Data commit

Task/Home-primes/00-META.yaml

@@ -0,0 +1,3 @@
+---
+from: http://rosettacode.org/wiki/Home_primes
+note: Prime Numbers

Task/Home-primes/00-TASK.txt

@@ -0,0 +1,43 @@
+In number theory, the '''home prime HP(n)''' of an integer '''n''' greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions.
+
+The traditional notation has the prefix "HP" and a postfix count of the number of iterations until the home prime is found (if the count is greater than 0), for instance HP4(2) === HP22(1) === 211 is the same as saying the home prime of 4 needs 2 iterations and is the same as the home prime of 22 which needs 1 iteration, and (both) resolve to 211, a prime.
+
+Prime numbers are their own home prime;
+
+So: 
+
+    HP2 = 2
+    
+    HP7 = 7
+
+If the integer obtained by concatenating increasing prime factors is not prime, iterate until you reach a prime number; the home prime.
+
+    HP4(2) = HP22(1) = 211
+    HP4(2) = 2 × 2 => 22; HP22(1) = 2 × 11 => 211; 211 is prime  
+    
+    HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773
+    HP10(4) = 2 × 5 => 25; HP25(3) = 5 × 5 => 55; HP55(2) = 5 × 11 => 511; HP511(1) = 7 × 73 => 773; 773 is prime  
+
+
+;Task
+
+* Find and show here, on this page, the home prime iteration chains for the integers 2 through 20 inclusive.
+
+
+;Stretch goal
+    
+* Find and show the iteration chain for 65.
+
+
+;Impossible goal
+
+* Show the the home prime for HP49.
+
+
+;See also
+
+;* [[oeis:A037274|OEIS:A037274 - Home primes for n >= 2]]
+;* [[oeis:A056938|OEIS:A056938 - Concatenation chain for HP49]]
+
+<br/>
+

Task/Home-primes/Factor/home-primes.factor

@@ -0,0 +1,21 @@
+USING: formatting kernel make math math.parser math.primes
+math.primes.factors math.ranges present prettyprint sequences
+sequences.extras ;
+
+: squish ( seq -- n ) [ present ] map-concat dec> ;
+
+: next ( m -- n ) factors squish ; inline
+
+: (chain) ( n -- ) [ dup prime? ] [ dup , next ] until , ;
+
+: chain ( n -- seq ) [ (chain) ] { } make ;
+
+: prime. ( n -- ) dup "HP%d = %d\n" printf ;
+
+: setup ( seq -- n s r ) unclip-last swap dup length 1 [a,b] ;
+
+: multi. ( n -- ) chain setup [ "HP%d(%d) = " printf ] 2each . ;
+
+: chain. ( n -- ) dup prime? [ prime. ] [ multi. ] if ;
+
+2 20 [a,b] [ chain. ] each

