Cousin primes
Cousin 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.
- Definitions
In mathematics, cousin primes are prime numbers that differ by four.
For the purposes of this task a cousin prime pair is a pair of non-negative integers of the form [n, n + 4] whose elements are both primes.
- Task
Write a program to determine (and show here) all cousin prime pairs whose elements are both less than 1,000.
Optionally, show the number of such pairs.
- Also see
-
- the Wikipedia entry: cousin prime.
- the OEIS entry: A094343.
- the MathWorld entry: cousin primes.
11l
V LIMIT = 1000
F isPrime(n)
I (n [&] 1) == 0
R n == 2
V m = 3
L m * m <= n
I n % m == 0
R 0B
m += 2
R 1B
V PrimeList = (2 .< LIMIT).filter(n -> isPrime(n))
V PrimeSet = Set(PrimeList)
V cousinList = PrimeList.filter(n -> (n + 4) C PrimeSet).map(n -> (n, n + 4))
print(‘Found #. cousin primes less than #.:’.format(cousinList.len, LIMIT))
L(cousins) cousinList
print(String(cousins).center(10), end' I (L.index + 1) % 7 == 0 {"\n"} E ‘ ’)
print()- Output:
Found 41 cousin primes less than 1000: (3, 7) (7, 11) (13, 17) (19, 23) (37, 41) (43, 47) (67, 71) (79, 83) (97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971)
Action!
INCLUDE "H6:SIEVE.ACT"
PROC Main()
DEFINE MAX="999"
BYTE ARRAY primes(MAX+1)
INT i,count=[0]
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FOR i=2 TO MAX-4
DO
IF primes(i)=1 AND primes(i+4)=1 THEN
PrintF("(%I,%I) ",i,i+4)
count==+1
FI
OD
PrintF("%E%EThere are %I pairs",count)
RETURN- Output:
Screenshot from Atari 8-bit computer
(3,7) (7,11) (13,17) (19,23) (37,41) (43,47) (67,71) (79,83) (97,101) (103,107) (109,113) (127,131) (163,167) (193,197) (223,227) (229,233) (277,281) (307,311) (313,317) (349,353) (379,383) (397,401) (439,443) (457,461) (463,467) (487,491) (499,503) (613,617) (643,647) (673,677) (739,743) (757,761) (769,773) (823,827) (853,857) (859,863) (877,881) (883,887) (907,911) (937,941) (967,971) There are 41 pairs
Ada
with Ada.Text_Io;
procedure Cousin_Primes is
type Number is new Long_Integer range 0 .. Long_Integer'Last;
package Number_Io is new Ada.Text_Io.Integer_Io (Number);
function Is_Prime (A : Number) return Boolean is
D : Number;
begin
if A < 2 then return False; end if;
if A in 2 .. 3 then return True; end if;
if A mod 2 = 0 then return False; end if;
if A mod 3 = 0 then return False; end if;
D := 5;
while D * D <= A loop
if A mod D = 0 then
return False;
end if;
D := D + 2;
if A mod D = 0 then
return False;
end if;
D := D + 4;
end loop;
return True;
end Is_Prime;
use Ada.Text_Io;
Count : Natural := 0;
begin
for N in Number range 1 .. 999 - 4 loop
if Is_Prime (N) and then Is_Prime (N + 4) then
Count := Count + 1;
Put("[");
Number_Io.Put (N, Width => 3); Put (",");
Number_Io.Put (N + 4, Width => 3);
Put("] ");
if Count mod 8 = 0 then
New_Line;
end if;
end if;
end loop;
New_Line;
Put_Line (Count'Image & " pairs.");
end Cousin_Primes;
- Output:
[ 3, 7] [ 7, 11] [ 13, 17] [ 19, 23] [ 37, 41] [ 43, 47] [ 67, 71] [ 79, 83] [ 97,101] [103,107] [109,113] [127,131] [163,167] [193,197] [223,227] [229,233] [277,281] [307,311] [313,317] [349,353] [379,383] [397,401] [439,443] [457,461] [463,467] [487,491] [499,503] [613,617] [643,647] [673,677] [739,743] [757,761] [769,773] [823,827] [853,857] [859,863] [877,881] [883,887] [907,911] [937,941] [967,971] 41 pairs.
