# Generate Sexy Primes

Sexy Primes are pairs of numbers $$\(n, n+6)\$$ such as $$\n\$$ and $$\n+6\$$ are both prime

You need to create a function which will take an integer, check for sexy primes from 0 to that integer, and return an array of arrays.

For example, listSexy(30) must return [[5,11], [7,13], [11,17], [13,19], [17,23], [23,29]] or some equivalent.

This is so the program with the shortest bytecount wins!

• Can you explain what the desired output format looks like? – Howard Jun 26 '12 at 14:34
• Bah, I hate it when the challenge changes after answers have been submitted. – Griffin Jun 26 '12 at 15:25
• Is there a certain reason to check from 0? Why shouldn't I check from (5,11)? A short definition of sexy primes should be given right here, while linking to Wikipedia for further reading is welcome. – user unknown Jun 27 '12 at 14:45
• In Portuguese Sexy Primes translates to the same as Sexy Cousins! – sergiol Nov 6 '17 at 23:35
• @sergiol haha... – Victor VosMottor Jul 28 '20 at 10:50

# MATLAB 32

i=1:n;i(isprime(i)&isprime(i+6))


n is your number

• +1 That is the right tool for the job: isprime. Not that the op intended it. – Johannes Kuhn Nov 19 '13 at 7:34
• This could be shortened by giving the isprime function a shorter name: i=1:n;p=@isprime;i(p(i)&p(i+6)) – Luis Mendo Jul 8 '20 at 17:22

## J, 3433313239 37 characters

s=.[:(,.-&6)[:I.1([:*/p:)"1 i.,.6-~i.


Lost a character keeping both primes below the limit...and another 7 declaring a function.

Usage:

   s 100
11  5
13  7
17 11
19 13
23 17
29 23
37 31
43 37
47 41
53 47
59 53
67 61
73 67
79 73
89 83


Edit

Seems like a lot of the new answers are not creating functions, taking input or limiting both numbers in the pair to be below n - if I ignore those restrictions too I can get down to 28 characters:

(,.6&+)I.*/"1[1 p:(i.,.6+i.)


## Mathematica, 35

{#,#+6}&~Array~#~Cases~{__?PrimeQ}&


### GolfScript, 32 characters

~),2>{:P{(.P\%}do(!},:L{6+L?)},p


Since the output format was not specified, the code above will print the lower prime of each pair. Thus a number x is included if x and x+6 are both prime and both are below n. Input is given as single number on STDIN.

> 150
[5 7 11 13 17 23 31 37 41 47 53 61 67 73 83 97 101 103 107 131]

• I think you should print both primes. It's a part of the task. – ugoren Jun 27 '12 at 8:45
• @ugoren The task was changed after I submitted my version. I'll try and add that to my version soon. – Howard Jun 27 '12 at 9:14
• Yes, your answer matches the original task. – ugoren Jun 27 '12 at 9:25

# 05AB1E, 7 bytes

ÅPãʒÆ7+


Explanation:

ÅP       # Push a list of primes smaller than or equal to the (implicit) input-integer
ã      # Create all possible pairs by taking the cartesian product with itself
# (which will include inverted duplicates - i.e. both [5,11] and [11,5])
ʒ     # Filter this list of pairs [a,b] by:
Æ    #  Reduce it by subtracting: a-b
7+  #  Add 7
#  (only 1 is truthy in 05AB1E, so this will keep pairs that satisfy a-b+7==1)
# (after which the resulting list of pairs is output implicitly)


# Python 2, 137 132 126 122 118

f=lambda x:not[y for y in range(2,x)if x%y==0]
i=30
print [(x,y)for x in range(i)for y in range(i)if f(x)&f(y)&x-6==y]


Try it online!

Using list comprehensions, as well as the fact that [] = False

f(x) actually returns all the factors of x, and you can then work out prime-ness from that.