Task/Home-primes/Go/home-primes.go

@@ -0,0 +1,146 @@
+package main
+
+import (
+    "fmt"
+    "math/big"
+    "rcu"
+    "sort"
+)
+
+var zero = new(big.Int)
+var one = big.NewInt(1)
+var two = big.NewInt(2)
+var three = big.NewInt(3)
+var four = big.NewInt(4)
+var five = big.NewInt(5)
+var six = big.NewInt(6)
+
+// simple wheel based prime factors routine for BigInt
+func primeFactorsWheel(m *big.Int) []*big.Int {
+    n := new(big.Int).Set(m)
+    t := new(big.Int)
+    inc := []*big.Int{four, two, four, two, four, six, two, six}
+    var factors []*big.Int
+    for t.Rem(n, two).Cmp(zero) == 0 {
+        factors = append(factors, two)
+        n.Quo(n, two)
+    }
+    for t.Rem(n, three).Cmp(zero) == 0 {
+        factors = append(factors, three)
+        n.Quo(n, three)
+    }
+    for t.Rem(n, five).Cmp(zero) == 0 {
+        factors = append(factors, five)
+        n.Quo(n, five)
+    }
+    k := big.NewInt(7)
+    i := 0
+    for t.Mul(k, k).Cmp(n) <= 0 {
+        if t.Rem(n, k).Cmp(zero) == 0 {
+            factors = append(factors, new(big.Int).Set(k))
+            n.Quo(n, k)
+        } else {
+            k.Add(k, inc[i])
+            i = (i + 1) % 8
+        }
+    }
+    if n.Cmp(one) > 0 {
+        factors = append(factors, n)
+    }
+    return factors
+}
+
+func pollardRho(n *big.Int) *big.Int {
+    g := func(x, n *big.Int) *big.Int {
+        x2 := new(big.Int)
+        x2.Mul(x, x)
+        x2.Add(x2, one)
+        return x2.Mod(x2, n)
+    }
+    x, y, d := new(big.Int).Set(two), new(big.Int).Set(two), new(big.Int).Set(one)
+    t, z := new(big.Int), new(big.Int).Set(one)
+    count := 0
+    for {
+        x = g(x, n)
+        y = g(g(y, n), n)
+        t.Sub(x, y)
+        t.Abs(t)
+        t.Mod(t, n)
+        z.Mul(z, t)
+        count++
+        if count == 100 {
+            d.GCD(nil, nil, z, n)
+            if d.Cmp(one) != 0 {
+                break
+            }
+            z.Set(one)
+            count = 0
+        }
+    }
+    if d.Cmp(n) == 0 {
+        return new(big.Int)
+    }
+    return d
+}
+
+func primeFactors(m *big.Int) []*big.Int {
+    n := new(big.Int).Set(m)
+    var factors []*big.Int
+    lim := big.NewInt(1e9)
+    for n.Cmp(one) > 0 {
+        if n.Cmp(lim) > 0 {
+            d := pollardRho(n)
+            if d.Cmp(zero) != 0 {
+                factors = append(factors, primeFactorsWheel(d)...)
+                n.Quo(n, d)
+                if n.ProbablyPrime(10) {
+                    factors = append(factors, n)
+                    break
+                }
+            } else {
+                factors = append(factors, primeFactorsWheel(n)...)
+                break
+            }
+        } else {
+            factors = append(factors, primeFactorsWheel(n)...)
+            break
+        }
+    }
+    sort.Slice(factors, func(i, j int) bool { return factors[i].Cmp(factors[j]) < 0 })
+    return factors
+}
+
+func main() {
+    list := make([]int, 20)
+    for i := 2; i <= 20; i++ {
+        list[i-2] = i
+    }
+    list[19] = 65
+    for _, i := range list {
+        if rcu.IsPrime(i) {
+            fmt.Printf("HP%d = %d\n", i, i)
+            continue
+        }
+        n := 1
+        j := big.NewInt(int64(i))
+        h := []*big.Int{j}
+        for {
+            pf := primeFactors(j)
+            k := ""
+            for _, f := range pf {
+                k += fmt.Sprintf("%d", f)
+            }
+            j, _ = new(big.Int).SetString(k, 10)
+            h = append(h, j)
+            if j.ProbablyPrime(10) {
+                for l := n; l > 0; l-- {
+                    fmt.Printf("HP%d(%d) = ", h[n-l], l)
+                }
+                fmt.Println(h[n])
+                break
+            } else {
+                n++
+            }
+        }
+    }
+}

Task/Home-primes/J/home-primes.j

@@ -0,0 +1,7 @@
+step =: -.&' '&.":@q:
+hseq =: [,$:@step`(0&$)@.(1&p:)
+fmtHP =: (' is prime',~":@])`('HP',":@],'(',":@[,')'&[)@.(*@[)
+fmtlist =: [:;@}.[:,(<' = ')&,"0@(|.@i.@# fmtHP each [)
+printHP =: 0 0&$@stdout@(fmtlist@hseq,(10{a.)&[)
+printHP"0 [ 2}.i.21
+exit 0

Task/Home-primes/Julia/home-primes.julia

@@ -0,0 +1,21 @@
+using Primes
+
+function homeprimechain(n::BigInt)
+    isprime(n) && return [n]
+    concat = prod(string(i)^j for (i, j) in factor(n).pe)
+    return pushfirst!(homeprimechain(parse(BigInt, concat)), n)
+end
+homeprimechain(n::Integer) = homeprimechain(BigInt(n))
+
+function printHPiter(n, numperline = 4)
+    chain = homeprimechain(n)
+    len = length(chain)
+    for (i, ent) in enumerate(chain)
+        print(i < len ? "HP$ent" * "($(len - i)) = " * (i % numperline == 0 ? "\n" : "") : "$ent is prime.\n\n")
+    end
+end
+
+for i in [2:20; 65]
+   print("Home Prime chain for $i: ")
+   printHPiter(i)
+end