ALGOL 68
BEGIN # find cousin primes - pairs of primes that differ by 4 #
# sieve the primes as required by the task #
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE 1000;
# returns text right padded to length, if it is shorter #
PROC right pad = ( STRING text, INT length )STRING:
IF INT t length = ( UPB text - LWB text ) + 1;
t length >= length
THEN text
ELSE text + ( ( length - t length ) * " " )
FI # right pad # ;
# look through the primes for cousins #
INT p count := 0;
FOR i TO UPB prime - 4 DO
IF prime[ i ] THEN
IF prime[ i + 4 ] THEN
# have a pair of cousin primes #
p count +:= 1;
print( ( whole( i, -5 ), "-", right pad( whole( i + 4, 0 ), 5 ) ) );
IF p count MOD 10 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline, "Found ", whole( p count, 0 ), " cousin primes", newline ) )
END- Output:
3-7 7-11 13-17 19-23 37-41 43-47 67-71 79-83 97-101 103-107 109-113 127-131 163-167 193-197 223-227 229-233 277-281 307-311 313-317 349-353 379-383 397-401 439-443 457-461 463-467 487-491 499-503 613-617 643-647 673-677 739-743 757-761 769-773 823-827 853-857 859-863 877-881 883-887 907-911 937-941 967-971 Found 41 cousin primes
ALGOL W
begin % find some cousin primes: primes p where p + 4 is also a prime %
integer MAX_PRIME;
MAX_PRIME := 1000;
begin
logical array prime( 1 :: MAX_PRIME );
integer cCount;
% sieve the primes to MAX_PRIME %
prime( 1 ) := false; prime( 2 ) := true;
for i := 3 step 2 until MAX_PRIME do prime( i ) := true;
for i := 4 step 2 until MAX_PRIME do prime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin
integer ii; ii := i + i;
if prime( i ) then for np := i * i step ii until MAX_PRIME do prime( np ) := false
end for_i ;
% find the cousin primes %
cCount := 0;
% two is not a cousin prime so we can start at 3 %
for i := 3 step 2 until MAX_PRIME - 4 do begin
if prime( i ) and prime( i + 4 ) then begin
% have another cousin prime pair %
writeon( i_w := 1, s_w := 0, " (", i, " ", i + 4, ")" );
cCount := cCount + 1;
if cCount rem 10 = 0 then write()
end if_have_a_cousin_prime_pair
end for_i ;
write( i_w := 1, s_w := 0, "Found ", cCount, " cousin prime pairs up to ", MAX_PRIME )
end
end.- Output:
(3 7) (7 11) (13 17) (19 23) (37 41) (43 47) (67 71) (79 83) (97 101) (103 107) (109 113) (127 131) (163 167) (193 197) (223 227) (229 233) (277 281) (307 311) (313 317) (349 353) (379 383) (397 401) (439 443) (457 461) (463 467) (487 491) (499 503) (613 617) (643 647) (673 677) (739 743) (757 761) (769 773) (823 827) (853 857) (859 863) (877 881) (883 887) (907 911) (937 941) (967 971) Found 41 cousin prime pairs up to 1000
APL
(⎕←'Amount:',⊃⍴P)⊢P,4+P←⍪((P+4)∊P)/P←(~P∊P∘.×P)/P←1↓⍳1000
- Output:
Amount: 41 3 7 7 11 13 17 19 23 37 41 43 47 67 71 79 83 97 101 103 107 109 113 127 131 163 167 193 197 223 227 229 233 277 281 307 311 313 317 349 353 379 383 397 401 439 443 457 461 463 467 487 491 499 503 613 617 643 647 673 677 739 743 757 761 769 773 823 827 853 857 859 863 877 881 883 887 907 911 937 941 967 971
AppleScript
on sieveOfEratosthenes(limit)
script o
property numberList : {missing value}
end script
repeat with n from 2 to limit
set end of o's numberList to n
end repeat
repeat with n from 2 to (limit ^ 0.5 div 1)
if (item n of o's numberList is n) then
repeat with multiple from (n * n) to limit by n
set item multiple of o's numberList to missing value
end repeat
end if
end repeat
return o's numberList's numbers
end sieveOfEratosthenes
local primes, output, p
set primes to sieveOfEratosthenes(999)
set output to {}
repeat with p in primes
if (p - 4 is in primes) then set end of output to {p - 4, p's contents}
end repeat
return {|cousin prime pairs < 1000|:output, |count thereof|:(count output)}
- Output:
{|cousin prime pairs < 1000|:{{3, 7}, {7, 11}, {13, 17}, {19, 23}, {37, 41}, {43, 47}, {67, 71}, {79, 83}, {97, 101}, {103, 107}, {109, 113}, {127, 131}, {163, 167}, {193, 197}, {223, 227}, {229, 233}, {277, 281}, {307, 311}, {313, 317}, {349, 353}, {379, 383}, {397, 401}, {439, 443}, {457, 461}, {463, 467}, {487, 491}, {499, 503}, {613, 617}, {643, 647}, {673, 677}, {739, 743}, {757, 761}, {769, 773}, {823, 827}, {853, 857}, {859, 863}, {877, 881}, {883, 887}, {907, 911}, {937, 941}, {967, 971}}, |count thereof|:41}
Arturo
cousins: function [upto][
primesUpto: select 0..upto => prime?
