# find $n$ for which $10^n+3(4^{n+2})+5$ is a prime number [closed]

if $10^n+3(4^{n+2})+5$ is a prime number, then which one is true for $n$

(a) $9$

(b) $5$

(c) $11$

(d) $14$

could some help me with this, thanks

## closed as off-topic by Namaste, Théophile, haqnatural, Vladhagen, Arnaud D.Jan 13 '17 at 23:23

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• May I ask if this is a homework problem? – awllower Jan 13 '17 at 18:09
• Try using modulo $3$ – lab bhattacharjee Jan 13 '17 at 18:10
• no actually it is from binomial theorem – DXT Jan 13 '17 at 18:10

This is greater than $3$ and multiple of $3$. Hence it is not prime.
The number cannot be a prime. Since whatever the value of $n$ may be the power of $10^n+5$ is divisible by $3$ hence the given number is a multiple of $3$. So, it cannot be a prime.