Introduction to prime numbers : let us first understand What is prime number in math ?A natural number greater than 1, which has no factors except 1 and itself is called a prime number.Example of prime numbers are: 2, 3, 5, 7, 11, 13, 17,…. and so on.what about 1 . Is the Number 1 a Prime Number? so , no 1 is not a prime number because 1 is neither prime nor composite. Every natural number except 1 is, either a prime number or a composite number.and now let us see Is Two a Prime Number?yes 2 is the only prime number which is even. All other prime numbers are odd.Let us now understand the concept of finding prime numbers.
How to find prime number?Eratosthenes, a Greek mathematician, gave a simple method to mark out primes. His method is known as the Sieve of Eratosthenes.We first list the numbers up to 100, except 1 which is neither prime nor composite.
1. Begin with 2 which is prime. So keep it but cross out all its multiples.
2. Next, the number is 3 is prime. Thus we keep it but cross out all its multiples. Some of these numbers have already been crossed out.
3. The next number not crossed out is 5. It is also prime. So, keep it and cross out all its multiples.
4. Continue this process keeping only the primes and striking off their multiples until we cannot strike off any more numbers.
Thus, the prime numbers from 1 to 100 are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.Eratosthenes, probably, made holes in the paper instead of crossing out the numbers. Therefore, his paper must have looked like a sieve. That is why perhaps this method is known as sieve method.
From the above set of primes between 1 and 100, we do not see any pattern. We will not see any regular pattern even if we take numbers between 1 and 10000. Mathematicians from ages tried unsuccessfully to find a simple formula which will give all the prime numbers and only the prime numbers. It is now known that no simple formula exists, so the only way to find whether the given number is prime is to see if it has any factor other than 1 and itself.now let us know What is the largest known prime number? The largest known prime number is 243112609 - 1, It is the largest integer that is currently known to be a prime number.
How to find prime number?Eratosthenes, a Greek mathematician, gave a simple method to mark out primes. His method is known as the Sieve of Eratosthenes.We first list the numbers up to 100, except 1 which is neither prime nor composite.
1. Begin with 2 which is prime. So keep it but cross out all its multiples.
2. Next, the number is 3 is prime. Thus we keep it but cross out all its multiples. Some of these numbers have already been crossed out.
3. The next number not crossed out is 5. It is also prime. So, keep it and cross out all its multiples.
4. Continue this process keeping only the primes and striking off their multiples until we cannot strike off any more numbers.
Thus, the prime numbers from 1 to 100 are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.Eratosthenes, probably, made holes in the paper instead of crossing out the numbers. Therefore, his paper must have looked like a sieve. That is why perhaps this method is known as sieve method.
From the above set of primes between 1 and 100, we do not see any pattern. We will not see any regular pattern even if we take numbers between 1 and 10000. Mathematicians from ages tried unsuccessfully to find a simple formula which will give all the prime numbers and only the prime numbers. It is now known that no simple formula exists, so the only way to find whether the given number is prime is to see if it has any factor other than 1 and itself.now let us know What is the largest known prime number? The largest known prime number is 243112609 - 1, It is the largest integer that is currently known to be a prime number.