return select primesUpto => [prime? & + 4]
]
print map cousins 1000 'c -> @[c, c + 4]
- Output:
[3 7] [7 11] [13 17] [19 23] [37 41] [43 47] [67 71] [79 83] [97 101] [103 107] [109 113] [127 131] [163 167] [193 197] [223 227] [229 233] [277 281] [307 311] [313 317] [349 353] [379 383] [397 401] [439 443] [457 461] [463 467] [487 491] [499 503] [613 617] [643 647] [673 677] [739 743] [757 761] [769 773] [823 827] [853 857] [859 863] [877 881] [883 887] [907 911] [937 941] [967 971]
AWK
# syntax: GAWK -f COUSIN_PRIMES.AWK
BEGIN {
start = 1
stop = 1000
for (i=start; i<=stop; i++) {
if (is_prime(i) && is_prime(i+4)) {
printf("%3d:%3d%1s",i,i+4,++count%10?"":"\n")
}
}
printf("\nCousin primes %d-%d: %d\n",start,stop,count)
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
- Output:
3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97:101 103:107 109:113 127:131 163:167 193:197 223:227 229:233 277:281 307:311 313:317 349:353 379:383 397:401 439:443 457:461 463:467 487:491 499:503 613:617 643:647 673:677 739:743 757:761 769:773 823:827 853:857 859:863 877:881 883:887 907:911 937:941 967:971 Cousin primes 1-1000: 41
BASIC
10 DEFINT A-Z: L=1000: DIM S(L)
20 FOR P=2 TO SQR(L)
30 IF S(P) THEN 50
40 FOR K=P*P TO L STEP P: S(K)=1: NEXT
50 NEXT
60 N=0
70 FOR P=2 TO L-4
80 IF S(P)+S(P+4)=0 THEN N=N+1: PRINT P,P+4
90 NEXT
100 PRINT "There are";N;"cousin prime pairs below";L
- Output:
3 7 7 11 13 17 19 23 37 41 43 47 67 71 79 83 97 101 103 107 109 113 127 131 163 167 193 197 223 227 229 233 277 281 307 311 313 317 349 353 379 383 397 401 439 443 457 461 463 467 487 491 499 503 613 617 643 647 673 677 739 743 757 761 769 773 823 827 853 857 859 863 877 881 883 887 907 911 937 941 967 971 There are 41 cousin prime pairs below 1000
BCPL
get "libhdr"
manifest $( LIMIT = 1000 $)
let sieve(prime,max) be
$( let i = 2
0!prime := false
1!prime := false
for i = 2 to max do i!prime := true
while i*i <= max do
$( if i!prime do
$( let j = i*i
while j <= max do
$( j!prime := false
j := j + i
$)
$)
i := i + 1
$)
$)
let start() be
$( let prime = vec LIMIT
let count = 0
sieve(prime, LIMIT)
for i = 2 to LIMIT-4 do
if i!prime & (i+4)!prime do
$( count := count + 1
writef("%N, %N*N", i, i+4)
$)
writef("*N%N pairs found.*N", count)
$)- Output:
3, 7 7, 11 13, 17 19, 23 37, 41 43, 47 67, 71 79, 83 97, 101 103, 107 109, 113 127, 131 163, 167 193, 197 223, 227 229, 233 277, 281 307, 311 313, 317 349, 353 379, 383 397, 401 439, 443 457, 461 463, 467 487, 491 499, 503 613, 617 643, 647 673, 677 739, 743 757, 761 769, 773 823, 827 853, 857 859, 863 877, 881 883, 887 907, 911 937, 941 967, 971 41 pairs found.
C
#include <stdio.h>
#include <string.h>
#define LIMIT 1000
void sieve(int max, char *s) {
int p, k;
memset(s, 0, max);
for (p=2; p*p<=max; p++)
if (!s[p])
for (k=p*p; k<=max; k+=p)
s[k]=1;
}
int main(void) {
char primes[LIMIT+1];
int p, count=0;
sieve(LIMIT, primes);
for (p=2; p<=LIMIT; p++) {
if (!primes[p] && !primes[p+4]) {
count++;
printf("%4d: %4d\n", p, p+4);
}
}
printf("There are %d cousin prime pairs below %d.\n", count, LIMIT);
return 0;
}
- Output:
3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97: 101 103: 107 109: 113 127: 131 163: 167 193: 197 223: 227 229: 233 277: 281 307: 311 313: 317 349: 353 379: 383 397: 401 439: 443 457: 461 463: 467 487: 491 499: 503 613: 617 643: 647 673: 677 739: 743 757: 761 769: 773 823: 827 853: 857 859: 863 877: 881 883: 887 907: 911 937: 941 967: 971 There are 41 cousin prime pairs below 1000.