Task/Home-primes/Mathematica/home-primes.math

@@ -0,0 +1,5 @@
+ClearAll[HP, HPChain]
+HP[n_] := FromDigits[Catenate[IntegerDigits /@ Sort[Catenate[ConstantArray @@@ FactorInteger[n]]]]]
+HPChain[n_] := NestWhileList[HP, n, PrimeQ/*Not]
+Row[Prepend["Home prime chain for " <> ToString[#] <> ": "]@Riffle[HPChain[#], ", "]] & /@ Range[2, 20] // Column
+Row[Prepend["Home prime chain for 65: "]@Riffle[HPChain[65], ", "]]

Task/Home-primes/Nim/home-primes.nim

@@ -0,0 +1,93 @@
+import algorithm, sequtils, strformat, strutils
+import bignum
+
+let
+  Two = newInt(2)
+  Three = newInt(3)
+  Five = newInt(5)
+
+
+proc primeFactorsWheel(n: Int): seq[Int] =
+  const Inc = [4, 2, 4, 2, 4, 6, 2, 6]
+  var n = n
+  while (n mod 2).isZero:
+    result.add Two
+    n = n div 2
+  while (n mod 3).isZero:
+    result.add Three
+    n = n div 3
+  while (n mod 5).isZero:
+    result.add Five
+    n = n div 5
+  var k = 7
+  var i = 0
+  while k * k <= n:
+    if (n mod k).isZero:
+      result.add newInt(k)
+      n = n div k
+    else:
+      inc k, Inc[i]
+      i = (i + 1) and 7
+  if n > 1: result.add n
+
+
+func pollardRho(n : Int): Int =
+
+  func g(x, y: Int): Int = (x * x + 1) mod y
+
+  var x, y = newInt(2)
+  var z, d = newInt(1)
+  var count = 0
+  while true:
+    x = g(x, n)
+    y = g(g(y, n), n)
+    d = abs(x - y) mod n
+    z *= d
+    inc count
+    if count == 100:
+      d = gcd(z, n)
+      if d != 1: break
+      z = newInt(1)
+      count = 0
+  if d == n: return newInt(0)
+  result = d
+
+
+proc primeFactors(n: Int): seq[Int] =
+  var n = n
+  while n > 1:
+    if n > 100_000_000:
+      let d = pollardRho(n)
+      if not d.isZero:
+        result.add primeFactorsWheel(d)
+        n = n div d
+        if n.probablyPrime(25) != 0:
+          result.add n
+          break
+      else:
+        result.add primeFactorsWheel(n)
+        break
+    else:
+      result.add primeFactorsWheel(n)
+      break
+  result.sort()
+
+
+let list = toSeq(2..20) & 65
+for i in list:
+  if i in [2, 3, 5, 7, 11, 13, 17, 19]:
+    echo &"HP{i} = {i}"
+    continue
+  var n = 1
+  var j = newInt(i)
+  var h = @[j]
+  while true:
+    j = newInt(primeFactors(j).join())
+    h.add j
+    if j.probablyPrime(25) != 0:
+      for k in countdown(n, 1):
+        stdout.write &"HP{h[n-k]}({k}) = "
+      echo h[n]
+      break
+    else:
+      inc n

Task/Home-primes/Perl/home-primes.pl

@@ -0,0 +1,12 @@
+use strict;
+use warnings;
+use ntheory 'factor';
+
+for my $m (2..20, 65) {
+    my (@steps, @factors) = $m;
+    push @steps, join '_', @factors while (@factors = factor $steps[-1] =~ s/_//gr) > 1;
+    my $step = $#steps;
+    if ($step >= 1) { print 'HP' . $_ . "($step) = " and --$step or last for @steps }
+    else            { print "HP$m = " }
+    print "$steps[-1]\n";
+}

