Mathematicians found a Strange & Unusual Pattern in the Final Digits of Prime Numbers

Prime Numbers Chart

Prime Numbers Chart

Mathematicians have found a strange and an unusual pattern in the final or last digits or numbers of prime numbers, which are not distributed as randomly as was once thought.


Below is the presently used theory of Prime Numbers and what it has changed to.

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. For example, 13 is prime, as only 1 and 13 divide it, whereas 14 is not, since it has the divisors 2 and 7 in addition to 1. Something new has changed as the Final digits tend to repel each other.

A lot of brilliant people have been involved in projects around the world to find the largest known prime number, since they are infinite. Just out of curiosity, you may want to know that the largest known prime number to date is a number with more than 17 million digits and can only be written with this notation:

2^57885161 – 1.

As we all know a prime number is divisible only by 1 and itself. For example, 11 can only be evenly divided by 1 or 11. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

The prime numbers seem to be randomly distributed, in that there is no discernible pattern to predict how often prime numbers occur.

However, Stanford University mathematicians Robert Lemke Oliver and Kannan Soundararajan have found a strange pattern in the final digits of prime numbers.

Prime numbers greater than 5 end in 1, 3, 7, or 9. Even numbers greater than 2 can be divided by 2, and thus numbers ending in 0, 2, 4, 6, and 8 are not prime. Numbers ending in 5 can be divided by 5 and so are also not prime.

If prime numbers were randomly distributed, there would be for a prime number like 242,413 a 25 percent chance that the next prime number would end in a 1, 25 percent for 3, 25 percent for 7, and 25 percent for 9. Each of the final four digits would be equally likely to occur. (The next prime is 242,419, by the way.)

This does not happen. Final digits tend to “repel” each other. In the first one billion primes, if a prime number ends in a 1, the next prime number ends in a 1 only 18 percent of the time. The same “repulsion” holds for the other three numbers.

It also seems to hold for other numerical bases, which suggests that it’s not just that primes don’t like to appear with gaps of 10 between them.

For example, it holds in base 3, which uses only the numbers 0, 1, and 2. As far as mathematicians have searched, the “repulsion” gets smaller but at a very slow rate.

Tor, Let’s just hope these new findings would lead to the invention of a simpler way of solving mathematics involving prime numbers. winx 🙂

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