Prime Numbers Are Not Random Proves Stanford Mathematicians

On March 11, 2016 mathematicians from Stanford University proved that prime numbers do not behave randomly as previously thought. You should read the article in Scientific American to learn more


Prime numbers are those numbers divisible only by 1 and themselves, not including 1.


So, the first prime number is 2 = 1 x 2

the second prime number is 3 = 1 x 3

the first composite number is 4 = 1 x 4 and  = 2 x 2


Mathematicians Kannan Soundararajan and Robert Oliver looked at the first billion prime numbers and their last digits. Other than 2 and 5, all prime numbers end in 1, 3, 7, or 9. Since prime numbers were thought to be random, they predicted that a prime number would have an equal chance of being followed by a prime ending in 1, 3, 7, or 9. So a prime number ending in 1 would be followed by a prime number ending in one 25% of the time, followed by a prime number ending in 3 25% of the time, followed by a prime number ending in 7 25% of the time, and followed by a prime number ending in 9 25% of the time. They predicted the same thing for prime numbers ending in 3, 7, and 9 but this was not the case. The result of their research was the exact opposite. 


If prime numbers are random, there should be an equal number of primes ending in 1, 3, 7, or 9 following each prime no matter what the end number. Primes ending in 1 were less likely to be followed by another prime ending in 1. That shouldn't happen if they are random. 


The attached pdfs provide the children with the first 1000 prime numbers separated in groups of 100s and worksheets for them to tally the end numbers of primes that follow primes with a specific end number. They will see the non-randomness of primes for their own eyes. First try the first 100 primes, and if time, the next 100 primes or more.



First_1000_Primes_by_100s.pdf197.53 KB
Prime_End_Number_Patterns.pdf322.96 KB