Double Twin Primes
Double Twin 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.
Definition
Let (p1,p2) and (p3,p4) be twin primes where p3 - p2 = 4.
Such primes called Double Twin Primes
Example
[5,7,11,13]
Task
Find and show here all Double Twin Primes under 1000.
- See also
ALGOL 68
BEGIN # find some sequences of primes where the gaps between the elements #
# are 2, 4, 2 - i.e., n, n+2, n+6 and n+8 are all prime #
PR read "primes.incl.a68" PR # include prime utilities #
[]BOOL prime = PRIMESIEVE 1 000;
INT count := 0;
INT p := 3; # 2 cannot be a twin prime, so start with 3 #
WHILE p <= UPB prime - 8 DO
BOOL is double twin := FALSE;
IF prime[ p ] THEN
IF prime[ p + 2 ] THEN
IF prime[ p + 6 ] THEN
IF prime[ p + 8 ] THEN
count +:= 1;
is double twin := TRUE;
print( ( "["
, whole( p, -4 ), whole( p + 2, -4 )
, whole( p + 6, -4 ), whole( p + 8, -4 )
, " ]"
, newline
)
)
FI
FI
FI
FI;
p +:= IF is double twin THEN 6 ELSE 2 FI
OD;
print( ( "Found ", whole( count, 0 ), " double twin primes below ", whole( UPB prime, 0 ), newline ) )
END- Output:
[ 5 7 11 13 ] [ 11 13 17 19 ] [ 101 103 107 109 ] [ 191 193 197 199 ] [ 821 823 827 829 ] Found 5 double twin primes beflow 1000
Arturo
r: range .step: 2 1 1000
r | map 'x -> @[x x+2 x+6 x+8]
| select => [every? & => prime?]
| loop => print
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
BASIC
BASIC256
#include "isPrime.kbs"
num = 3
while num < 992
if isPrime(num) then
if isPrime(num+2) then
if isPrime(num+6) then
if isPrime(num+8) then print num; " "; num+2; " "; num+6; " "; num+8
end if
end if
end if
num += 2
end while
end
- Output:
Same as FreeBASIC entry.
Gambas
Public Sub Main()
Dim num As Integer = 3
Do
If isPrime(num) Then
If isPrime(num + 2) Then
If isPrime(num + 6) Then
If isPrime(num + 8) Then Print num; " "; num + 2; " "; num + 6; " "; num + 8
End If
End If
End If
num += 2
Loop Until num > 992
End
Public Sub isPrime(ValorEval As Long) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Long = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
Wend
Return True
End Function
- Output:
Same as FreeBASIC entry.
PureBasic
Procedure.b isPrime(v.i)
If v <= 1 : ProcedureReturn #False
ElseIf v < 4 : ProcedureReturn #True
ElseIf v % 2 = 0 : ProcedureReturn #False
ElseIf v < 9 : ProcedureReturn #True
ElseIf v % 3 = 0 : ProcedureReturn #False
Else
Protected r = Round(Sqr(v), #PB_Round_Down)
Protected f = 5
While f <= r
If v % f = 0 Or v % (f + 2) = 0
ProcedureReturn #False
EndIf
f + 6
Wend
EndIf
ProcedureReturn #True
EndProcedure
OpenConsole()
num.I = 3
While num < 992
If isPrime(num):
If isPrime(num+2):
If isPrime(num+6):
If isPrime(num+8):
PrintN(Str(num) + " " + Str(num+2) + " " + Str(num+6) + " " + Str(num+8))
EndIf
EndIf
EndIf
EndIf
num + 2
Wend
Input()
CloseConsole();
- Output:
Same as FreeBASIC entry.
Run BASIC
function isPrime(n)
if n < 2 then isPrime = 0 : goto [exit]
if n = 2 then isPrime = 1 : goto [exit]
if n mod 2 = 0 then isPrime = 0 : goto [exit]
isPrime = 1
for i = 3 to int(n^.5) step 2
if n mod i = 0 then isPrime = 0 : goto [exit]
next i
[exit]
end function
num = 3
while num < 992
if isPrime(num) then
if isPrime(num+2) then
if isPrime(num+6) then
if isPrime(num+8) then print num; " "; num+2; " "; num+6; " "; num+8
end if
end if
end if
num = num + 2
wend
end
- Output:
Same as FreeBASIC entry.
