Vedic Maths to Check Whether A Number is Prime

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A Prime Number is a number which is divisible by only 1 and itself.

1 Digit Primes

  • 1 is neither Prime nor composite.
  • 2 is the only even Prime.
  • 2 and 3 are known as fundamental prime numbers.
  • The other two single digit prime numbers are 5 and 7.

Thus, there exist four single-digit prime numbers out of 9 single digits – 2, 3, 5 and 7.

2 Digit Primes

  • There are 90 two-digit numbers from 10 to 99.
  • Out of these 90, there are 45 odd numbers and 45 even numbers.
  • All even numbers are Composite since they are multiples of 2. So, all the 45 even numbers of two-digits are Composite.
  • It is evident that an odd number is a number which ends with 1 or 3 or 5 or 7 or 9. So, in the 45 odd number, each set has 9 odd numbers having two-digits.
  • All numbers ending with 0 or 5 are always divisible by 5. Thus all the 9 two-digit numbers ending with 5 are Composite. Now the remaining 36 may be Prime numbers, i. e, the two-digit numbers ending with 1, 3, 7 or 9 may be Prime.

To check whether a given two-digit number is Prime or not.

  1. Step 1: Check if the given two-digit number is ending with 1 or 3 or 7 or 9. If it is, then Go to Step 2. Otherwise it is Composite.
  2. Step 2: Check if the number is either 49 or 77 or 91 (7×7 or 7×11 or 7×13, 7 multiples of consecutive primes 7, 11 and 13). If the answer is ‘ No’, then Go to Step 3. Else it is Composite.
  3. Step 3(a): Check if the given number is ending in 1 or 7 – if it is, check the tenth digit of the given number. If that tenth digit is other than 2 or 5 or 8, then we conclude that the given number is definitely Prime. (21, 27, 51, 57, 81 and 87 are composite with 3 multiples)
  4. Step 3(b): Check if the given number is ending with 3 or 9 – if it is, check the tenth digit of the given number. If that tenth digit is other than 3 or 6 or 9, then we conclude that the given number is Prime number. (33, 39, 63, 69, 93 and 99 are composite with 3 multiples )

Is 73 Prime?

  1. Step 1: 73 ends with 3 which means it may be Prime. Move on to Step 2.
  2. Step 2: 73 is not in the category of numbers 49 or 77 or 91. Move to Step 3.
  3. Step 3: The tenth digit of 73 is other than 3 or 6 or 9 {Using Step 3(b)}

We conclude that 73 is definitely a prime number.

Digital Extract Concept

In the above case of determining the nature of the number 73, instead of Step 3, we can use the concept of Digital Extract. If the Digital Extract of any given number is other than 3 or 6 or 9, the number 73 is definitely a prime number. Here DE (73) = 7 + 3 -> 10 -> 1 + 0 = 1 which is other than the digits 3 or 6 or 9. Thus, 73 is a prime number.

Is 83 Prime?

  • Step 1: 87 ends with 7 which means it may be Prime. Move to Step 2.
  • Step 2: 87 is not in the category of numbers 49 or 77 or 91. Move to Step 3.
  • Step 3: The tenth digit of 87 is 8. Using Step 3(b), we can conclude that 87 is Composite. Hence 87 is not Prime.
  • Using Digital extract, DE(87) = 6 which helps us conclude that 87 is not Prime.

Thus, to check whether the given two-digit number is prime or not, we are not using any Multiplication Table or Divisibility Rules.

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