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.
ALGOL 68
Reusing some code from the Successive prime differences task.
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 #
PR read "rows.incl.a68" PR # include row (array) utilities #
# attempts to find patterns in the differences of primes and prints the results #
PROC try differences = ( []INT primes, []INT pattern, INT max prime )VOID:
BEGIN
INT pattern length = ( UPB pattern - LWB pattern ) + 1;
[ 1 : pattern length + 1 ]INT first; FOR i TO UPB first DO first[ i ] := 0 OD;
[ 1 : pattern length + 1 ]INT last; FOR i TO UPB last DO last[ i ] := 0 OD;
INT count := 0;
FOR p FROM LWB primes + pattern length TO UPB primes DO
BOOL matched := TRUE;
INT e pos := LWB pattern;
FOR e FROM p - pattern length TO p - 1
WHILE matched := primes[ e + 1 ] - primes[ e ] = pattern[ e pos ]
DO
e pos +:= 1
OD;
IF matched THEN
# found a matching sequence #
count +:= 1;
print( ( "[" ) );
SHOW primes[ p - pattern length : p ];
print( ( " ]", newline ) )
FI
OD;
print( ( "Found ", whole( count, 0 ), " prime sequences with differences: [" ) );
SHOW pattern;
print( ( " ] up to ", whole( max prime, 0 ) ) );
print( ( newline ) )
END # try differences # ;
INT max number = 1 000;
[]INT p list = EXTRACTPRIMESUPTO max number FROMPRIMESIEVE PRIMESIEVE max number;
try differences( p list, ( 2, 4, 2 ), max number )
END- Output:
[ 5 7 11 13 ] [ 11 13 17 19 ] [ 101 103 107 109 ] [ 191 193 197 199 ] [ 821 823 827 829 ] Found 5 prime sequences with differences: [ 2 4 2 ] up to 1000
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.
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
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 >= 1000-8
Sleep- Output:
5 7 11 13 11 13 17 19 101 103 107 109 191 193 197 199 821 823 827 829
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]
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.
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
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 "works..." + nl
primes = []
limit = 1000
for n =1 to limit
if isPrime(n)
add(primes,n)
ok
next
lenPrimes = len(primes)-3
for m = 1 to lenPrimes
if isPrime(primes[m]) and isPrime(primes[m+1]) and
isPrime(primes[m+2]) and isPrime(primes[m+3])
if (primes[m+1] - primes[m] = 2) and (primes[m+2] - primes[m+1] = 4) and
(primes[m+3] - primes[m+2] = 2)
see " " + primes[m]+ " " + primes[m+1] + " " +
primes[m+2] + " " + primes[m+3] + nl
ok
ok
next
see "done..." + nl
func isPrime 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...
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