• You can turn f(x) into f=lambda x:not[y for y in range(2,x)if x%y==0] to save a few characters. You can also reduce the ifs at the end of your list comprehension with f(x)&f(y)&(x-6==y). – beary605 Jul 20 '12 at 23:20
• @beary605 I don't really know a lot about lamdas (well, I know nothing), so I'll look in to that, but yes, anda not ifs. – ACarter Jul 27 '12 at 21:32
• A lambda is an anonymous function which returns a value. a=lambda x,y,z:(value here) is the same as def a(x,y,z):return (value here). – beary605 Jul 28 '12 at 3:21
• Awesome, I seem to get the hang. Updated. Thanks! – ACarter Jul 28 '12 at 19:01

# K3 / Kona, 45

{a@&6=(-).'a:,/a,\:/:a:&{(x>1)&&/x!'2_!x}'!x}


.

{a@&6=(-).'a:,/a,\:/:a:&{(x>1)&&/x!'2_!x}'!x}100
(11 5
13 7
17 11
19 13
23 17
29 23
37 31
43 37
47 41
53 47
59 53
67 61
73 67
79 73
89 83)


And the same solution in the current incarnation of K which is identical to the K3 solution except for the fact that it does not have an inbuilt mod operator, which adds about 14 chars for 59

{a@&6=(-).'a:,/a,\:/:a:&{(x>1)&&/{x-y*x div y}[x;2_!x]}'!x}


## Python (93 90 99 95)

Yay for quick and dirty isprime functions!

a=lambda x:all(x%i for i in range(2,x));b=2
while b<input():
b+=1
if a(b)&a(b+6):print b,b+6

• 1 instead of True will save you 3 characters... – Wooble Jun 26 '12 at 17:54
• Why do I keep missing that? Fixed. – beary605 Jun 27 '12 at 5:44
• You don't get a limit parameter. Also, [] in all() isn't needed (at least in Python 2.7). – ugoren Jun 27 '12 at 8:43
• Wow, really? Cool! I will implement the parameter. – beary605 Jun 27 '12 at 14:13
• I don't know why you subtract 1 from x, but you can remove that for 2 characters. Then you can replace the while loop with a for loops from 2 to input()+1 for another 2 characters. – JPvdMerwe Jul 20 '12 at 22:33

## x86-Assembly (78 Bytes)

This example uses Intel syntax. Besides, here the fastcall or register calling convention is used (the latter from 32-bit Delphi), so the parameter is in ecx. I also introduce a second parameter that points to a free space for the result and is saved in edx. A function for allocating memory space would be specific to the operating system and a transfer via the stack would be problematic, so I chose this option.

listSexy:
mov   ebp, esp      ; 89E5    Save initial esp
mov   edi, edx      ; 89D7    Save second parameter in edx

; Part One: Save all prime numbers from 3 to the limit on the stack
; (This takes 32 Bytes)
xor   eax, eax      ; 31C0    set eax = 1 (shorter than mov eax, 1)
inc   eax           ; 40
checkComplete:
add   eax, 2        ; 83C002  Go to next possible number (first is 3)
cmp   eax, ecx      ; 39C8    Has the limit, i.e. the parameter, been skipped?
jae   partTwo       ; 7316
mov   ebx, esp      ; 89E3    Check it against all previous prime numbers
checkNext:             ;         which are stored between ebp and esp
cdq                 ; 99      Clear edx for the later division
push  eax           ; 50      Put the number on the stack
cmp   ebx, ebp      ; 39E5    Has the check already completed?
je    partTwo       ; 74F1    The comfirmed prime number remains on stack
mov   esi, [ebx]    ; 8B33    Load a previous prime
div   esi           ; F7F6
pop   eax           ; 58
test  edx, edx      ; 85D2    Is esi a divider?
je    checkComplete ; 74E8
add   ebx, 4        ; 83C304  Let ebx point to the next possible divisor
jmp   checkNext     ; EBEC

