The negative order integer challenge, but it's Prime Time!

Processing, 161 bytes

int p(int n){for(int k=1;++k<=sqrt(n);)if(n%k<1)return 0;return 1;}void t(int n){for(int i=1,j;i<=n;i++){if(p(i)<1)continue;for(j=i;j>0;j--)print(p(j)<1?"":j);}}

One function does the primality checking, the other does the printing. Call it by t(7)

Ungolfed

The first function does the primality checking. It returns an int instead of a boolean since this way more bytes are saved. (int instead of boolean, 0 instead of false, 1 instead of true)

int Q103891p(int n){
  for(int k=1;++k<=sqrt(n);)
    if(n%k<1)return 0;
  return 1;
}

The second function prints out the string. It iterates through every number, if it is not a prime, skip to the next iteration. If it is a prime, it continues down to the printing inside another for-loop. Again, if the number is prime, then we print it, otherwise not.

void Q103891(int n){
  for(int i=1,j;i<=n;i++){
    if(p(i)<1)continue;
    for(j=i;j>0;j--)
      print(p(j)<1?"":j);
  }
}

Jelly, 12 bytes

ÆR;@1
ÇÇ€UVV

Try it online!

If it hadn't been for 1s at all, my code would have just been ÆRÆRUVV for 7 bytes.

Enhanced explanation:

ÇÇ€UVV Main link. Arguments: z.
Ç      Run link1 on z.
 ǀ    Run link1 on z's elements.
   U   Reverse z's elements.
    V  Flatten z.
     V Concatenate z's elements.

ÆR;@1 Link 1. Arguments: z.
ÆR    Range of primes [2..z].
    1 Integer: 1.
  ;@  Concatenate x to y.

The Irish guy (called Dennis?) somehow outgolfed me lol.

Jelly, 9 bytes

ÆR1;;\UFV

Try it online!

How it works

ÆR1;;\UFV  Main link. Argument: n

ÆR         Prime range; yield all primes up to n.
  1;       Prepend the "prime" 1.
    ;\     Cumulative concatenation; yield all prefixes of the prime range.
      U    Upend; reverse each prefix.
       F   Flatten the resulting 2D array.
        V  Eval. This casts the integer array to string first, thus concatenating
           the integers.