SOLUTION: the sum of the digits of a two-digit prime number is subtracted from the number. Prove that the difference cannot be a prime nuber.

Question 592549: the sum of the digits of a two-digit prime number is subtracted from the number. Prove that the difference cannot be a prime nuber.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The fact that the original number is prime is just a red herring. In fact, if you subtract the sum of the digits from any integer, the result is divisible by 9 and therefore not prime.

Proof for two-digit integers:

Let

represent the 10s digit and let

represent the 1s digit.

Then the original integer is

and the sum of the digits is

.

Subtracting:

Which is divisible by 9. So if ANY two digit integer less the sum of its digits is non-prime, any prime two digit integer must exhibit the same characteristic.

Q.E.D.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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