The next prime, 3, has only 2 factors, so all the other factors of 3 cannot be primes. So take your pencil and mark out all multiples of 2: 4, 6, …., 98, 100. Since all other even numbers are divisible by 2, they cannot be primes, so all other prime numbers must be odd. The first prime number-and the only even prime number-is 2. Using the grid, it is clear that 1 is not a prime number, since its only factor is 1. Get your number grid ( Click here for a copy that you may print out) and your pencil out! We will use Eratosthenes’ sieve to discover the prime numbers between 1 and 100. A few decades later Eratosthenes developed his method, which can be extended to uncover primes.
These included the fact that every integer can be written as a product of prime numbers, or it is itself prime. In his Elements, Euclid (about 300 BCE) stated many properties of both composite numbers (integers above one that can be made by multiplying other integers) and primes. The Greeks understood the importance of primes as the building blocks of all positive integers. By inventing his “sieve” to eliminate nonprimes-using a number grid and crossing off multiples of 2, 3, 5, and above-Eratosthenes made prime numbers considerably more accessible.Įach prime number has exactly 2 factors: 1 and the number itself. Such numbers, divisible only by 1 and themselves, had intrigued mathematicians for centuries. 194 BCE) devised a method for finding prime numbers. In addition to calculating the earth’s circumference and the distances from the earth to the moon and sun, the Greek polymath Eratosthenes (c. Let’s try an ancient way to find the prime numbers between 1 and 100. A positive integer is a prime number if it is bigger than 1, and its only divisors are itself and 1.
Each positive integer has at least two divisors, one and itself.
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