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Time for Primes Phase II: Experimental Verification of the Prime Number Theorem

CSEF · 2008 Mathematics & Software

Robyn J. Swift · Bloomington Middle School, Bloomington, San Bernardino County

Overview

Objectives/Goals 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.

Summary statement

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

Help received

Parents helped assemble display board.

Competition history

  • CSEF 2008 Mathematics & Software · Entry J1320

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