COBOL
IDENTIFICATION DIVISION.
PROGRAM-ID. COUSIN-PRIMES.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 PRIME-SIEVE.
02 PRIME-FLAG PIC 9 OCCURS 1000 INDEXED BY P, Q.
88 PRIME VALUE 1.
02 STEP-SIZE PIC 999.
02 X PIC 999.
02 P-START PIC 999.
02 AMOUNT PIC 999 VALUE 0.
01 OUTPUT-FORMAT.
02 COUSIN1 PIC ZZ9.
02 COUSIN2 PIC ZZ9.
PROCEDURE DIVISION.
BEGIN.
PERFORM SIEVE.
PERFORM TEST-COUSINS VARYING P FROM 2 BY 1
UNTIL P IS GREATER THAN 996.
MOVE AMOUNT TO COUSIN1.
DISPLAY COUSIN1 ' pairs found.'
STOP RUN.
TEST-COUSINS.
IF PRIME(P) AND PRIME(P + 4)
SET X TO P
MOVE X TO COUSIN1
ADD X, 4 GIVING COUSIN2
DISPLAY COUSIN1 ' ' COUSIN2
ADD 1 TO AMOUNT.
SIEVE SECTION.
BEGIN.
PERFORM FLAG-PRIME VARYING Q FROM 1 BY 1
UNTIL Q IS GREATER THAN 1000.
PERFORM SIEVE-PRIME VARYING P FROM 2 BY 1
UNTIL P IS GREATER THAN 32.
GO TO DONE.
SIEVE-PRIME.
IF PRIME(P)
SET X TO P
COMPUTE P-START = X ** 2
PERFORM UNFLAG-PRIME VARYING Q FROM P-START BY X
UNTIL Q IS GREATER THAN 1000.
FLAG-PRIME. MOVE 1 TO PRIME-FLAG(Q).
UNFLAG-PRIME. MOVE 0 TO PRIME-FLAG(Q).
DONE. EXIT.
- Output:
3 7 7 11 13 17 19 23 37 41 43 47 67 71 79 83 97 101 103 107 109 113 127 131 163 167 193 197 223 227 229 233 277 281 307 311 313 317 349 353 379 383 397 401 439 443 457 461 463 467 487 491 499 503 613 617 643 647 673 677 739 743 757 761 769 773 823 827 853 857 859 863 877 881 883 887 907 911 937 941 967 971 41 pairs found.
Cowgol
include "cowgol.coh";
const LIMIT := 1000;
var sieve: uint8[LIMIT + 1];
MemZero(&sieve[0], @bytesof sieve);
var p: @indexof sieve := 2;
loop
var n := p*p;
if n >= LIMIT then break; end if;
if sieve[p] == 0 then
while n < LIMIT loop
sieve[n] := 1;
n := n + p;
end loop;
end if;
p := p + 1;
end loop;
var count: uint8 := 0;
n := 2;
while n < LIMIT-4 loop
if sieve[n] + sieve[n+4] == 0 then
count := count + 1;
print_i32(n as uint32);
print_char('\t');
print_i32(n as uint32+4);
print_nl();
end if;
n := n + 1;
end loop;
print("There are ");
print_i8(count);
print(" cousin prime pairs below ");
print_i16(LIMIT);
print_nl();- Output:
3 7 7 11 13 17 19 23 37 41 43 47 67 71 79 83 97 101 103 107 109 113 127 131 163 167 193 197 223 227 229 233 277 281 307 311 313 317 349 353 379 383 397 401 439 443 457 461 463 467 487 491 499 503 613 617 643 647 673 677 739 743 757 761 769 773 823 827 853 857 859 863 877 881 883 887 907 911 937 941 967 971 There are 41 cousin prime pairs below 1000
F#
This task uses Extensible Prime Generator (F#)
// Cousin Primes: Nigel Galloway. April 2nd., 2021
primes32()|>Seq.pairwise|>Seq.takeWhile(fun(_,n)->n<1000)|>Seq.filter(fun(n,g)->g-n=4)|>Seq.iter(fun(n,g)->printf "(%d,%d) "n g); printfn ""
- Output:
(7,11) (13,17) (19,23) (37,41) (43,47) (67,71) (79,83) (97,101) (103,107) (109,113) (127,131) (163,167) (193,197) (223,227) (229,233) (2http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]77,281) (307,311) (313,317) (349,353) (379,383) (397,401) (439,443) (457,461) (463,467) (487,491) (499,503) (613,617) (643,647) (673,677) (739,743) (757,761) (769,773) (823,827) (853,857) (859,863) (877,881) (883,887) (907,911) (937,941) (967,971)
Factor
USING: kernel lists lists.lazy math math.primes prettyprint
sequences ;
: lcousins ( -- list )
L{ { 3 7 } } 7 11 [ [ 6 + ] lfrom-by ] bi@ lzip lappend-lazy
[ [ prime? ] all? ] lfilter ;
lcousins [ last 1000 < ] lwhile [ . ] leach
- Output:
{ 3 7 }
{ 7 11 }
{ 13 17 }
{ 19 23 }
{ 37 41 }
{ 43 47 }
{ 67 71 }
{ 79 83 }
{ 97 101 }
{ 103 107 }
{ 109 113 }
{ 127 131 }
{ 163 167 }
{ 193 197 }
{ 223 227 }
{ 229 233 }
{ 277 281 }
{ 307 311 }
{ 313 317 }
{ 349 353 }
{ 379 383 }
{ 397 401 }
{ 439 443 }
{ 457 461 }
{ 463 467 }
{ 487 491 }
{ 499 503 }
{ 613 617 }
{ 643 647 }
{ 673 677 }
{ 739 743 }
{ 757 761 }
{ 769 773 }
{ 823 827 }
{ 853 857 }
{ 859 863 }
{ 877 881 }
{ 883 887 }
{ 907 911 }
{ 937 941 }
{ 967 971 }
FOCAL
01.10 S C=0
01.20 T %4
01.30 F N=3,2,996;D 2
01.40 T "AMOUNT OF COUSIN PRIME PAIRS",C,!
01.50 Q
02.10 S P=N;D 3;S D=A
02.20 S P=N+4;D 3
02.30 I (-A*D)2.4;R
02.40 T N,P,!
02.50 S C=C+1
03.10 S K=2
03.20 I (K-P)3.3;S A=-1;R
03.30 S B=P/K
03.40 I (FITR(B)-B)3.5,3.7,3.5
03.50 S K=K+1
03.60 G 3.2
03.70 S A=0- Output:
= 3= 7 = 7= 11 = 13= 17 = 19= 23 = 37= 41 = 43= 47 = 67= 71 = 79= 83 = 97= 101 = 103= 107 = 109= 113 = 127= 131 = 163= 167 = 193= 197 = 223= 227 = 229= 233 = 277= 281 = 307= 311 = 313= 317 = 349= 353 = 379= 383 = 397= 401 = 439= 443 = 457= 461 = 463= 467 = 487= 491 = 499= 503 = 613= 617 = 643= 647 = 673= 677 = 739= 743 = 757= 761 = 769= 773 = 823= 827 = 853= 857 = 859= 863 = 877= 881 = 883= 887 = 907= 911 = 937= 941 = 967= 971 AMOUNT OF COUSIN PRIME PAIRS= 41
Forth
: prime? ( n -- ? ) here + c@ 0= ;
: not-prime! ( n -- ) here + 1 swap c! ;
: prime-sieve ( n -- )
here over erase
0 not-prime!
1 not-prime!
2
begin
2dup dup * >
while
dup prime? if
2dup dup * do
i not-prime!
dup +loop
then
1+
repeat
2drop ;
: cousin-primes ( n -- )
dup prime-sieve
0
over 4 - 0 do
i prime? if i 4 + prime? if
1+
." (" i 3 .r ." , " i 4 + 3 .r ." )"
dup 5 mod 0= if cr else space then
then then
loop
swap
cr ." Number of cousin prime pairs < " . ." is " . cr ;
1000 cousin-primes
bye
- Output:
( 3, 7) ( 7, 11) ( 13, 17) ( 19, 23) ( 37, 41) ( 43, 47) ( 67, 71) ( 79, 83) ( 97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971) Number of cousin prime pairs < 1000 is 41
FreeBASIC
Use one of the primality testing examples as an include.
