SOLUTION: Find the greatest prime divisor of the value of the arithmetic series 5 + 6 + 7 + \dots + 135.

This sum, as for any arithmetic progression, is the product of the mean by the number of terms.


The mean is   =  = 70.

The number of terms is  135-4 = 131.


So, the sum is  70*131.


Decomposition of the sum to product of primes is  70*131 = 2*5*7*131.


The greatest prime divisor is 131.


ANSWER.  The greatest prime divisor is 131.

It's interesting that the greatest prime divisor of the sum happened to turn out
to be the same as the number of terms, 135-5+1=131.  

It's further interesting that the greatest prime term of the series is also 131. 
[Note that 133 is not prime since 133=7x19].

[Some more workout for the brain. lol]

Edwin