Cubic special primes: Difference between revisions
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Revision as of 15:19, 2 April 2021
- Task
n is smallest prime such that the difference of successive terms are the smallest cubics of positive integers,
where n < 15000.
F#
<lang fsharp> // Cubic Special Primes: Nigel Galloway. March 30th., 2021 let fN=let N=[for n in [0..25]->n*n*n] in let mutable n=2 in (fun g->match List.contains(g-n)N with true->n<-g; true |_->false) primes32()|>Seq.takeWhile((>)16000)|>Seq.filter fN|>Seq.iter(printf "%d "); printfn "" </lang>
- Output:
2 3 11 19 83 1811 2027 2243 2251 2467 2531 2539 3539 3547 4547 5059 10891 12619 13619 13627 13691 13907 14419
Go
<lang go>package main
import (
"fmt" "math"
)
func sieve(limit int) []bool {
limit++
// True denotes composite, false denotes prime.
c := make([]bool, limit) // all false by default
c[0] = true
c[1] = true
// no need to bother with even numbers over 2 for this task
p := 3 // Start from 3.
for {
p2 := p * p
if p2 >= limit {
break
}
for i := p2; i < limit; i += 2 * p {
c[i] = true
}
for {
p += 2
if !c[p] {
break
}
}
}
return c
}
func isCube(n int) bool {
s := int(math.Cbrt(float64(n))) return s*s*s == n
}
func commas(n int) string {
s := fmt.Sprintf("%d", n)
if n < 0 {
s = s[1:]
}
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
if n >= 0 {
return s
}
return "-" + s
}
func main() {
c := sieve(14999)
fmt.Println("Cubic special primes under 15,000:")
fmt.Println(" Prime1 Prime2 Gap Cbrt")
lastCubicSpecial := 3
gap := 1
count := 1
fmt.Printf("%7d %7d %6d %4d\n", 2, 3, 1, 1)
for i := 5; i < 15000; i += 2 {
if c[i] {
continue
}
gap = i - lastCubicSpecial
if isCube(gap) {
cbrt := int(math.Cbrt(float64(gap)))
fmt.Printf("%7s %7s %6s %4d\n", commas(lastCubicSpecial), commas(i), commas(gap), cbrt)
lastCubicSpecial = i
count++
}
}
fmt.Println("\n", count+1, "such primes found.")
}</lang>
- Output:
Same as Wren example.
Julia
<lang julia>using Primes
function cubicspecialprimes(N = 15000)
pmask = primesmask(1, N)
cprimes, maxidx = [2], isqrt(N)
while (n = cprimes[end]) < N
for i in 1:maxidx
q = n + i * i * i
if q > N
return cprimes
elseif pmask[q] # got next qprime
push!(cprimes, q)
break
end
end
end
end
println("Cubic special primes < 15000:") foreach(p -> print(rpad(p[2], 6), p[1] % 10 == 0 ? "\n" : ""), enumerate(cubicspecialprimes()))
</lang>
- Output:
Cubic special primes < 16000: 2 3 11 19 83 1811 2027 2243 2251 2467 2531 2539 3539 3547 4547 5059 10891 12619 13619 13627 13691 13907 14419
Phix
See Quadrat_Special_Primes#Phix
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
REXX
<lang rexx>/*REXX program finds the smallest primes such that the difference of successive terms */ /*───────────────────────────────────────────────────── are the smallest cubic numbers. */ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 15000 /* " " " " " " */ if cols== | cols=="," then cols= 10 /* " " " " " " */ call genP /*build array of semaphores for primes.*/ w= 10 /*width of a number in any column. */
@cbp= 'the smallest primes < ' commas(hi) " such that the" ,
'difference of successive terma are the smallest cubic numbers'
if cols>0 then say ' index │'center(@cbp , 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') cbp= 0; idx= 1 /*initialize number of cbp and index.*/ op= 1 $= /*a list of nice primes (so far). */
do j=0 by 0
do k=1 until !.np; np= op + k**3 /*find the next square + oldPrime.*/
if np>= hi then leave j /*Is newPrime too big? Then quit.*/
end /*k*/
cbp= cbp + 1 /*bump the number of cbp's. */
op= np /*assign the newPrime to the oldPrime*/
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(np) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a nice prime ──► list, allow big#*/
if cbp//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say say 'Found ' commas(cbp) " of " @cbp exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: !.= 0 /*placeholders for primes (semaphores).*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; s.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 to hi /*find odd primes from here on. */
parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
/* [↑] the above five lines saves time*/
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</lang>
- output when using the default inputs:
index │ the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 2 3 11 19 83 1,811 2,027 2,243 2,251 2,467 11 │ 2,531 2,539 3,539 3,547 4,547 5,059 10,891 12,619 13,619 13,627 21 │ 13,691 13,907 14,419 Found 23 of the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers
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 Cbrt" + nl for n = 1 to Len(Primes)-1
diff = Primes[n+1] - Primes[n]
for m = 1 to diff
if pow(m,3) = diff
cbrt = m
exit
ok
next
see ""+ Primes[n] + " " + Primes[n+1] + " " + diff + " " + cbrt + 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 Cbrt 2 3 1 1 3 11 8 2 11 19 8 2 19 83 64 4 83 1811 1728 12 1811 2027 216 6 2027 2243 216 6 2243 2251 8 2 2251 2467 216 6 2467 2531 64 4 2531 2539 8 2 2539 3539 1000 10 3539 3547 8 2 3547 4547 1000 10 4547 5059 512 8 5059 10891 5832 18 10891 12619 1728 12 12619 13619 1000 10 13619 13627 8 2 13627 13691 64 4 13691 13907 216 6 13907 14419 512 8 Found 23 of the smallest primes < 15,000 such that the difference of successive terma are the smallest cubic numbers done...
Wren
<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.