Nice primes

Nice primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

1.   Take an integer n, greater than zero.
2.   sumn is sum of n's digits
3.   If sumn's lenght greater than 1 repeat the (2) for n = sumn
4.   Stop when sumn's length equal to 1

If n and sumn are prime then n is Nice prime
Let 500 < n < 1000

Example

       853 (prime)
       8 + 5 + 3 = 16
       1 + 6 = 7 (prime)

Factor

<lang factor>USING: math math.primes prettyprint sequences ;

digital-root ( m -- n ) 1 - 9 mod 1 + ;

500 1000 primes-between [ digital-root prime? ] filter .</lang>

Output:

V{
    509
    547
    563
    569
    587
    599
    601
    617
    619
    641
    653
    659
    673
    677
    691
    709
    727
    743
    761
    797
    821
    839
    853
    857
    887
    907
    911
    929
    941
    947
    977
    983
    997
}

Ring

<lang ring> load "stdlib.ring"

num = 0 limit1 = 500 limit2 = 1000

see "working..." + nl see "Nice numbers are:" + nl

for n = limit1 to limit2

   strn = string(n)
   while true
         sumn = 0
         for m = 1 to len(strn)
             sumn = sumn + number(strn[m])
         next
         if len(string(sumn)) = 1
            exit
         ok
         strn = string(sumn)
   end
   if isprime(n) and isprime(sumn)
      num = num + 1
      see "" + num + ": " + n + " sumn = " + sumn + nl
   ok

next

see "done..." + nl </lang>

Output:

working...
Nice numbers are:
1: 509 sumn = 5
2: 547 sumn = 7
3: 563 sumn = 5
4: 569 sumn = 2
5: 587 sumn = 2
6: 599 sumn = 5
7: 601 sumn = 7
8: 617 sumn = 5
9: 619 sumn = 7
10: 641 sumn = 2
11: 653 sumn = 5
12: 659 sumn = 2
13: 673 sumn = 7
14: 677 sumn = 2
15: 691 sumn = 7
16: 709 sumn = 7
17: 727 sumn = 7
18: 743 sumn = 5
19: 761 sumn = 5
20: 797 sumn = 5
21: 821 sumn = 2
22: 839 sumn = 2
23: 853 sumn = 7
24: 857 sumn = 2
25: 887 sumn = 5
26: 907 sumn = 7
27: 911 sumn = 2
28: 929 sumn = 2
29: 941 sumn = 5
30: 947 sumn = 2
31: 977 sumn = 5
32: 983 sumn = 2
33: 997 sumn = 7
done...