9514 1404 393
Answer:
A = 9
Step-by-step explanation:
Beyond the first few primes, all prime numbers end in one of the odd digits, 1, 3, 7, or 9. We can reduce this list by using a couple of simple divisibility rules.
The sum of the digits is 2+0+2+1+0+A = A+5. The number will be divisible by 3 if A+5 is divisible by 3. That will be the case for A=1 and A=7.
The sum of odd digits is A+1+0 = A+1. The sum of even digits is 0+2+2 = 4. When these sums are equal, the number is divisible by 11. That will be the case for A=3.
So, we have ruled out all digits except 9. If the number is prime it must be ...
202109
A = 9
_____
<em>Additional comment</em>
To make sure the number is prime, we would need to check divisibility by all primes less than √202109 ≈ 449.
