"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 x 7 = 700 and 200 x 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?