A prime pyramid is a triangular arrangement of numbers in which each row has the integers from 1 to 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 , 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 and that is a prime number, one could just copy the previous row and add 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.
- 1 R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: C1