; Part Zwo: Check all prime numbers if they are sexy primes
; (This takes 39 Bytes)
partTwo:
mov   ebx, ebp      ; 89E5    Start with the first prime number, i.e. 3
NextPrime:
sub   ebx, 4        ; 83EB04  Let ebx point to the next prime number
cmp   ebx, esp      ; 39E3    Has the last number been reached? It cant be sexy,
;         since it has no successors here
jmp   Finished      ; 761E
mov   edx, ebx      ; 89DA    Check all successors up to a distance of 6
mov   eax, [ebx]    ; 8B03    eax is the prime number whose successors are checked
add   eax, 6        ; 83C006
GoFurther:
sub   edx, 4        ; 83EA04
cmp   eax, [edx]    ; 8B02
jb    NextPrime     ; 72EB    If the successor is too large, x can no longer be sexy
ja    GoFurther     ; 77F7    If the successor is too small, take the next one
mov   eax, [ebx]    ; 8B03    Load eax again (shorter than sub eax, 6)
mov   ecx, [edx]    ; 8B0A    Load the successor which makes eax a sexy prime
mov   [edi], eax    ; 8907    Store both in their intended place
mov   [edi+4], ecx  ; 894F04
add   edi, 8        ; 83C708
jmp   NextPrime     ; EBDB

Finished:
mov   esp, ebp      ; 89EC    Restore stack
ret                 ; C3


The opcodes (and thus the size of the instruction) are given in the comment. The function can be called from C with, for example

int n = 100;
int resultList = { };
listSexy(n, resultList);


The result list should be initialized with zero, since no final null byte sequence or similar is written into.

Online working example: http://tpcg.io/mEPb1Wy9

• Welcome to the site! I'm not too familiar with Assembly, but I just wanted to make sure that your program follows the standard allowed input/output methods? It seems as though it does, but the snippet of C code is making me unsure. Furthermore, make sure to take a look at TryItOnline to see if any of the languages included can run your program, so that others can verify and help improve your answer – caird coinheringaahing Jul 5 '20 at 12:08
• @cairdcoinheringaahing Thanks for your comment, I added a corresponding link and was able to fix a few typing errors too. From your link of the allowed input/output methods, however, I do not quite understand. My example provides a function, memory space for the return value is passed as a parameter at function call. – fcdt Jul 5 '20 at 14:53
• As I said, I‘m not very familiar with Assembly, so I can’t pass judgement on it’s validity. You can ask in our Chatroom, TNB, and I‘m sure someone more knowledgeable could answer – caird coinheringaahing Jul 5 '20 at 15:00

# 05AB1E, 10 bytes

Outputs in reversed order, because the K3 answer also seems to do that.

LεD6-‚}ʒpP


Try it online!

# Explanation

L           Length range
ε          Map:
D             Duplicate
6-           Minus 6
‚          Pair
}         Reverse the pair
ʒ    Filter:
p       Is_prime
P      in both items


Perl: 73 char

sub p{(1x$_)!~/^(11+?)\1+$/}map{$x=$_+6;p($_)&&p($x)&&say"$_,$x"}2..<>


usage:

echo 30 | perl -E 'sub p{(1x$_)!~/^(11+?)\1+$/}map{$x=$_+6;p($_)&&p($x)&&say"$_,$x"}2..<>'


output:

5,11
7,13
11,17
13,19
17,23
23,29

• Nice sulution with the regex. You can even shorten by 3 bytes: sub p{(1x$_)!~/^(11+?)\1+$/}map{p($_)&&p($_+6)&&say"$_,",$_+6}2..<> – Donat Jul 8 '20 at 20:50

# Octave 39

Modified my MATLAB answer to comply with the new (annoying) rules. n is your value.

p=@isprime;i=1:n;[j=i(p(i)&p(i+6));j+6]


Can be tested here

## C, 10299 95 chars

Returning an array in C is something you try to avoid. So the function s gets the limit n and a pointer to an array of integers, and fills it with the data. Each pair of sexy primes is placed in two positions in the array. So o=5, o=11, o=7, o=13. The function assumes the array is large enough.

x=7,l;
p(){
return++l>=x/2||x*(x-6)%l&&p();
}
s(int n,int*o){
for(;l=++x<=n;)p()?*o++=x-6,*o++=x:0;
}


## R, 83 characters

f=function(n){library(gmp);p=isprime;for(i in 1:n)if(p(i)&p(i+6)){print(c(i,i+6))}}