Tiny BASIC
REM Rosetta Code problem: https://rosettacode.org/wiki/Double_Twin_Primes
REM by Jjuanhdez, 03/2023
LET I = 3
10 LET X = I
GOSUB 100
IF Z = 1 THEN LET X = I + 2
IF Z = 1 THEN GOSUB 100
IF Z = 1 THEN LET X = I + 6
IF Z = 1 THEN GOSUB 100
IF Z = 1 THEN LET X = I + 8
IF Z = 1 THEN GOSUB 100
IF Z = 1 THEN PRINT I, " ", I + 2, " ", I + 6, " ", I + 8
LET I = I + 2
IF I > 992 THEN GOTO 20
GOTO 10
20 END
100 REM is X a prime? Z=1 for yes, 0 for no
LET Z = 1
IF X = 3 THEN RETURN
IF X = 2 THEN RETURN
LET A = 1
110 LET A = A + 1
IF (X / A) * A = X THEN GOTO 120
IF A * A <= X THEN GOTO 110
RETURN
120 LET Z = 0
RETURN
Same as FreeBASIC entry.
XBasic
PROGRAM "DoubleTwinPrimes"
VERSION "0.0000"
DECLARE FUNCTION Entry ()
INTERNAL FUNCTION ISPrime(n%%)
FUNCTION Entry ()
num%% = 3
DO
IF ISPrime(num%%) THEN
IF ISPrime(num%%+2) THEN
IF ISPrime(num%%+6) THEN
IF ISPrime(num%%+8) THEN
PRINT num%%; num%%+2; num%%+6; num%%+8
ENDIF
ENDIF
ENDIF
ENDIF
num%% = num%% + 2
LOOP UNTIL num%% > 992
END FUNCTION
FUNCTION ISPrime(n%%)
IF n%% < 2 THEN RETURN $$FALSE
IF n%% MOD 2 = 0 THEN RETURN n%% = 2
IF n%% MOD 3 = 0 THEN RETURN n%% = 3
d%% = 5
DO WHILE d%% * d%% <= n%%
IF n%% MOD d%% = 0 THEN RETURN $$FALSE ELSE d%% = d%% + 2
LOOP
RETURN $$TRUE
END FUNCTION
END PROGRAM
- Output:
Same as BASIC256 entry.
Yabasic
//import isPrime
num = 3
repeat
if isPrime(num) if isPrime(num+2) if isPrime(num+6) if isPrime(num+8) print num, " ", num+2, " ", num+6, " ", num+8
num = num + 2
until num > 992
end- Output:
Same as FreeBASIC entry.
C
#include <stdio.h>
#include <stdbool.h>
bool isPrime(int n) {
if (n < 2) return false;
if (n%2 == 0) return n == 2;
if (n%3 == 0) return n == 3;
int d = 5;
while (d*d <= n) {
if (n%d == 0) return false;
d += 2;
if (n%d == 0) return false;
d += 4;
}
return true;
}
int main() {
printf("Double twin primes under 1,000:\n");
for (int i = 3; i < 992; i+=2) {
if (isPrime(i) && isPrime(i+2) && isPrime(i+6) && isPrime(i+8)) {
printf("%4d %4d %4d %4d\n", i, i+2, i+6, i+8);
}
}
return 0;
}
- Output:
Double twin primes under 1,000: 5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
Dart
import 'dart:math';
void main() {
for (int num = 3; num < 992; num += 2) {
if (isPrime(num) &&
isPrime(num + 2) &&
isPrime(num + 6) &&
isPrime(num + 8)) {
print("$num ${num + 2} ${num + 6} ${num + 8}");
}
}
}
bool isPrime(int n) {
if (n <= 1) return false;
if (n == 2) return true;
for (int i = 2; i <= sqrt(n); ++i) {
if (n % i == 0) return false;
}
return true;
}
- Output:
Same as FreeBASIC entry.
