other triangular arrangements of numbers.

Title	prime pyramid
Canonical name	PrimePyramid
Date of creation	2013-03-22 17:00:03
Last modified on	2013-03-22 17:00:03
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A41