Probably an interesting question is why it seems that with base $2$ instead of $10$ and the same procedure, we get large primes: (Notice that for $d=2$ the starting number $20$ gets a prime).

    def ff(n,d=10):
        ll = []
        for p in sorted(prime_divisors(n)):
            dd = Integer(p).digits(d)
            dd.reverse()
            ll.extend(dd)
            if valuation(n,p)>1:
                dd = Integer(valuation(n,p)).digits(d)
                dd.reverse()
                ll.extend(dd)
        return sum(ll[len(ll)-1-i]*d**i for i in range(len(ll)))
    
    def iter_ff(n,k,d):
        if k==0:
            return n
        else:
            return ff(iter_ff(n,k-1,d),d)
    
    x = 2**2*5       
    while not is_prime(Integer(x)):
        x = ff(x,d=2)
        print(x)    
        
    maxIter = 55    
    for d in range(2,11):
         for n in range(2,100):
            x = n
            i = 0
            while not is_prime(Integer(x)) and i < maxIter:
                x = ff(x,d=d)
                print("base = ",d,"starting number = ",n,"current number = ",x,"iteration count = ", i+1)
                i+=1
            #print(d,n,iter_ff(n,k,d),is_prime(Integer(iter_ff(n,k,d))))
    
            
Output:

    85
    177
    251
    base =  2 starting number =  4 current number =  10 iteration count =  1
    base =  2 starting number =  4 current number =  21 iteration count =  2
    base =  2 starting number =  4 current number =  31 iteration count =  3
    base =  2 starting number =  6 current number =  11 iteration count =  1
    base =  2 starting number =  8 current number =  11 iteration count =  1
    base =  2 starting number =  9 current number =  14 iteration count =  1
    base =  2 starting number =  9 current number =  23 iteration count =  2
    base =  2 starting number =  10 current number =  21 iteration count =  1
    base =  2 starting number =  10 current number =  31 iteration count =  2
    base =  2 starting number =  12 current number =  43 iteration count =  1
    base =  2 starting number =  14 current number =  23 iteration count =  1
    base =  2 starting number =  15 current number =  29 iteration count =  1
    base =  2 starting number =  16 current number =  20 iteration count =  1
    base =  2 starting number =  16 current number =  85 iteration count =  2
    base =  2 starting number =  16 current number =  177 iteration count =  3
    base =  2 starting number =  16 current number =  251 iteration count =  4
    base =  2 starting number =  18 current number =  46 iteration count =  1
    base =  2 starting number =  18 current number =  87 iteration count =  2
    base =  2 starting number =  18 current number =  125 iteration count =  3
    base =  2 starting number =  18 current number =  23 iteration count =  4
    base =  2 starting number =  20 current number =  85 iteration count =  1
    base =  2 starting number =  20 current number =  177 iteration count =  2
    base =  2 starting number =  20 current number =  251 iteration count =  3
    base =  2 starting number =  21 current number =  31 iteration count =  1
    base =  2 starting number =  22 current number =  43 iteration count =  1
    base =  2 starting number =  24 current number =  47 iteration count =  1
    base =  2 starting number =  25 current number =  22 iteration count =  1
    base =  2 starting number =  25 current number =  43 iteration count =  2
    base =  2 starting number =  26 current number =  45 iteration count =  1
    base =  2 starting number =  26 current number =  117 iteration count =  2
    base =  2 starting number =  26 current number =  237 iteration count =  3
    base =  2 starting number =  26 current number =  463 iteration count =  4
    base =  2 starting number =  27 current number =  15 iteration count =  1
    base =  2 starting number =  27 current number =  29 iteration count =  2
    base =  2 starting number =  28 current number =  87 iteration count =  1
    base =  2 starting number =  28 current number =  125 iteration count =  2
    base =  2 starting number =  28 current number =  23 iteration count =  3
    base =  2 starting number =  30 current number =  93 iteration count =  1
    base =  2 starting number =  30 current number =  127 iteration count =  2
    base =  2 starting number =  32 current number =  21 iteration count =  1
    base =  2 starting number =  32 current number =  31 iteration count =  2
    base =  2 starting number =  33 current number =  59 iteration count =  1
    base =  2 starting number =  34 current number =  81 iteration count =  1
    base =  2 starting number =  34 current number =  28 iteration count =  2
    base =  2 starting number =  34 current number =  87 iteration count =  3
    base =  2 starting number =  34 current number =  125 iteration count =  4
    base =  2 starting number =  34 current number =  23 iteration count =  5
    base =  2 starting number =  35 current number =  47 iteration count =  1
    base =  2 starting number =  36 current number =  174 iteration count =  1
    base =  2 starting number =  36 current number =  381 iteration count =  2
    base =  2 starting number =  36 current number =  511 iteration count =  3 
    base =  2 starting number =  36 current number =  969 iteration count =