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 code-golf so the program with the shortest bytecount wins!
i=1:n;i(isprime(i)&isprime(i+6))
n is your number
isprime. Not that the op intended it.
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Nov 19, 2013 at 7:34
isprime function a shorter name: i=1:n;p=@isprime;i(p(i)&p(i+6))
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Jul 8, 2020 at 17:22
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.)
{#,#+6}&~Array~#~Cases~{__?PrimeQ}&
~),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]
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]
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.
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).
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a=lambda x,y,z:(value here) is the same as def a(x,y,z):return (value here).
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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[0]=5, o[1]=11, o[2]=7, o[3]=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;
}
{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}
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...
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[] in all() isn't needed (at least in Python 2.7).
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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[50] = { };
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
ÅPãʒÆ7+
Try it online or verify a few more test cases.
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)
-2 thanks to @Fatalize
≥Iṗ-₆ṗ;I≜ᶠ
≥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])
≥Iṗ-₆ṗ;I≜ᶠ
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Perl: 73 char
sub p{(1x$_[0])!~/^(11+?)\1+$/}map{$x=$_+6;p($_)&&p($x)&&say"$_,$x"}2..<>
usage:
echo 30 | perl -E 'sub p{(1x$_[0])!~/^(11+?)\1+$/}map{$x=$_+6;p($_)&&p($x)&&say"$_,$x"}2..<>'
output:
5,11
7,13
11,17
13,19
17,23
23,29
sub p{(1x$_[0])!~/^(11+?)\1+$/}map{p($_)&&p($_+6)&&say"$_,",$_+6}2..<>
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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
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)
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
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]]
(#~*/"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.
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
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}
Outputs in reversed order, because the K3 answer also seems to do that.
LεD6-‚}ʒpP
L Length range
ε Map:
D Duplicate
6- Minus 6
‚ Pair
} Reverse the pair
ʒ Filter:
p Is_prime
P in both items
Rż+¥6ẒẠ$Ƈ
Rż+¥6ẒẠ$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?
=LET(x,SEQUENCE(A1),y,TRANSPOSE(x),z,x*(MMULT((MOD(x,y)=0)*1,x^0)=2),a,IFERROR(INDEX(z,x+{0,6}),),FILTER(a,MMULT(SIGN(a),{1;1})=2))
=LET( allows defined names within formulas.x,SEQUENCE(A1), x = 1..A1 listed vertically.y,TRANSPOSE(x), y = 1..A1 listed horizontally.(MOD(x,y)=0)*1 creates a matrix this is 1 if x mod y = 0 and 0 otherwise.MMULT(~,x^0) sums the elements of each row with matrix multiplication. x^0 is a vertical matrix of 1s.z,x*(~=2), if the sum = 2 then x is prime and z=x else z=0.,a,IFERROR(INDEX(z,x+{0,6}),), creates an array a where the first column is z and the second is z offset by 6 rows.FILTER(a,MMULT(SIGN(a),{1;1})=2) returns the rows of a that have no zeros.-29 bytes thanks to @emanresuA
g=x=>--x>6&&g(x,(f=(n,t=2)=>t<n?n%t&&f(n,t+1):n>1)(x)*f(x-6)&&print(x-6,x))
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[0])).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[0]) with the actual int value, as I cannot supply command line arguments to programs running on ideone.com)
Assuming m has been assigned a value
p=PrimeQ;Cases[Range@m,n_/;p@n&&p[n+6]:>{n,n+6}]
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))
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]]
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.
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
