Challenge Level

"Guess my number," said Tom, "I'll only answer yes or no."

"OK. Is it less than $1000$?" "No."

"Is it less than $2000$?" "Yes."

"Is it even?" "No."

"So it's an odd number between $1000$ and $2000$?"

"Yes, but you knew that already. It's a wasted question!"

"Is it divisible by $3$?" "No."

"Is it divisible by $5$?" "No."

"Is it divisible by $7$?" "Yes."

"If I divide it by $7$ do I get a number that is less than $100$?" "No."

"Do I get a number that is less than $200$?" "Yes."

"Ah! $100 \times 7$ = $700$ and $200 \times 7 = 1400$. So your number is less than $1400$?"

"Yes, but that's another wasted question."

"Ha! $14$ squared is $196$.

So your number is $7$ times the product of two prime numbers less than $14$?"

"Yes."

"I am sure I know your number and this question is just checking.

Is your number palendromic? Does it read the same in both directions?"

"Yes."

What was Tom's number?