Cubic special primes

Cubic special 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.

Task

n   is smallest prime such that the difference of successive terms are the smallest cubics of positive integers, where     n   <   15000.

Raku

A two character difference from the Quadrat Special Primes entry. (And it could have been one.) <lang perl6>my @sqp = 2, -> $previous {

   my $next;
   for (1..∞).map: *³ {
       $next = $previous + $_;
       last if $next.is-prime;
   }
   $next

} … *;

say "{+$_} matching numbers:\n", $_».fmt('%5d').batch(7).join: "\n" given

   @sqp[^(@sqp.first: * > 15000, :k)];</lang>

Output:

23 matching numbers:
    2     3    11    19    83  1811  2027
 2243  2251  2467  2531  2539  3539  3547
 4547  5059 10891 12619 13619 13627 13691
13907 14419

Ring

<lang ring> load "stdlib.ring"

see "working..." + nl

Primes = [] limit1 = 50 oldPrime = 2 add(Primes,2)

for n = 1 to limit1

   nextPrime = oldPrime + pow(n,3)
   if isprime(nextPrime)
      n = 1
      add(Primes,nextPrime)
      oldPrime = nextPrime
   else
      nextPrime = nextPrime - oldPrime
   ok

next

see "prime1 prime2 Gap" + nl for n = 1 to Len(Primes)-1

   diff = Primes[n+1] - Primes[n]
   see ""+ Primes[n] + "      " + Primes[n+1] + "    " + diff + nl

next

see "Found " + Len(Primes) + " of the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers" + nl

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

Output:

working...
prime1 prime2 Gap
2      3    1
3      11    8
11      19    8
19      83    64
83      1811    1728
1811      2027    216
2027      2243    216
2243      2251    8
2251      2467    216
2467      2531    64
2531      2539    8
2539      3539    1000
3539      3547    8
3547      4547    1000
4547      5059    512
5059      10891    5832
10891      12619    1728
12619      13619    1000
13619      13627    8
13627      13691    64
13691      13907    216
13907      14419    512
Found 23 of the smallest primes < 15,000  such that the difference of successive terma are the smallest cubic numbers
done...