#include "isprime.bas"
dim as uinteger c=0, i
for i = 3 to 995
if isprime(i+4) andalso isprime(i) then
c += 1
print using "Pair ##: #### and ####"; c; i; i+4
end if
next i- Output:
Pair 1: 3 and 7 Pair 2: 7 and 11 Pair 3: 13 and 17 Pair 4: 19 and 23 Pair 5: 37 and 41 Pair 6: 43 and 47 Pair 7: 67 and 71 Pair 8: 79 and 83 Pair 9: 97 and 101 Pair 10: 103 and 107 Pair 11: 109 and 113 Pair 12: 127 and 131 Pair 13: 163 and 167 Pair 14: 193 and 197 Pair 15: 223 and 227 Pair 16: 229 and 233 Pair 17: 277 and 281 Pair 18: 307 and 311 Pair 19: 313 and 317 Pair 20: 349 and 353 Pair 21: 379 and 383 Pair 22: 397 and 401 Pair 23: 439 and 443 Pair 24: 457 and 461 Pair 25: 463 and 467 Pair 26: 487 and 491 Pair 27: 499 and 503 Pair 28: 613 and 617 Pair 29: 643 and 647 Pair 30: 673 and 677 Pair 31: 739 and 743 Pair 32: 757 and 761 Pair 33: 769 and 773 Pair 34: 823 and 827 Pair 35: 853 and 857 Pair 36: 859 and 863 Pair 37: 877 and 881 Pair 38: 883 and 887 Pair 39: 907 and 911 Pair 40: 937 and 941 Pair 41: 967 and 971
Go
package main
import "fmt"
func isPrime(n int) bool {
switch {
case n < 2:
return false
case n%2 == 0:
return n == 2
case n%3 == 0:
return n == 3
default:
d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}
}
func main() {
count := 0
fmt.Println("Cousin prime pairs whose elements are less than 1,000:")
for i := 3; i <= 995; i += 2 {
if isPrime(i) && isPrime(i+4) {
fmt.Printf("%3d:%3d ", i, i+4)
count++
if count%7 == 0 {
fmt.Println()
}
if i != 3 {
i += 4
} else {
i += 2
}
}
}
fmt.Printf("\n\n%d pairs found\n", count)
}
- Output:
Cousin prime pairs whose elements are less than 1,000: 3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97:101 103:107 109:113 127:131 163:167 193:197 223:227 229:233 277:281 307:311 313:317 349:353 379:383 397:401 439:443 457:461 463:467 487:491 499:503 613:617 643:647 673:677 739:743 757:761 769:773 823:827 853:857 859:863 877:881 883:887 907:911 937:941 967:971 41 pairs found
Haskell
import Data.List (intercalate, transpose)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime, primes)
import Text.Printf (printf)
---------------------- COUSIN PRIMES ---------------------
cousinPrimes :: [(Integer, Integer)]
cousinPrimes = concat $ (zipWith go <*> fmap (+ 4)) primes
where
go a b = [(a, b) | isPrime b]
--------------------------- TEST -------------------------
main :: IO ()
main = do
let cousins = takeWhile ((< 1000) . snd) cousinPrimes
mapM_
putStrLn
[ (show . length) cousins <> " cousin prime pairs:",
"",
table " " $
chunksOf 5 $ show <$> cousins
]
------------------------ FORMATTING ----------------------
table :: String -> [[String]] -> String
table gap rows =
let ws = maximum . fmap length <$> transpose rows
pw = printf . flip intercalate ["%", "s"] . show
in unlines $ intercalate gap . zipWith pw ws <$> rows
- Output:
41 cousin prime pairs:
(3,7) (7,11) (13,17) (19,23) (37,41)
(43,47) (67,71) (79,83) (97,101) (103,107)
(109,113) (127,131) (163,167) (193,197) (223,227)
(229,233) (277,281) (307,311) (313,317) (349,353)
(379,383) (397,401) (439,443) (457,461) (463,467)
(487,491) (499,503) (613,617) (643,647) (673,677)
(739,743) (757,761) (769,773) (823,827) (853,857)
(859,863) (877,881) (883,887) (907,911) (937,941)
(967,971)
J
(":,'Amount: ',":@#) ([,.4+]) (]#~1:p:4:+]) i.&.(p:inv)1000
- Output:
3 7 7 11 13 17 19 23 37 41 43 47 67 71 79 83 97 101 103 107 109 113 127 131 163 167 193 197 223 227 229 233 277 281 307 311 313 317 349 353 379 383 397 401 439 443 457 461 463 467 487 491 499 503 613 617 643 647 673 677 739 743 757 761 769 773 823 827 853 857 859 863 877 881 883 887 907 911 937 941 967 971 Amount: 41
(In this example, we can get away with finding primes where adding 4 gives us another prime. But if the task had asked for cousin prime pairs less than 100, we would want to avoid the pair 97,101. And the simplest way of addressing that issue would have been to find primes where subtracting 4 gives us another prime.)
jq
Works with gojq, the Go implementation of jq
For the definition of `is_prime` used here, see https://rosettacode.org/wiki/Additive_primes
# Output: a stream
def cousins:
# [2,6] is not a cousin so we can start at 3
range(3;.;2)
| select(is_prime and (.+4 | is_prime))
| [., .+4];
997 | cousins- Output:
See below.
