A problem about differences in reduced residue system.

Here M=2*3*p(3)*p(4)*p(5)*p(6)*…*p(n) is the product of consecutive prime numbers. p(n) is n-th prime number.

Then the minimal reduced residue system modulo M is:
1<a(1)< a(2) <a(3)<…<a(n) <M, That is to say every a(i) is relatively prime to M.

Obviously, a(1) is (n+1)th prime number.
Could we prove a(1)-1 is bigger than difference of any other two consecutive elements of a(i):
a(i+1)-a(i)<a(1)-1?
.

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