A significant discovery has shook the mathematical
world: Prime numbers are not actually random. Apart from two and five, every single
prime number finishes with either one, three, seven, or nine. If there was no arrangement,
then the chance of having two consecutive primes ending with either number
should constantly be 25 percent, but that's not always the case. Kannan
Soundararajan and Robert Lemke Oliver of Stanford University in California have
revealed that in the first 100 million prime numbers, a prime ending in one is
followed by another ending in one 18.5 percent of the time, by three 29.7
percent, by seven 30 percent, and by nine 21.8 percent. In other words, the
prime's final number is most likely not to be repeated.
A very similar pattern is seen for primes ending
in 3, 7, and 9, as the researchers show in a paper available online. Prime
numbers are predetermined by the laws of mathematics, so there’s nothing to
suggest that they should care what their neighbors look like, but somehow they
do. “It was very weird,” Soundararajan told New Scientist. “It’s like some
painting you are very familiar with, and then suddenly you realize there is a
figure in the painting you’ve never seen before.”
Prime numbers are numbers that are divisible only
by themselves and one. They are of the uttermost importance in math because
they are the building blocks of larger numbers, and they are the cornerstone of
encryption in modern communication. Primes are not only present in our base-10
numbering system but also in other bases, and the phenomenon Soundararajan and
Lemke Oliver have observed is found there as well.
Understanding where the phenomenon comes from
could help us crack the mystery of prime numbers, namely that we don't have a
formula to predict them. Their explanation is based on the k-tuple conjecture,
a mathematical supposition for the apparent grouping of prime numbers,
indicating that at least some of them can be grouped in patterns.
“Our initial thought was if there was an
explanation to be found, we have to find it using the k-tuple conjecture,” says
Soundararajan. “We felt that we would be able to understand it, but it was a
real puzzle to figure out.”
The findings won’t help us solve any of the most
important mysteries of prime numbers just yet, but they are telling us that
something very interesting is going on.
