Is there a pattern to the sequential distribution of prime numbers?

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53...

The space between is, in order : 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6...

Is there some sort of formula or algorithm?There is unfortunately no known pattern to the sequence of gaps between consecutive primes, but mathematicians did manage to prove that the density of primes below a given number x converges to a nice function of x. That function is Li(x), the logarithmic integral function. See Mathworld reference:

http://mathworld.wolfram.com/LogarithmicIntegral.html

This theorem about the density of primes is known as the Prime Number Theorem. You can read more about the math behind it and the history of its study here:

http://en.wikipedia.org/wiki/Prime_number_theoremLike bubba-math said, there is no pattern in the sequence of prime numbers. I wish there was, though. The largest known prime number right now has nearly 13 million digits and the computer that got the answer was able to claim a $100,000 for being the first to find a prime number with more than 10 million digits.

Prizes are still available for the first ones who can find a prime number with more than 100 million digits ($150,000) and another for one with a billion digits ($250,000).

Related Discussions

- 3
### what are co prime numbers

by devbhagat8 years ago

what are co prime numbers

- 5
### What are prime numbers?

by maria.rose7 years ago

What are prime numbers?

- 2
### How can I generate sieres of prime number using function in C++?

by yosiyas6 years ago

How can I generate sieres of prime number using function in C++?#include #include bool isprime (int num);int main(){int num=0;int i=0;printf("Enter numbers > ");scanf("%d", &num);while...

- 3
### What number can be divided by 7, 9, & 11?

by Grace Marguerite Williams15 months ago

What number can be divided by 7, 9, & 11?

- 3
### Do you see a number repeatedly?

by Mahaveer Sanglikar3 years ago

Do you see a number repeatedly?Many people see a specific number repeatedly in specific period of life. For example, I saw number 22 again and again, here and there for many years. Do you see such a number...

- 2
### Are there negative prime numbers?

by BravexxxHeart5 years ago

Are there negative prime numbers?

Copyright © 2018 HubPages Inc. and respective owners.

Other product and company names shown may be trademarks of their respective owners.

HubPages^{®} is a registered Service Mark of HubPages, Inc.

HubPages and Hubbers (authors) may earn revenue on this page based on affiliate relationships and advertisements with partners including Amazon, Google, and others.

terms of use privacy policy (0.56 sec)

working