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Two digit Prime numbers

To identify a given 2-digit number is a prime or not.

STEP 1 : Check the unit digit of the given number. If that unit digit is any one of the odd digits 1 or 3 or 7 or 9,  then the given number may be Prime. ( There are thirty six such 2-digit numbers)

STEP 2 : Check the given 2-digit number is either  49 or 77 or 91. If it is so, then the given number is composite.

STEP 3 : Check the unit digit. If it is either 1 or 7 and the tenth digit is either 2 or 5 or 8, then the given 2-digit number is composite. If the unit digit of the given number is either 3 or 9 and the tenth digit is 3 or 6 or 9 (3-multiples), then the given 2-digit number is composite.

Otherwise the given 2-digit number is definitely Prime.

Example 1 : Whether 73 is a prime number?

From Step 1 and Step 2, it is clear that 73 may be a prime number. The unit digit of 73 is 3 and the tenth digit of 73 is not a multiple of 3 (3 or 6 or 9). From Step 3, we conclude 73 is a prime number.

Example 2 : Whether 87 is a prime or not?

From Step 1 and Step 2, it is evident that 87 may be a prime number. The unit digit of 87 is 7 and the tenth digit is 8. From Step 3, we conclude that 87 is composite, not a prime.