What is the um of the two smallest distinct prime factors of 2^27+3^27?

2^27 + 3^27   =  7625731702715  

This number is not divisible by 2

It is also not divisible by 3 because the sum of its digits is not divisible by 3

It is divisible by 5     because   it ends in  a "5" 

To test whether it is divisible by 7, double the last interger  and subtract the remaining part.....if the result is divisible by 7, then the number itself is divisible by 7....so we have.....

[2* 5 -  762573170271] / 7  = -108939024323

So.......5   and 7 are the smallest distinct prime divisors  of  7625731702715  

And their sum is 12

Here is a more "mathematical"  way of doing this......

2^27   +  3^27   =

[ (2⁹)³ + (3⁹)³ ]  =  

[ 2⁹ + 3⁹ ] [ 2¹⁸  - (2 * 3)⁹  + 3¹⁸ ]  =

[ (2³)³ + (3³)³ ]  [ 2¹⁸  - (2*3)⁹  + 3¹⁸ ]  =

[ 2³ + 3³] [ 2⁶ - (2 * 3)³ + 3⁶] [ 2¹⁸  - (2*3)⁹  + 3¹⁸ ]  =

[2 + 3] [ 2² - 6 + 3² ]   [ 2⁶ - (2 * 3)³ + 3⁶] [ 2¹⁸  - (2*3)⁹  + 3¹⁸ ]  =

[5] [ 13 - 6] [577] [377604937]  =

[ 5 ] [ 7 ]  [577] [377604937]  

So.......the sum of the two smallest distinct prime factors of  2^27 + 3^27    =    12

2^27+3^27?=134,217,728 + 7,625,597,484,987 =7,625,731,702,715

Prime factors of:7,625,731,702,715 =5 * 7 * 577 * 377604937

Therefore: 5 + 7 =12 sum of 2 smallest prime factors.