Le Monde puzzle [#967]

A Sudoku-like Le Monde mathematical puzzle for a come-back (now that it competes with The Riddler!):

Does there exist a 3×3 grid with different and positive integer entries such that the sum of rows, columns, and both diagonals is a prime number? If there exist such grids, find the grid with the minimal sum?

I first downloaded the R package primes. Then I checked if by any chance a small bound on the entries was sufficient:

cale<-function(seqe){ 
 ros=apply(seqe,1,sum)
 cole=apply(seqe,2,sum)
 dyag=sum(diag(seqe))
 dayg=sum(diag(seqe[3:1,1:3]))
 return(min(is_prime(c(ros,cole,dyag,dayg)))>0)}

Running the blind experiment

for (t in 1:1e6){
  n=sample(9:1e2,1)
  if (cale(matrix(sample(n,9),3))) print(n)}

I got 10 as the minimal value of n. Trying with n=9 did not give any positive case. Running another blind experiment checking for the minimal sum led to the result

> A
 [,1] [,2] [,3]
[1,] 8 3 6
[2,] 1 5 7
[3,] 2 11 4

with sum 47.