New discovery by a pair of mathematicians puts to question the previously held notion that prime numbers are random.
Remember how the early scientists visited Africa and some other parts of the world and ‘discovered’ naturally existing things like mountains, rivers and other places, something close to that has happened again.
This time round, though, it is not in either of the above areas.
Two mathematicians have uncovered a simple, yet previously unnoticed quality of prime numbers. So, apparently, the prime number sequence isn’t as random as earlier thought.
Prime numbers as you will hopefully recall from your early formation years in primary school, are whole numbers that are only divisible by 1 and themselves. They include 2,3,5,7,11and so on.
In a paper by researchers studying the primes at Stanford University, the prime numbers, it seems, are trying very hard not to be similar.
Kannan Soundararajan and Robert Lemke Oliver, present new evidence that prime numbers ward off other would-be primes that end in the same digits.
From the initial set (numbers less than ten) 2 and 5 were part of the primes, but when they appear next as in 12, 15, 22, 25, they are no longer primes as they are divisible by other numbers other than 1, and themselves. Thus, all other prime numbers can only end in one of four digits: 1, 3, 7, or 9.
Armed with the fact that prime numbers appear to be random, or so it was thought, the pair of mathematicians decided to test this ‘randomness’ assumption on primes. They discovered a strange phenomenon entrenched among the integers that prove there’s certainly an un-random pattern at play.
If they were truly random as earlier thought, primes ending in 1 would be followed by a prime ending in 1 about 25% of the time. However, the mathematicians found this order occurred in only 18.5 percent of cases.
It was discovered that a prime number was followed by a prime ending in 3 or 7 was about 30 percent of the time and about 22 percent for 9.
Although their study is yet to checked and approved by experts before it can be officially published in a peer-reviewed journal, the study has received a lot of attention from other mathematicians.
Speaking to Nature, Soundararajan said: “Every single person we’ve told this ends up writing their own computer program to check it for themselves.”
This new discovery has astounded mathematicians with some terming it as a “crazy” finding.
“I can’t believe anyone in the world would have guessed this,” Andrew Granville at the University of Montreal said. Even after having seen Lemke Oliver and Soundararajan’s analysis of their phenomenon, he said, “it still seems like a strange thing.”
As fascinating as the new study appears, George Dvorsky in an article argues that it likely won’t help with other prime-related challenges including the twin-prime conjecture or the Riemann hypothesis. He adds that the new discovery may not have any practical implications or use to math and number theory.
Now that the study is out for public scrutiny, let us wait and see what new discoveries will be made concerning primes or improvements that will be included in the ‘new’ but already existing discovery.
Image credit: Getty
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