Cubic special primes: Difference between revisions

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Found 23 of the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers
Found 23 of the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers
done...
done...
</pre>

=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<lang ecmascript>import "/math" for Int, Math
import "/fmt" for Fmt

var isCube = Fn.new { |n|
var c = Math.cbrt(n).round
return c*c*c == n
}

var primes = Int.primeSieve(14999)
System.print("Cubic special primes under 15,000:")
System.print(" Prime1 Prime2 Gap Cbrt")
var lastCubicSpecial = 3
var gap = 1
var count = 1
Fmt.print("$,7d $,7d $,6d $4d", 2, 3, 1, 1)
for (p in primes.skip(2)) {
gap = p - lastCubicSpecial
if (isCube.call(gap)) {
Fmt.print("$,7d $,7d $,6d $4d", lastCubicSpecial, p, gap, Math.cbrt(gap).round)
lastCubicSpecial = p
count = count + 1
}
}
System.print("\n%(count+1) such primes found.")</lang>

{{out}}
<pre>
Cubic special primes under 15,000:
Prime1 Prime2 Gap Cbrt
2 3 1 1
3 11 8 2
11 19 8 2
19 83 64 4
83 1,811 1,728 12
1,811 2,027 216 6
2,027 2,243 216 6
2,243 2,251 8 2
2,251 2,467 216 6
2,467 2,531 64 4
2,531 2,539 8 2
2,539 3,539 1,000 10
3,539 3,547 8 2
3,547 4,547 1,000 10
4,547 5,059 512 8
5,059 10,891 5,832 18
10,891 12,619 1,728 12
12,619 13,619 1,000 10
13,619 13,627 8 2
13,627 13,691 64 4
13,691 13,907 216 6
13,907 14,419 512 8

23 such primes found.
</pre>
</pre>

Revision as of 10:10, 29 March 2021

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...

Wren

Library: Wren-math
Library: Wren-fmt

<lang ecmascript>import "/math" for Int, Math import "/fmt" for Fmt

var isCube = Fn.new { |n| 

   var c = Math.cbrt(n).round
   return c*c*c == n

}

var primes = Int.primeSieve(14999) System.print("Cubic special primes under 15,000:") System.print(" Prime1 Prime2 Gap Cbrt") var lastCubicSpecial = 3 var gap = 1 var count = 1 Fmt.print("$,7d $,7d $,6d $4d", 2, 3, 1, 1) for (p in primes.skip(2)) { 

   gap = p - lastCubicSpecial
   if (isCube.call(gap)) {
       Fmt.print("$,7d $,7d $,6d $4d", lastCubicSpecial, p, gap, Math.cbrt(gap).round)
       lastCubicSpecial = p
       count = count + 1
   }

} System.print("\n%(count+1) such primes found.")</lang>

Output:
Cubic special primes under 15,000:
 Prime1  Prime2    Gap  Cbrt
      2       3      1    1
      3      11      8    2
     11      19      8    2
     19      83     64    4
     83   1,811  1,728   12
  1,811   2,027    216    6
  2,027   2,243    216    6
  2,243   2,251      8    2
  2,251   2,467    216    6
  2,467   2,531     64    4
  2,531   2,539      8    2
  2,539   3,539  1,000   10
  3,539   3,547      8    2
  3,547   4,547  1,000   10
  4,547   5,059    512    8
  5,059  10,891  5,832   18
 10,891  12,619  1,728   12
 12,619  13,619  1,000   10
 13,619  13,627      8    2
 13,627  13,691     64    4
 13,691  13,907    216    6
 13,907  14,419    512    8

23 such primes found.
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