## 11/13/2015

### Primitives - Prime factors

**v.2.4 Primitives, by Alec McEachran**

**Primitives **

Primitives represents numbers in terms of their prime factors, offering unusual insights into their structure. Numbers are presented as nested sets of small black dots. Three is presented as a blue circle enclosing three dots; a ‘set of three’. Six is presented as a set of three sets of two dots, or as a set of two sets of three dots.

When a number has many different prime factors, such as 30 = 3·2·5, the factors can be rearranged to offer different images of the same number.

Primitives is tailored for classroom use and perfectly suited for use with an interactive whiteboard.

Grid primitives combines the ‘Primitive’ visualisations with the Sieve of Eratosthenes. The Primitive visualisations of the first 42 numbers are arranged into a six column grid that is often used when finding prime numbers by elimination using the Sieve of Eratosthenes algorithm.

The visualisations are reduced in size to conform to the size of the grid, and behind them the pattern of multiples of 2, 3, 5 and 7 are each highlighted in the colour corresponding to the respective prime number. The prime numbers are particularly highlighted by an 11-pointed star behind each one.

The choice of a six column structure may lead students to question why after the bottom row, primes only appear in the first and fifth columns, or to put it mathematically, why all primes other than 2 and 3 are in the pattern 6n±1, where n is a positive integer, but that not all such numbers are prime. In each column, 25 and 35 disrupt the apparent pattern of primes. Studying this may lead students to futher questions about prime numbers for further study.

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