(Can you find all the twin primes up to 200?) Some twin primes are 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29 and 31, …. “Twin primes” are primes that are exactly two apart. There is a theorem that is designed to calculate approximately how many primes there are that are less than or equal to any number x.Ī few other very cool things about prime numbers You will never factor it with different prime numbers.)
(So once you factor a number, it is unique. Prime numbers become less common as numbers get larger.Įven Euclid knew that there are infinitely many primes! (The proof is easy!)įYI, Euclid proved the “fundamental theorem of arithmetic”, that every integer greater than one can be expressed as a product of primes in only one way.
There are 16 prime numbers between 201 and 300. There are 21 prime numbers between 101 to 200. There are 25 prime numbers between 1 and 100. Notice that we don’t have to go above multiples of nine to get the non-prime (i.e. Which number in the list is actually composite? 91 = 7*13! Oh, no! This list contains 26 numbers, and there are only 25 prime numbers less than 100. We continue this process, crossing out multiplies of 5 (I found 25, 35, 65, 85, 95), multiples of 7 (49, 77, 91), 11 (none), 13 (none).(In general we need to test divisors only up to the square root of the number.) And finally we have: 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. These are 8 numbers in total.Each positive integer has at least two divisors, one and itself. Now, if we look at the prime numbers from 1 to 20, then those are 2,3,5,7,11,13,17,19.
See if we consider the numbers from 1 to 20, there are 20 numbers in total. How many prime numbers are there between 1 and 20? This leaves 29 and 31, the only primes between 25 and 35. Of the remaining odd numbers, 27 = 3*3*3 and 33 = 3*11. We can eliminate all the even numbers: 26, 28, 30, 32 and 34. Similarly, how many prime numbers are there between 25 and 50? 6 prime numbersĪlso asked, how many prime numbers are there between 25 and 35? For 25 to be a prime number, it would have been required that 25 has only two divisors, i.e., itself and 1. The list of all positive divisors (i.e., the list of all integers that divide 25) is as follows: 1, 5, 25. Similarly, you may ask, is 25 a prime number Yes or no?įor 25, the answer is: No, 25 is not a prime number.