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

1. 72
stanwshuraposted 6 years ago

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?

2. 60
bubba-mathposted 6 years ago

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_theorem

3. 95
dezalyxposted 6 years ago

Like 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).

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