The Count
To compute the pairs and the count at the same time without saving them as an array:
# Use null as the EOS marker
foreach ((997|cousins),null) as $c (-1; .+1; if $c == null then "\nCount is \(.)" else $c end)- Output:
[3,7] [7,11] [13,17] [19,23] [37,41] [43,47] [67,71] [79,83] [97,101] [103,107] [109,113] [127,131] [163,167] [193,197] [223,227] [229,233] [277,281] [307,311] [313,317] [349,353] [379,383] [397,401] [439,443] [457,461] [463,467] [487,491] [499,503] [613,617] [643,647] [673,677] [739,743] [757,761] [769,773] [823,827] [853,857] [859,863] [877,881] [883,887] [907,911] [937,941] [967,971] Count is 41
Julia
using Primes
let
p = primesmask(1000)
println("Cousin prime pairs under 1,000:")
pcount = 0
for i in 2:996
if p[i] && p[i + 4]
pcount += 1
print(lpad(i, 4), ":", rpad(i + 4, 4), pcount % 8 == 0 ? "\n" : "")
end
end
println("\n\n$pcount pairs found.")
end
- Output:
Cousin prime pairs under 1,000: 3:7 7:11 13:17 19:23 37:41 43:47 67:71 79:83 97:101 103:107 109:113 127:131 163:167 193:197 223:227 229:233 277:281 307:311 313:317 349:353 379:383 397:401 439:443 457:461 463:467 487:491 499:503 613:617 643:647 673:677 739:743 757:761 769:773 823:827 853:857 859:863 877:881 883:887 907:911 937:941 967:971 41 pairs found.
Lua
do -- find primes p where p+4 is also prime
local MAX_PRIME = 1000
local p = {} -- sieve the odd primes to MAX_PRIME
for i = 3, MAX_PRIME, 2 do p[ i ] = true end
for i = 3, math.floor( math.sqrt( MAX_PRIME ) ), 2 do
if p[ i ] then
for s = i * i, MAX_PRIME, i + i do p[ s ] = false end
end
end
local function fmt ( n ) return string.format( "%3d", n ) end
io.write( "Cousin primes under ", MAX_PRIME, ":\n" )
local cCount = 0
for i = 3, MAX_PRIME - 4, 2 do
if p[ i ] and p[ i + 4 ] then
cCount = cCount + 1
io.write( "[ ", fmt( i ), " ", fmt( i + 4 ), " ]"
, ( cCount % 8 == 0 and "\n" or " " )
)
end
end
io.write( "\nFound ", cCount, " cousin primes\n" )
end
- Output:
Cousin primes under 1000: [ 3 7 ] [ 7 11 ] [ 13 17 ] [ 19 23 ] [ 37 41 ] [ 43 47 ] [ 67 71 ] [ 79 83 ] [ 97 101 ] [ 103 107 ] [ 109 113 ] [ 127 131 ] [ 163 167 ] [ 193 197 ] [ 223 227 ] [ 229 233 ] [ 277 281 ] [ 307 311 ] [ 313 317 ] [ 349 353 ] [ 379 383 ] [ 397 401 ] [ 439 443 ] [ 457 461 ] [ 463 467 ] [ 487 491 ] [ 499 503 ] [ 613 617 ] [ 643 647 ] [ 673 677 ] [ 739 743 ] [ 757 761 ] [ 769 773 ] [ 823 827 ] [ 853 857 ] [ 859 863 ] [ 877 881 ] [ 883 887 ] [ 907 911 ] [ 937 941 ] [ 967 971 ] Found 41 cousin primes
MAD
NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(1000)
THROUGH SET, FOR P=2, 1, P.G.1000
SET PRIME(P) = 1B
THROUGH SIEVE, FOR P=2, 1, P*P.G.1000
WHENEVER PRIME(P)
THROUGH MARK, FOR K=P*P, P, K.G.1000
MARK PRIME(K) = 0B
END OF CONDITIONAL
SIEVE CONTINUE
COUNT = 0
THROUGH TEST, FOR P=2, 1, P.G.1000-4
WHENEVER PRIME(P) .AND. PRIME(P+4)
COUNT = COUNT + 1
PRINT FORMAT COUSIN, P, P+4
END OF CONDITIONAL
TEST CONTINUE
PRINT FORMAT TOTAL, COUNT
VECTOR VALUES COUSIN = $I4,2H: ,I4*$
VECTOR VALUES TOTAL = $15HTOTAL COUSINS: ,I2*$
END OF PROGRAM- Output:
