National Classics Week Packet National Classics Week Packet | Page 9

April 18

Written by NJCL Parliamentarian Joe Giambrone

Continuing , 3 is noted as prime while 6 , 9 , 12 , and so on are marked as composite due to their divisibility by 3 . Once all of the composite numbers are marked , the only numbers that remain are prime . While prime factorization is fun , Eratosthenes could not have possibly imagined what realworld applications it could have . In 1977 , the three cryptographers Ron Rivest , Adi Shamir , and Leonard Adleman created the RSA cryptosystem , an acronym for their names . This algorithm is used to encode data by encrypting and decrypting with the product two massively large prime numbers . Because there is no inexpensive way to factor such large integers , the RSA system is very secure and heavily resistant to brute force attacks . It is really amazing how something studied in pure mathematics over two thousand years ago can be so vital in encrypting valuable data today .

Activities

Complete a Sieve of Eratosthenes on your own , finding every prime up to a certain number . Encode your own message using the RSA cryptosystem . Have a friend decode it . Research other ideas researched in classical times and how their uses have evolved in the modern era .