Delphi
Uses standard TList as FIFO to hold and test groups of four sequentail prime numbers.
function IsPrime(N: integer): boolean;
{Fast, optimised prime test}
var I,Stop: integer;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function GetNextPrime(var Start: integer): integer;
{Get the next prime number after Start}
{Start is passed by "reference," so the
{original variable is incremented}
begin
repeat Inc(Start)
until IsPrime(Start);
Result:=Start;
end;
procedure ShowDoubleTwinPrimes(Memo: TMemo);
{Find sets of four primes P1,P2,P3,P4, where}
{P2-P1=2 P4-P3=2 and P3-P2=4 }
{Use TList as FIFO to test all four-prime combinations}
var LS: TList;
var Start: integer;
begin
LS:=TList.Create;
try
Start:=0;
while true do
begin
{Put four primes in the list}
repeat LS.Add(Pointer(GetNextPrime(Start)))
until LS.Count=4;
if Integer(LS[3])>=1000 then break;
{Test if they are double twin prime}
if (Integer(LS[1])-Integer(LS[0])=2) and
(Integer(LS[3])-Integer(LS[2])=2) and
(Integer(LS[2])-Integer(LS[1])=4) then
begin
{Display the result}
Memo.Lines.Add(IntToStr(Integer(LS[0]))+' '+
IntToStr(Integer(LS[1]))+' '+
IntToStr(Integer(LS[2]))+' '+
IntToStr(Integer(LS[3])));
end;
{Delete the first prime}
LS.Delete(0);
end;
finally LS.Free; end;
end;
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
FreeBASIC
#include "isprime.bas"
Dim As Uinteger num = 3
Do
If isPrime(num) Then
If isPrime(num+2) Then
If isPrime(num+6) Then
If isPrime(num+8) Then Print num; " "; num+2; " "; num+6; " "; num+8
End If
End If
End If
num += 2
Loop Until num > 992
Sleep
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
FutureBasic
local fn IsPrime( n as long ) as BOOL
long i
BOOL result = YES
if ( n < 2 ) then result = NO : exit fn
for i = 2 to n + 1
if ( i * i <= n ) and ( n mod i == 0 )
result = NO : exit fn
end if
next
end fn = result
local fn DoubleTwinPrimes( limit as long )
NSUInteger num = 3
printf @"Double twin primes < %ld:", limit
do
if fn IsPrime( num )
if fn IsPrime( num + 2 )
if fn IsPrime( num + 6 )
if fn IsPrime( num + 8 ) then printf @"%4lu%7lu%7lu%7lu", num, num + 2, num + 6, num + 8
end if
end if
end if
num += 2
until ( num > limit )
end fn
fn DoubleTwinPrimes( 2000 )
HandleEvents- Output:
Double twin primes < 2000: 5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829 1481 1483 1487 1489 1871 1873 1877 1879
Go
package main
import (
"fmt"
"rcu"
)
func main() {
p := rcu.Primes(1000)
fmt.Println("Double twin primes under 1,000:")
for i := 1; i < len(p)-3; i++ {
if p[i+1]-p[i] == 2 && p[i+2]-p[i+1] == 4 && p[i+3]-p[i+2] == 2 {
fmt.Printf("%4d\n", p[i:i+4])
}
}
}
- Output:
Double twin primes under 1,000: [ 5 7 11 13] [ 11 13 17 19] [ 101 103 107 109] [ 191 193 197 199] [ 821 823 827 829]
J
_6 _4 0 2+/~(#~ 0,4=2-~/\])p:~.,0 1+/~/I.2=2 -~/\ i.&.(p:inv) 1000
5 7 11 13
11 13 17 19
101 103 107 109
191 193 197 199
821 823 827 829
Breaking this down:
primes=: i.&.(p:inv) 1000
twinprimes=: p:~.,0 1+/~/I.2=2 -~/\ primes
doubletwinprimes=: _6 _4 0 2+/~(#~ 0,4=2-~/\])
The first two expressions rely on the primitive p: which translates between the index of a prime number and the prime itself. The final expression instead filters the remaining primes (because the sequence of primes which was its argument had already been filtered enough to have made indices into that sequence into relevant information which was not worth recalculating).
