S(n) is sum of first n natural numbers, Z(n) = 2S(n)+41, lowest value of n such that Z(n) is NOT a prime.	Choose the correct answer.
A) 7
B) 6
C) 40
D) always a prime
E) none
as the sum of first N natural numbers is   S(n)=n/2(1+n)   so z(n)=2(s(n))+41=2*n/2(1+n)+41=n(1+n)+41   Now put all the given options one by one   take n=7   z(7)=7(7+1)+41=56+41= 
<gadget id="calculator">56+41</gadget>
<output>97</output>
97 a prime number   take n=6   z(6)=6(6+1)+41=41+41=83 again a prime number   now take n=40   z(40)=40(40+1)+41=40*41+41=41(40+1)=41*41= 
<gadget id="calculator">41*41</gadget>
<output>1_681</output>
1681 not a prime number   ANSWER:40
<result>C</result>
S(n) is sum of first n natural numbers, Z(n) = 2S(n)+41, lowest value of n such that Z(n) is NOT a prime.