Verification of the Prime Number Theorem

The Objective

The average distance between prime numbers is calculated using a random sampling method. The average distance between the primes up to a positive integer n is numerically showed to be approximately ln(n)-1.

Methods/Materials

A random sampling method is used both by hand and using the computer program mathematica to calculate the average distance between consecutive prime numbers.

Results

The average distance between prime numbers is shown to be approximately ln(n).

Conclusions/Discussion

The data obtained experimentally verifies the prime number theorem.

To experimentally show that the average distance between consecutive primes increases.

Science Fair Project done By Robyn J. Swift

 

 

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