Usage:

f(150)


## Ruby 75 74

The new version uses Artem Ice's prime test method:

z=->x{(9..x).map{|i|[i-6,i]}.select{|a|a.all?{|r|(2...r).all?{|m|r%m>0}}}}


Online test: http://ideone.com/yaOdn

# Ruby, 99 88 86 84 82 78

f=->x{(9..x).map{|n|[n-6,n]if[n,n-6].all?{|t|(2...t).all?{|m|t%m>0}}}.compact}


Sample output:

[[5, 11], [7, 13], [11, 17], [13, 19], [17, 23], [23, 29], [31, 37], [37, 43], [41, 47], [47, 53], [53, 59], [61, 67], [67, 73], [73, 79], [83, 89]]

# J, 25 chars

(#~*/"1@p:~&1)(,+&6)"0 i.


i.n creates a range of [0,n)

(,+&6)"0 takes each integer n in the list and makes a pair n, n+6

(#~ condition) is basically a filter, and the condition in this case, */"1@p:~&1, just checks if a pair is composed solely of primes.

# C# (279 characters)

Basically, it's Saumil's solution with a couple of tweaks. I don't have enough any reputation for commenting though, so...

using System;namespace X{public class P{static int l=100;static void Main(){F(0);}static bool I(int n){bool b=1>0;if(n==1){b=1<0;}for(int i=2;i<n;++i){if(n%i==0){b=1<0;break;}}return b;}static void F(int p){if((p+6)<=l){if(I(p+6)&&I(p)){Console.WriteLine(p+6+","+p);}F(p+1);}}}}


Output:

11,5
13,7
17,11
19,13
23,17
29,23
37,31
43,37
47,41
53,47
59,53
67,61
73,67
79,73
89,83


# Jelly, 13 bytes (non-competing)

‘Ḷµż+6$ÆPẠ$Ðf


Try it online!

Enhanced explanation:

‘Ḷµż+6$ÆPẠ$Ðf Main link. Arguments: z.
‘Ḷ            Range: [0..z].
µ           Start a new monadic chain.
+6        Add 6 to each element of x. (implicit x=⁸).
$Last two links (+6) as a monad. ż Interleave x and y. ÆP Do a primality check every element of every element of z. Ạ Do an "all" check on every element of z.$   Last two links as a monad.
Ðf Keep the elements of z that return a truthy value given this monad.

• I know you posted this 3.5 years ago, but this fails for input n=47, since it includes [47,53]. – Kevin Cruijssen Jul 7 '20 at 13:17

## JavaScript (140 113 Characters)

t=(i,n)=>{for(n=i;n%--i;);return 1==i};s=(n,p)=>{for(p=[],i=2;i<n-6;i++)if(t(i)&&t(i+6))p.push([i,i+6]);return p}

Try s(30).

Updated to use the shorter primality test from here, and to use the new arrow notation.

Old version (140 characters):

function t(n,i){for(i=2;i<n;i++)if(!(n%i))return!1;return!0}function s(n,p){for(p=[],i=2;i<n-6;i++)if(t(i)&&t(i+6))p.push([i,i+6]);return p}

# Brachylog, 12 10 bytes

-2 thanks to @Fatalize

≥Iṗ-₆ṗ;I≜ᶠ


Try it online!

### How it works

≥Iṗ-₆ṗ;I≜ᶠ
ᶠ find all …
≜   force number-finding of constraints that fulfill …
(strictly not necessary, but otherwise constraints will be returned)
≥             any number less than the input
I            assign it to I
ṗ           must be prime
-₆ṗ        minus 6 must also be prime
;I      append I again (so we have [I-6,I])


# Jelly, 9 bytes

Rż+¥6ẒẠ$Ƈ  Try it online! ## How it works Rż+¥6ẒẠ$Ƈ - Main link. Takes N on the left
R         - Range; R = [1, 2, ..., N]
¥6     - Previous 2 links as a dyad f(R, 6):
+       -   Add 6 to each element in R
ż        -   Zip together
\$Ƈ - Keep those pairs for which the following is true:
Ạ   -   Are all elements...
Ẓ    -   ...prime?


