Conjecture 56. One  more SMR conjecture.

Sebastián Martín Ruiz sends the following conjecture:

Can anyone prove this conjecture?: For all n>2 ; for all i:  1<= i<= n   exist  j:  n+1 <= j <= n^(3/2), (1+pj)/(-1+pi) is integer. pi is the ith prime number.