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Nila added to the discussion: “I found out that in the mid-1800s, an astronomer named J.P. Kulik used the Sieve of Eratosthenes to find the prime numbers up to 100,000,000. He spent 20 years of his life doing this.”
“I can't believe anyone would spend 20 years finding prime numbers!” exclaimed Michael.
“The sad part is that Kulik gave his manuscript to a library in Prague and they lost the sections that had the prime numbers from 12,642,000 to 22,852,800,” added Mr. Moreno. “The good news is that mathematicians don't have to find large prime numbers by hand anymore. Today they use computers to do the work.”
“I also found some interesting information,” said John. “I found out that in 1742 a Russian mathematician named Christian Goldbach made a conjecture that every even number except 2 can be written as a sum of two prime numbers. For example, 10 = 3 + 7.”
“Right,” said Mr. Moreno, “and it is called a conjecture because up to now no one has been able to prove or disprove it. Who knows, maybe someday one of you will be the person to do this!”
“I found a modern use for prime numbers,” said Lin. “Prime numbers are used in cryptography. Cryptography is the study of secret codes. Some codes are based on the fact that it is hard to factor very large numbers into primes. To keep information secret, they use numbers with prime factors of 100 or more digits. One use of these codes is to protect information stored on computers. Many banks and other businesses use these codes to make sure that nobody can change or steal the information from their computers.”
“Wow,” said Michael, “with all this information we should be able to write a great report for class. Let's get started.”
“Wow,” said Michael, “with all this information we should be able to write a great report for class. Let's get started.”
Use the Sieve of Eratosthenes to find all of the prime numbers between 1 and 100. Fold the 200 Chart page in the Student Activity Book in half. Follow the directions below.
- Begin by crossing out the number 1. (Remember, 1 is not a prime number.)
- The next number is 2. This is the first prime number. Circle the number 2. Cross out all of the multiples of 2 up to 100. (A multiple of 2 is the product of 2 and any whole number. 2 1 = 2, 2 2 = 4, 2 3 = 6, so 2, 4, and 6 are multiples of 2.)
- Are any of the numbers you crossed out prime numbers? How do you know?