It all started out of a conversation between students during a short break in one of my maths classes. The focus of their conversation was a poster I have in my classroom which lists all the prime numbers below 10,000. One was commenting to the other that there seemed to be more prime numbers between 1 and 100 (25 primes) than there are between 100 and 200 (21 primes), and so they started counting. Then they counted that there only 16 primes between 200 and 300. They started wondering whether this decline in the distribution of primes continued - but then counted that there were 17 primes between 400 and 500 (more than between 200 and 300). But they thought there was something to their first hunch when they went to the end of the list and counted that there were only 9 primes in the last group of hundred - between 9,900 and 10,000. I entered the conversation around this time and suggested they do something to investigate further - but more than just searching around the internet. So they decided to write a computer program which motivated me to write a program on my TI-Nspire to count the number of primes in intervals of my choosing between a pair of integers.

The image below left shows the scatter plot on my TI-Nspire created using the results from my program (shown right) which counted the number of primes between 1 to 10,000 in intervals of 100. That is, it counted the number of primes between 1 to 100, 100 to 200, 200 to 300, etc, up to between 9,900 to 10,000.