Virginia's Mathematics Standards of Learning prescribe that Virginia students should be able to identify and describe the characteristics of prime and composite numbers. A prime number is a positive whole number other than 1 that has only two whole divisors: itself and 1.
Positive whole numbers that are not prime numbers are called composite numbers, because they can be expressed as the product of two or more prime numbers. Trial division is the easiest method to understand, but students have to be able to divide in order to use it. This flowchart illustrate the steps required to determine whether any number less than or equal to 100 is prime or composite.
The Sieve of Eratosthenes is named for Eratosthenes of Cyrene, a brilliant third century BC Greek mathematician and geographer. Knowing how to construct a Sieve of Eratosthenes can help your students solve a few additional SOL test problems.
In the physical world, a sieve is a device that separates objects, usually by placing them on a screen that is sized so that smaller objects fall through and bigger ones are retained.
The Sieve of Eratosthenes is a very fast method of finding prime numbers, especially when it is computerized. The largest known prime number as of March 2014 is 257885161-1; that is, 2 multiplied by itself almost 58 million times, less 1. The prime number described in Fact 1 was discovered with the aid of a large network of computers.
Currently the Mayor of London, he previously served as the Member of Parliament for Henley-on-Thames and as editor of The Spectator magazine. Johnson was educated at the European School of Brussels, Ashdown House School, Eton College and Balliol College, Oxford, where he read Literae Humaniores. On his father's side Johnson is a great-grandson of Ali Kemal Bey, a liberal Turkish journalist and the interior minister in the government of Damat Ferid Pasha, Grand Vizier of the Ottoman Empire, who was murdered during the Turkish War of Independence.[5] During World War I, Boris's grandfather and great aunt were recognised as British subjects and took their grandmother's maiden name of Johnson. Try as I might, I could not look at an overhead projection of a growth profit matrix, and stay conscious.
He wrote an autobiographical account of his experience of the 2001 election campaign Friends, Voters, Countrymen: Jottings on the Stump. Johnson is a popular historian and his first documentary series, The Dream of Rome, comparing the Roman Empire and the modern-day European Union, was broadcast in 2006. After being elected mayor, he announced that he would be resuming his weekly column for The Daily Telegraph. After having been defeated in Clwyd South in the 1997 general election, Johnson was elected MP for Henley, succeeding Michael Heseltine, in the 2001 General Election.
He was appointed Shadow Minister for Higher Education on 9 December 2005 by new Conservative Leader David Cameron, and resigned as editor of The Spectator soon afterwards. A report in The Times[22] stated that Cameron regarded the possible affair as a private matter, and that Johnson would not lose his job over it. The Conservative Party hired Australian election strategist Lynton Crosby to run Johnson's campaign. Johnson pledged to introduce new Routemaster-derived buses to replace the city's fleet of articulated buses if elected Mayor. I believe Londoners should have a greater say on how their city is run, more information on how decisions are made and details on how City Hall money is spent.
Ken Livingstone presides over a budget of more than ?10billion and demands ?311 per year from the average taxpaying household in London.
Under my Mayoralty I am certain that London will be judged as a civilised place; a city that cares for and acknowledges its older citizens. The Mayor’s biggest area of responsibility is transport, and I intend to put the commuter first by introducing policies that will first and foremost make journeys faster and more reliable. Let's say that we have been given the task of determining if the number 51 is prime or composite.
53 is not divisible by 3, so we would keep trying until we divided 53 by 53, which is the first trial division of 53 that has no remainder. If so, it is not prime, because 2 is the only even prime number and we eliminated 2 in the previous step. To determine whether any number less than 121 is prime, you only have to do, at most, two trial divisions: once by 3 and once by 7.


It is a very simple and fast method of finding prime numbers, and it doesn't require any division. You can do this easily by striking through all of the numbers in the column below 2 and all of the numbers in the columns that begin with 4, 6, 8, and 10.
If you count the number of yellow squares in each row, you see that number generally decreases as you go from smaller to larger numbers. Knowing why the sieve works can help them develop more a more fundamental knowledge of numbers and number theory. The Sieve of Eratosthenes retains the prime numbers by striking through, or sieving out, all the numbers that multiples of prime numbers. Here is a computer program that uses the Sieve to generate all of the prime numbers up to 10,000,000. Mathematicians have been using computers for several decades to determine whether a given number is prime or composite. If you or your parents have ever purchased anything online, you have benefited from this property of prime numbers. To discover this property, enter 379,009 into a handheld calculator, then turn the calculator upside down.
In reference to his cosmopolitan ancestry, Johnson has described himself as a "one-man melting pot" — with a combination of Muslims, Jews and Christians comprising his great-grandparentage.[6] His father's maternal grandmother, Marie Louise de Pfeffel, was a descendant of Prince Paul of Wurttemberg through his relationship with a German actress. They have two sons—Milo Arthur (born 1995) and Theodore Apollo (born 1999)—and two daughters—Lara Lettice (born 1993) and Cassia Peaches (born 1997).[13] Boris Johnson and his family currently live in Holloway, North London.
