Find the number of 6-digit numbers of the form ababab (in base 10) each of which is a product of exactly `6 `distinct primes.

Options

A. 8
B. 10
C. 13
D. 15

Answer

C

Explanation

`100000leababab lt1000000`
`le10^(5)a+10^(4)b+10^(3)a+100b+10a+c lt1000000`
`lea(10^(5)+10^(3)+10)+b(10^(4)+10^(2)+1)le1000000`
`100000le(10^(4)+10^(3)+1)+b(10a+b)lt1000000`
`100000le10101(ab)lt1000000`
`9.9le" ab " lt99`
'ab' number can be obtained as product of orderes pairs
`(2,5), (2,11),(2,17),(2,19),(2,23),(2,29),(2,31),(2,41),(2,43),(2,47),(5,11),(5,17),(5,19)`
Total numbers = 13