Task/Home-primes/Phix/home-primes.phix

@@ -0,0 +1,37 @@
+(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.0"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lastp</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">}</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
+     <span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
+         <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"_"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
+         <span style="color: #004080;">sequence</span> <span style="color: #000000;">rr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_pollard_rho</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rr</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"_"</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">niter</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">iter</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">niter</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"(%d)"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">niter</span><span style="color: #0000FF;">):</span><span style="color: #008000;">""</span><span style="color: #0000FF;">),</span>
+            <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">></span><span style="color: #000000;">0.1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">" ["</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"]"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"HP%d%s = "</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">iter</span><span style="color: #0000FF;">})</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">niter</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+         <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s%d %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
+     <span style="color: #008080;">else</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">niter</span> <span style="color: #008080;">do</span>
+             <span style="color: #000000;">niter</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
+             <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%sHP%s(%d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">niter</span><span style="color: #0000FF;">})</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
+                 <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
+                 <span style="color: #000000;">s</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'='</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+         <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s%s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
+ <span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)&</span><span style="color: #000000;">65</span><span style="color: #0000FF;">,</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
+<!--

Task/Home-primes/REXX/home-primes.rexx

@@ -0,0 +1,46 @@
+/*REXX program finds and displays the   home prime   of a range of positive integers.   */
+numeric digits 20                                /*ensure handling of larger integers.  */
+parse arg  LO HI .                               /*obtain optional arguments from the CL*/
+if LO=='' | LO=="," then LO=  2                  /*Not specified?  Then use the default.*/
+if HI=='' | HI=="," then HI= 20                  /* "     "         "   "   "     "     */
+@hpc= 'home prime chain for '                    /*a literal used in two SAY statements.*/
+                                 w= length(HI)   /*HI width, used for output alignment. */
+       do j=max(2, LO)  to HI                    /*find home primes for an integer range*/
+       pf= factr(j);             f= words(pf)    /*get prime factors; number of factors.*/
+       if f==1  then do;  say @hpc j": "  j  ' is prime.';  iterate;  end   /*J is prime*/
+       xxx.1= j                                  /*save  J  in the first array element. */
+                do n=2  until #==1               /*keep processing until we find a prime*/
+                xxx.n= space(pf, 0)              /*obtain factors of a concatenated p.f.*/
+                pf= factr(xxx.n);   #= words(pf) /*assign factors to PF;  # of factors. */
+                end   /*n*/
+       ee= n                                     /*save  EE  as the final (last) prime. */
+       n= n - 1;   z= n                          /*adjust N (for DO loop); assign N to Z*/
+       $=                                        /*nullify the string of   home primes. */
+                do m=1  for n                    /*build a list  ($)  of     "     "    */
+                $= $  'HP'xxx.m"("z') ─► '       /*concatenate to string of  "     "    */
+                z= z - 1                         /*decrease the index counter by unity. */
+                end   /*m*/                      /* [↑]  the index counter is decreasing*/
+
+       say @hpc right(j, w)":"   $   xxx.ee  ' is prime.'  /*show string of home primes.*/
+       end   /*n*/
+exit 0                                           /*stick a fork in it,  we're all done. */
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+factr: procedure;  parse arg x 1 d,$             /*set X, D  to argument 1;  $  to null.*/
+       if x==1  then return ''                   /*handle the special case of   X = 1.  */
+         do  while x//2==0; $= $ 2; x= x% 2; end /*append all the  2  factors of new  X.*/
+         do  while x//3==0; $= $ 3; x= x% 3; end /*   "    "   "   3     "     "  "   " */
+         do  while x//5==0; $= $ 5; x= x% 5; end /*   "    "   "   5     "     "  "   " */
+         do  while x//7==0; $= $ 7; x= x% 7; end /*   "    "   "   7     "     "  "   " */
+       q= 1;                              r= 0   /*R:  will be iSqrt(x).             ___*/
+         do  while q<=x; q=q*4; end              /*these two lines compute integer  √ X */
+         do  while q>1;  q=q%4; _= d-r-q; r= r%2; if _>=0  then do; d= _; r= r+q; end; end
+
+         do k=11  by 6  to r                     /*insure that  J  isn't divisible by 3.*/
+         parse var k  ''  -1  _                  /*obtain the last decimal digit of  K. */
+         if _\==5  then  do  while x//k==0;  $=$ k;  x=x%k;  end    /*maybe reduce by K.*/
+         if _ ==3  then iterate                  /*Is next  Y  is divisible by 5?  Skip.*/
+         y= k+2;         do  while x//y==0;  $=$ y;  x=x%y;  end    /*maybe reduce by Y.*/
+         end   /*k*/
+                                                 /* [↓]  The $ list has a leading blank.*/
+       if x==1  then return $                    /*Is residual=unity? Then don't append.*/
+                     return $ x                  /*return   $   with appended residual. */