In 1999 he became editor of The Spectator, where he stayed until December 2005 upon being appointed Shadow Minister for Higher Education. He is also author of three collections of journalism, Johnson's Column, Lend Me Your Ears and Have I Got Views For You. On 2 April 2006 it was alleged in the News of the World that Johnson had had another extramarital affair, this time with Times Higher Education Supplement journalist Anna Fazackerley. Yet Londoners have little confidence in the Mayor spending their money with care and prudence.
It was here that David Cameron and all his supporters gathered to congratulate him on becoming Mayor of London. It describes two simple methods that elementary students can use to identify prime numbers: trial division and the Sieve of Eratosthenes.
By agreement, mathematicians do not consider 0 and 1 to be prime, so the first prime number is 2. That tells us that 53's only whole factors are itself and 1; therefore it is a prime number.
First I will present the steps for constructing the sieve for all whole numbers <=100, then explain how the sieve works. Strike out all of the remaining multiples of 5 by striking through all of the numbers in the column below 5.
For example, four of the numbers between 1 and 10 are prime, but there is only 1 prime number between 91 and 100. Advanced students may even begin to develop the concept of an algorithm and how to measure the efficiency of different algorithms that accomplish the same task, like trial division and the Sieve of Eratosthenes.
So when we struck out all of the even numbers except two, we sieved out all of the composite numbers that have 2 as one of their prime factors.
Its speed depends on your computer's processing power, but on recent computers, it can generate all of the primes less than 10,000,000 in about five seconds. The largest prime discovered by hand calculation is 2127-1, or 170,141,183,460,469,231,731,687,303,715,884,105,727.
Most secure websites use the RSA encryption method, developed in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman. Through Prince Paul, Johnson is a descendant of King George II, and through George's great-great-great grandfather King James I a descendant of all of the previous British royal houses. His comic first novel Seventy-Two Virgins was published in 2004,[16] and his next book will be The New British Revolution, though he has put publication on hold until after the London Mayoral election.[17] He was nominated in 2004 for a British Academy Television Award, and has attracted several unofficial fan clubs and sites. In 2004 he was appointed to the front bench as Shadow Minister for the Arts in a small reshuffle resulting from the resignation of the Shadow Home Affairs Spokesman, Nick Hawkins. It also describes some practical uses for prime numbers and has links to additional resources on primes for students who show above average interest in mathematics or computer science.


Remember that the fundamental theorem of arithmetic says that any composite number can be expressed as the product of a unique combination of two or more prime numbers. This understanding leads to the fundamental theorem of arithmetic: that any composite number can be written as the product of a unique combination of two or more prime numbers. In practice, there are several ways to optimize the trial division method that reduce the number of divisions that students have to perform. Note that every other multiple of 3 will already have been struck through as a result of eliminating all of the multiples of 2. You don't have to worry about getting multiples of 5 that have 0 in the ones place, because you eliminated those when you struck through the multiples of 2. The Greek mathematician Euclid proved that there are infinite prime numbers, but we can see that they are not evenly distributed. When we started counting by 3s, we sieved out all of composite numbers that have 3 as one of their prime factors.
Hint: 7 is the largest prime number that is less than or equal to the square root of 100, which is 10. French mathematician A‰douard Lucas proved this number was prime in 1876, after working on the problem for 19 years.
In 1995 a recording of a telephone conversation was made public revealing a plot by a friend to physically assault a News of the World journalist. If we consider 1 to be prime, then a composite number such as 9 could be expressed as 3 x 3 or 1 x 3 x 3, or even 1 x 1 x 3 x 3.
If we get a remainder, we know that 2 is not a whole divisor of 51, so we proceed to divide 51 by the next lowest number: 3. Using the following optimizations, we can identify any prime number less than 121 by performing, at most, two trial divisions. That means that any composite numbers less than the square of 11 (121) must be divisible by 2, 3, 5, or 7. You can take advantage of this fact by counting by 6's instead of by 3's.Your table should like this. For example, among the prime numbers which have 1,000 or fewer digits, about 1 in 2,300 is prime. In this case we don't get a remainder (51 divided by 3 = 17), so we have just proved that 51 is not a prime number, because it has whole divisors (3 and 17) other than itself and 1. The initial steps in this method eliminated all of the composite numbers divisible by 2 or 5 without having to do any trial divisions.
Any numbers not eliminated by these initial steps are either divisible by 3 or 7, or are prime numbers themselves.
The prime number theorem is a formal statement of the idea that primes become less common as they get larger. If you have a large number of students reading this page in a computer lab, do not have them click on the link in the prime number page that displays the entire number.
Since 4 and all even numbers greater than 4 are divisible by 2, no even number other than 2 is prime.
Trying to have a large number of computers display that number at the same time will overload your network!
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