smartPaper Sieve

Eratosthenes of Cyrene c276 bc – c194 bc

Director of the Great Library in Alexandria, astronomer, mathematician, poet, geographer. He suggested a calendar with leap years, made credible estimates of the distance to the Sun and Moon, accurate estimates of the circumference of the Earth, the angle of tilt of the Earth's axis with respect to the solar orbit.

Eratosthenes devised a method of identifying prime numbers that bears his name.

theSieve of Eratosthenes

Prime numbers have no factors other than the number and 1. Eratosthenes' Sieve is a simple method of identifying prime numbers. First, list the span of integers to test. Ignore 1, it has special meaning. Starting with 2 repeat these two steps until all numbers are either Prime or marked off.

designate lowest unmarked integer as Prime.
mark off all multiples of the designated number. They are nonPrime.

Example

Find prime numbers from 2 to 50.

– reset –
nextPrime

Next Prime
Mark Off Multiples

Do it

Calculate and display 2 through — 10,000 100,000

Show — sieve

Bonus

The computer uses a special version of the Sieve optimized for web browsers. In addition to highlighting Prime numbers the prime factors of nonPrime numbers are available. Click any number on the display grid to see its prime factors.

Initializing Workspace …

Creating workspace to sieve prime numbers. Includes the following assumptions …

1 is not prime
2 is the only even prime #
3 is the first odd prime #

Initialized

ET =

primes 2 to 10,000
	calc ET –
	total ET –
back


1	501
1001	1501
2001	2501
3001	3501
4001	4501
5001	5501
6001	6501
7001	7501
8001	8501
9001	9501

17may2004