Task/Home-primes/Raku/home-primes.raku

@@ -0,0 +1,24 @@
+use Prime::Factor;
+
+my $start = now;
+
+(flat 2..20, 65).map: -> $m {
+    my ($now, @steps, @factors) = now, $m;
+
+    @steps.push: @factors.join('_') while (@factors = prime-factors @steps[*-1].Int) > 1;
+
+    say (my $step = +@steps) > 1 ?? (@steps[0..*-2].map( { "HP$_\({--$step})" } ).join: ' = ') !! ("HP$m"),
+      " = ", @steps[*-1], "  ({(now - $now).fmt("%0.3f")} seconds)";
+}
+
+say "Total elapsed time: {(now - $start).fmt("%0.3f")} seconds\n";
+
+say 'HP49:';
+my ($now, @steps, @factors) = now, 49;
+my $step = 0;
+while (@factors = prime-factors @steps[*-1].Int) > 1 {
+    @steps.push: @factors.join('_');
+    say "HP{@steps[$step].Int}\(n - {$step++}) = ", @steps[*-1], "  ({(now - $now).fmt("%0.3f")} seconds)";
+    $now = now;
+    last if $step > 30;
+}

Task/Home-primes/Sidef/home-primes.sidef

@@ -0,0 +1,13 @@
+for n in (2..20, 65) {
+
+    var steps = []
+    var orig = n
+
+    for (var f = n.factor; true; f = n.factor) {
+        steps << f
+        n = Num(f.join)
+        break if n.is_prime
+    }
+
+    say ("HP(#{orig}) = ", steps.map { .join('_') }.join(' -> '))
+}

Task/Home-primes/Transd/home-primes.transd

@@ -0,0 +1,23 @@
+#lang transd
+
+MainModule: {
+    homePrime: (λ i BigLong()
+        (if (is-prime i) (lout "HP" i " = " i) continue)
+        (with n BigLong(i) ch Vector<BigLong>() st 1
+            (append ch n)
+            (while true
+                (= n (join (prime-factors n) ""))
+                (append ch n)
+                (if (is-probable-prime n 15)
+                    (for l in Range(in: ch 0 -1)  do
+                        (textout "HP" l "("(- (size ch) @idx 1) ") = "))
+                    (lout (back ch)) (ret)
+                else (+= st 1))
+            )
+        )
+    ),
+    _start: (λ
+        (for i in Range(2 21) do (homePrime BigLong(i)))
+        (homePrime BigLong(65))
+    )
+}

Task/Home-primes/Wren/home-primes-1.wren

@@ -0,0 +1,26 @@
+import "/math" for Int
+import "/big" for BigInt
+
+var list = (2..20).toList
+list.add(65)
+for (i in list) {
+    if (Int.isPrime(i)) {
+        System.print("HP%(i) = %(i)")
+        continue
+    }
+    var n = 1
+    var j = BigInt.new(i)
+    var h = [j]
+    while (true) {
+        var k = BigInt.primeFactors(j).reduce("") { |acc, f| acc + f.toString }
+        j = BigInt.new(k)
+        h.add(j)
+        if (j.isProbablePrime(2)) {
+            for (l in n...0) System.write("HP%(h[n-l])(%(l)) = ")
+            System.print(h[n])
+            break
+        } else {
+            n = n + 1
+        }
+    }
+}

Task/Home-primes/Wren/home-primes-2.wren

@@ -0,0 +1,28 @@
+/* home_primes_gmp.wren */
+
+import "./gmp" for Mpz
+import "./math" for Int
+
+var list = (2..20).toList
+list.add(65)
+for (i in list) {
+    if (Int.isPrime(i)) {
+        System.print("HP%(i) = %(i)")
+        continue
+    }
+    var n = 1
+    var j = Mpz.from(i)
+    var h = [j.copy()]
+    while (true) {
+        var k = Mpz.primeFactors(j).reduce("") { |acc, f| acc + f.toString }
+        j = Mpz.fromStr(k)
+        h.add(j)
+        if (j.probPrime(15) > 0) {
+            for (l in n...0) System.write("HP%(h[n-l])(%(l)) = ")
+            System.print(h[n])
+            break
+        } else {
+            n = n + 1
+        }
+    }
+}