## C# 295

using System;using System.Linq;namespace K{class C{public static void Main(string[]a){Func<int,bool>p=i=>Enumerable.Range(2,i-3).All(x=>i%x>0);Console.WriteLine("["+String.Join(",",Enumerable.Range(0,int.Parse(a)).Where(i=>i>9&&p(i)&&p(i-6)).Select(i=>"["+(i-6)+","+i+"]").ToArray())+"]");}}}


Online test: http://ideone.com/4PwTW (in this test I've replaced int.Parse(a) with the actual int value, as I cannot supply command line arguments to programs running on ideone.com)

# Mathematica - 69 48 chars

Assuming m has been assigned a value

p=PrimeQ;Cases[Range@m,n_/;p@n&&p[n+6]:>{n,n+6}]


# Scala (82)

def p(n:Int)=9 to n map(x=>List(x-6,x))filter(_.forall(l=>2 to l-1 forall(l%_>0)))


Sample output: Vector(List(5, 11), List(7, 13), List(11, 17), List(13, 19), List(17, 23), List(23, 29), List(31, 37), List(37, 43), List(41, 47), List(47, 53), List(53, 59), List(61, 67), List(67, 73), List(73, 79), List(83, 89))

# Factor 140

This language is fun and interesting. My first script.

:: i ( n -- ? )
n 1 - 2 [a,b] [ n swap mod 0 > ] all? ;
:: s ( n -- r r )
11 n [a,b] [ i ] filter [ 6 - ] map [ i ] filter dup [ 6 + ] map ;


Usage:

( scratchpad ) 100 f

--- Data stack:
V{ 5 7 11 13 17 23 31 37 41 47 53 61 67 73 83 }
V{ 11 13 17 19 23 29 37 43 47 53 59 67 73 79 89 }


PARI/GP (62 characters)

f(a)=w=[];forprime(x=0,a,isprime(x+6)&w=concat(w,[[x,x+6]]));w


Example:

 (00:01) gp > f(a)=w=[];forprime(x=0,a,isprime(x+6)&w=concat(w,[[x,x+6]]));w
(00:01) gp > f(30)
%1 = [[5, 11], [7, 13], [11, 17], [13, 19], [17, 23], [23, 29]]


C# ( 321 303 290 characters )

using System;namespace X{public class P{ static int l=100;static void Main(){F(0);}static bool I(int n){bool b=true;if(n==1){b=false;}for(int i=2;i<n;++i){if(n%i==0){b=false;break;}}return b;}static void F(int p){if((p+6)<=l){int m=p+6;if(I(m)&&I(p)){Console.WriteLine(m+","+p);}F(p+1);}}}}

Output:
11,5
13,7
17,11
19,13
23,17
29,23
37,31
43,37
47,41
53,47
59,53
67,61
73,67
79,73
89,83

• Welcome to CodeGolf! You can save some chars if you give the class and methods one-letter names (ex: class P instead of class Program). – Cristian Lupascu Jul 20 '12 at 12:16

# Haskell (65 chars)

p n=[(x,x+6)|x<-[3..n-6],all(\k->all((>0).mod k)[2..k-1])[x,x+6]]


The output:

Prelude> p 100
[(5,11),(7,13),(11,17),(13,19),(17,23),(23,29),(31,37),(37,43),(41,47),(47,53),(
53,59),(61,67),(67,73),(73,79),(83,89)]


About the MATLAB answer here:

(I spent all my rep on a bounty so can't comment just yet). Google says: " the Matlab's isprime function ... is based on the probabilistic Miller-Rabin". So it seems that the MATLAB entry should be disqualified.

## R 85 81 characters

f=function(n){m=2:n;a=m[rowSums(!outer(m,m,%%))<2];cbind(b<-a[(a+6)%in%a],b+6)}


Example run:

f(50)
[,1] [,2]
[1,]    5   11
[2,]    7   13
[3,]   11   17
[4,]   13   19
[5,]   17   23
[6,]   23   29
[7,]   31   37
[8,]   37   43
[9,]   41   47