jq
Also works with gojq, the Go implementation of jq
# Input: a positive integer
# Output: an array, $a, of length .+1 such that
# $a[$i] is $i if $i is prime, and false otherwise.
def primeSieve:
# erase(i) sets .[i*j] to false for integral j > 1
def erase(i):
if .[i] then
reduce (range(2*i; length; i)) as $j (.; .[$j] = false)
else .
end;
(. + 1) as $n
| (($n|sqrt) / 2) as $s
| [null, null, range(2; $n)]
| reduce (2, 1 + (2 * range(1; $s))) as $i (.; erase($i)) ;
def double_twin_primes($n):
[$n|primeSieve|range(0;length) as $i | select(.[$i]) | $i] as $p
| range(1; $p|length-3) as $i
| select( ($p[$i+1] - $p[$i]) == 2 and ($p[$i+2] - $p[$i+1]) == 4 and ($p[$i+3] - $p[$i+2]) == 2 )
| [$p[$i, $i+1, $i+2, $i+3]] ;
"Double twin primes under 1,000:",
double_twin_primes(1000)- Output:
Double twin primes under 1,000: [5,7,11,13] [11,13,17,19] [101,103,107,109] [191,193,197,199] [821,823,827,829]
Julia
using Primes
using Printf
function printdt(N)
@printf("Double twin primes under 1,000:\n")
for i in 3:2:N-8
if isprime(i) && isprime(i+2) && isprime(i+6) && isprime(i+8)
@printf("%4d %4d %4d %4d\n", i, i+2, i+6, i+8)
end
end
end
printdt(1000)
- Output:
Same as C example.
Nim
import std/strformat
func isPrime(n: Positive): bool =
if n < 2: return false
if (n and 1) == 0: return n == 2
if n mod 3 == 0: return n == 3
var k = 5
var delta = 2
while k * k <= n:
if n mod k == 0: return false
inc k, delta
delta = 6 - delta
result = true
echo "Double twin primes under 1000:"
for n in countup(3, 991, 2):
if isPrime(n) and isPrime(n + 2) and isPrime(n + 6) and isPrime(n + 8):
echo &"({n:>3}, {n+2:>3}, {n+6:>3}, {n+8:>3})"
- Output:
( 5, 7, 11, 13) ( 11, 13, 17, 19) (101, 103, 107, 109) (191, 193, 197, 199) (821, 823, 827, 829)
Perl
use v5.36;
use ntheory 'is_prime';
sub dt ($p) { map { $p + $_ } <0 2 6 8> }
for my $n (1..1000) { say "@{[dt $n]}" if 4 == +(grep { is_prime $_ } dt $n) }
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
Phix
with javascript_semantics sequence p = get_primes_le(1000) for i=1 to length(p)-3 do if p[i+3]-p[i]=8 and p[i+2]-p[i]!=4 then printf(1,"%s\n",join(p[i..i+3],fmt:="%4d")) end if end for
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
Python
#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
if __name__ == "__main__":
num = 3
while num <= 1000:
if isPrime(num):
if isPrime(num+2):
if isPrime(num+6):
if isPrime(num+8):
print(num, num+2, num+6, num+8, sep="\t")
num += 2
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
Quackery
isprime is defined at Primality by trial division#Quackery.
