2023/028) what is the integer value n can take such that 3n - 10, 6n-13, and 5n-13 are prime

ew have 5n-13- (3n -10) = 2n -3 which is odd. So all 3 cannot be odd so one of them has to be 2 for all to prime.

and n has to be greater than 3 for all numbers to be positive

3n-10 = 2 gives n =4 and numebr are 2, 11, 7 all are prime 

$6n - 13 \ge 11$ and $5n - 13 'ge 7$ as $n > 3$ so other numbers cannot be 2

so only solution n = 4