What are the numbers strictly having "prime" factors between 30 & 140 only? It should be between 10000 & 20000

What are the numbers? Do you want us to list them? All 10 to 20 thousand of them?

10001 to 19321, having prime factors between 30 & 140 only

10001 is 73 x 137 and 19321 is square of 139

Firstly you need to work out how many prime factors there are between 30 and 140

You can do that with a seive of Eratosthense.

How about use 24(nCr)2 =276+ 24squares(31^2, 37^2, 41^2, 43^2, 47^2,.....and so on to 139^2