A sphenic number S.N. is a product of three distinct prime numbers.
a. Clearly each S.N. has 8 divisors. Show that not only S.N.s claim this feature.
b. Find the smallest consecutive pair n,n+1 of sphenic numbers.
c. Same for the smallest triplet.
d. Prove that sphenic quadruplet n,n+1,n+2,n+3 is "mission impossible".