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

Step-by-step solution

N=a b a b a b array llll 1 < a 9 & 0 < b 9 & a, b l array N=10⁵ a+10⁴ b+10³ a+10² b+10 a+b= (10⁴+10²+1 )(10 a+b)= (10²+10+1 ) (10²-10+1 )(10 a+b)=3 37 13 7(10 a+b) ...... (1) array lcc then & 10 a + b = P ₁ P ₂ & p ₁, p ₂ prime and 10 10 a + b 99 a & b & 10 a + b 1 & 0 & 10=2 5 2 & 2 & 22=2 11 3 & 4 & 34=2 17 3 & 8 & 38=2 19 4 & 6 & 46=2 33 5 & 5 & 55=5 11 5 & 8 & 58=2 29 6 & 2 & 62=2 31 7 & 4 & 74=2 37 8 & 2 & 82=2 41 8 & 5 & 85=5 17 9 & 4 & 94=2 47 9 & 5 & 95=5 19 array