Prime Numbers and Methods to Find Prime Numbers

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Grace
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A prime number has two factors, which are the number itself and 1. Prime numbers can be divided by 1 and the number itself, without any remainder. For example, the number 3 is a prime number because it is not divisible by any other number, only 3 and 1.

This article will cover in detail the concept of prime numbers and how to easily find them. The prime numbers chart will also give you an idea of prime numbers between 1 to 1000. 

 

Prime Numbers

Important properties of a prime number are:

  • A prime number is a whole number. 
  • A prime number is always greater than 1.
  • There is only one even prime number, that is, 2.
  • Any two given prime numbers are co-prime to each other.
  • All prime numbers are odd numbers except 2.
  • All numbers can be expressed as the product of prime numbers.

If a number is not a prime number, then it is a composite number. A composite number is a number greater than 1, with more than two factors. The table below explains the difference between prime and composite numbers.

Prime Numbers Composite Numbers
Prime numbers have only two factors, 1 and the number itself. Composite numbers greater than 1, have at least three factors.
The smallest prime number and the only even prime number is 2. The smallest composite number is 4.
A few examples of prime numbers are 2, 3, 5, 7, 11, etc A few examples of composite numbers are 4, 6, 8, 9, etc

Facts and Examples of Prime Numbers

Some facts about prime numbers which should be remembered:

  • There is only one even prime number, that is, 2. Every other prime number is divisible by 2.
  • There is no prime number greater than 5, which ends with 5 as the last digit. Any number with the last digit as 5 is divisible by 5. 
  • 1 and 0 are not prime numbers.
  • If the sum of digits of a number is a multiple of 3, then that number is divisible by 3.
  • If a number is not a prime number, it is a composite number, except for 1 and 0. 
List of Numbers Prime Numbers
1 to 10 2, 3, 5, 7
11 to 20 11, 13, 17, 19
21 to 30 23, 29

Methods to Find Prime Numbers

There are many methods to determine if the number is a prime number. To find out whether a number is a prime number, the method of factorisation works the best. By obtaining factors of a number, it can be easily found out if the number is prime or not.

The steps to find a prime number using factorisation:

  1. Find out the factors of the given number.
  2. Count the number of factors of the given number.
  3. If the total number of factors is more than two, then the number is not a prime number.

For example, if we take the number 45. 45 can be written as: 3 * 3 * 5, so the factors for 45 are 1, 3, 5, 9, 15, 45. The total number of factors is 6, which is more than 2. So, 45 is not a prime number.

Suppose we take the number 43. The prime factorisation of 43 is 1 * 43, so the factors are 1, 43. The total number of factors is 2, which means 43 is a prime number.

The steps to find if a large number is a prime number:

  1. If the unit place of a number is 0, 2, 4, 6 or 8, then the number is not a prime number.
  2. Find the total sum of the digits of the number. If the sum is divisible by 3, then the number is not a prime number.
  1. If points 1 and 2 are false, take out the square root of the given number. 
  2. Divide the number by all the prime numbers below the square root. 
  3. If it is not divisible by any prime numbers below its square root value, then it is a prime number. If it is divisible, then the number is not prime.

For example, if we take the number 432454. The last digit of the number is 4, which is divisible by 2. Hence, 432454 is not a prime number.

Suppose we take the number 32553. The unit digit of this number is not 0, 2, 4, 6, 8. So, we take another method of finding the sum of all digits of the number. The sum of all digits: 3 2 5 5 3 = 18. 18 is divisible by 3, so 32553 is not a prime number.

Suppose we take the number 1315. The unit digit is not 0, 2, 4, 6, 8. Upon checking the sum of this number: 1 3 1 5 = 10, which is not divisible by 3. We see that the last digit is 5, so the number is divisible by 5. 1315 / 5 = 263. Hence, 1315 is not a prime number.

 

Prime Numbers 1 – 1000

2 3 5 7 11 13 17 19 23  
29 31 37 41 43 47 53 59 61 67
71 73 79 83 89 97 101 103 107 109
113 127 131 137 139 149 151 157 163 167
173 179 181 191 193 197 199 211 223 227
229 233 239 241 251 257 263 269 271 277
281 283 293 307 311 313 317 331 337 347
349 353 359 367 373 379 383 389 397 401
409 419 421 431 433 439 443 449 457 461
463 467 479 487 491 499 503 509 521 523
541 547 557 563 569 571 577 587 593 599
601 607 613 617 619 631 641 643 647 653
659 661 673 677 683 691 701 709 719 727
733 739 743 751 757 761 769 773 787 797
809 811 821 823 827 829 839 853 857 859
863 877 881 883 887 907 911 919 929 937
941 947 953 967 971 977 983 991 997  

Wrapping Up

If all the methods of finding the prime numbers are memorised, identifying any given number as a prime or composite number comes very easy. The whole number system comprises either prime numbers or composite numbers, except for 0 and 1.

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Grace
Vivek is a published author of Meidilight and a cofounder of Zestful Outreach Agency. He is passionate about helping webmaster to rank their keywords through good-quality website backlinks. In his spare time, he loves to swim and cycle. You can find him on Twitter and Linkedin.