[ 992 times
[ i^ isprime while
i^ 2 + isprime while
i^ 6 + isprime while
i^ 8 + isprime while
i^ i^ 2 + i^ 6 + i^ 8 +
3 times join echo cr ] ]- Output:
[ 5 7 11 13 ] [ 11 13 17 19 ] [ 101 103 107 109 ] [ 191 193 197 199 ] [ 821 823 827 829 ]
Raku
Cousin twin primes:
sub dt { $^p, $p+2, $p+6, $p+8 }
.&dt.say for (^1000).grep: { all .&dt».is-prime };
- Output:
(5 7 11 13) (11 13 17 19) (101 103 107 109) (191 193 197 199) (821 823 827 829)
Ring
see "working..." + nl
P = []
limit = 1000
for n =1 to limit
if isP(n)
add(P,n)
ok
next
lenP = len(P)-3
for m = 1 to lenP
if isP(P[m]) AND isP(P[m+1]) AND isP(P[m+2]) AND isP(P[m+3])
if (P[m+1] - P[m] = 2) AND (P[m+2] - P[m+1] = 4) AND (P[m+3] - P[m+2] = 2)
see " " + P[m]+ " " + P[m+1] + " " + P[m+2] + " " + P[m+3] + nl
ok
ok
next
see "done..." + nl
func isP num
if (num <= 1) return 0 ok
if (num % 2 = 0 AND num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1- Output:
works... 5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829 done...
RPL
« 2 { }
WHILE OVER 1000 < REPEAT
OVER { 2 6 8 } ADD
IF DUP ISPRIME? ΠLIST
THEN PICK3 SWAP + 1 →LIST +
ELSE DROP END
SWAP NEXTPRIME SWAP
END NIP
» 'TASK' STO
- Output:
1: {{5 7 11 13} {11 13 17 19} {101 103 107 109} {191 193 197 199} {821 823 827 829}}
Ruby
require 'prime'
res = Prime.each(1000).each_cons(4).select do |p1, p2, p3, p4|
p1+2 == p2 && p2+4 == p3 && p3+2 == p4
end
res.each{|slice| puts slice.join(", ")}
- Output:
5, 7, 11, 13 11, 13, 17, 19 101, 103, 107, 109 191, 193, 197, 199 821, 823, 827, 829
Sidef
1000.primes.each_cons(4, {|*a|
if (a.diffs == [2, 4, 2]) {
say a
}
})
- Output:
[5, 7, 11, 13] [11, 13, 17, 19] [101, 103, 107, 109] [191, 193, 197, 199] [821, 823, 827, 829]
V (Vlang)
import math
fn main() {
limit := 1000
mut parr := []int{}
for n in 1..limit {
if is_prime(n) {parr << n}
}
for m in 1..parr.len - 3 {
if is_prime(parr[m]) && is_prime(parr[m + 1]) && is_prime(parr[m + 2]) && is_prime(parr[m + 3]) {
if parr[m + 1] - parr[m] == 2 && parr[m + 2] - parr[m + 1] == 4 && parr[m + 3] - parr[m + 2] == 2 {
println("${parr[m]} ${parr[m + 1]} ${parr[m + 2]} ${parr[m + 3]}")
}
}
}
}
fn is_prime(num i64) bool {
if num <= 1 {return false}
if num % 2 == 0 && num != 2 {return false}
for idx := 3; idx <= math.floor(num / 2) - 1; idx += 2 {
if num % idx == 0 {return false}
}
return true
}
- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
Wren
import "./math" for Int
import "./fmt" for Fmt
var p = Int.primeSieve(1000)
System.print("Double twin primes under 1,000:")
for (i in 1...p.count-3) {
if (p[i+1] - p[i] == 2 && p[i+2] - p[i+1] == 4 && p[i+3] - p[i+2] == 2) {
Fmt.aprint(p[i..i+3], 4, 0, "")
}
}
- Output:
Double twin primes under 1,000: 5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
XPL0
func IsPrime(N); \Return 'true' if odd N is prime
int N, D;
[for D:= 3 to sqrt(N) do
[if rem(N/D) = 0 then return false;
D:= D+1;
];
return true;
];
int N;
[N:= 3;
repeat if IsPrime(N) then
if IsPrime(N+2) then
if IsPrime(N+6) then
if IsPrime(N+8) then
[IntOut(0, N); ChOut(0, ^ );
IntOut(0, N+2); ChOut(0, ^ );
IntOut(0, N+6); ChOut(0, ^ );
IntOut(0, N+8); CrLf(0);
];
N:= N+2;
until N >= 1000-8;
]- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829