3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97: 101 103: 107 109: 113 127: 131 163: 167 193: 197 223: 227 229: 233 277: 281 307: 311 313: 317 349: 353 379: 383 397: 401 439: 443 457: 461 463: 467 487: 491 499: 503 613: 617 643: 647 673: 677 739: 743 757: 761 769: 773 823: 827 853: 857 859: 863 877: 881 883: 887 907: 911 937: 941 967: 971 TOTAL COUSINS: 41
Mathematica/Wolfram Language
primes = Prime@Range[PrimePi[1000] - 1];
primes = {primes, primes + 4} // Transpose;
Select[primes, AllTrue[PrimeQ]]
Length[%]
- Output:
{{3,7},{7,11},{13,17},{19,23},{37,41},{43,47},{67,71},{79,83},{97,101},{103,107},{109,113},{127,131},{163,167},{193,197},{223,227},{229,233},{277,281},{307,311},{313,317},{349,353},{379,383},{397,401},{439,443},{457,461},{463,467},{487,491},{499,503},{613,617},{643,647},{673,677},{739,743},{757,761},{769,773},{823,827},{853,857},{859,863},{877,881},{883,887},{907,911},{937,941},{967,971}}
41
Nim
We use a simple primality test (which is in fact executed at compile time). For large values of N, it would be better to use a sieve of Erathostenes and to replace the constants “PrimeList” and “PrimeSet” by read-only variables.
import sets, strutils, sugar
const N = 1000
func isPrime(n: Positive): bool {.compileTime.} =
if (n and 1) == 0: return n == 2
var m = 3
while m * m <= n:
if n mod m == 0: return false
inc m, 2
result = true
const
PrimeList = collect(newSeq):
for n in 2..N:
if n.isPrime: n
PrimeSet = PrimeList.toHashSet
let cousinList = collect(newSeq):
for n in PrimeList:
if (n + 4) in PrimeSet: (n, n + 4)
echo "Found $# cousin primes less than $#:".format(cousinList.len, N)
for i, cousins in cousinList:
stdout.write ($cousins).center(10)
stdout.write if (i+1) mod 7 == 0: '\n' else: ' '
echo()
- Output:
Found 41 cousin primes less than 1000: (3, 7) (7, 11) (13, 17) (19, 23) (37, 41) (43, 47) (67, 71) (79, 83) (97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971)
Pascal
Sieving only odd numbers.
program Cousin_primes;
//Free Pascal Compiler version 3.2.1 [2020/11/03] for x86_64fpc
{$IFDEF FPC}
{$MODE DELPHI}
{$Optimization ON,ALL}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
const
MAXNUMBER = 100*1000*1000;// > 3
MAXLIMIT = (MAXNUMBER-1) DIV 2;
type
tChkprimes = array of byte;//prime == 1 , nonprime == 0
tPrimes = array of Uint32;
var
primes :tPrimes; //here starting with 3
procedure OutCount(lmt,cnt:NativeInt);
Begin
writeln(cnt,' cousin primes up to ',lmt);
end;
procedure InitPrimes;
var
Chkprimes:tChkprimes;
//NativeUInt i DIV 2 is only SHR 1,otherwise extension to Int64
i,j,CountOfPrimes : NativeUInt;
begin
SetLength(Chkprimes,MAXLIMIT+1);
fillchar(Chkprimes[0],length(Chkprimes),#1);
//estimate count of primes
CountOfPrimes := trunc(MAXNUMBER/(ln(MAXNUMBER)-1.08))+100;
SetLength(primes,CountOfPrimes+1);
//sieve of eratosthenes only odd numbers
// i = 2*j+1
Chkprimes[0] := 0;// 0 -> 2*0+1 = 1
i := 1;
repeat
if Chkprimes[(i-1) DIV 2] <> 0 then
Begin
// convert i*i into j
j := (i*i-1) DIV 2;
if j> MAXLIMIT then
break;
repeat
Chkprimes[j]:= 0;
inc(j,i);
until j> MAXLIMIT;
end;
inc(i,2);
until false;
j := 0;
For i := 1 to MAXLIMIT do
IF Chkprimes[i]<>0 then
Begin
primes[j] := 2*i+1;
inc(j);
if j>CountOfPrimes then
Begin
CountOfPrimes += 400;
setlength(Primes,CountOfPrimes);
end;
end;
setlength(primes,j);
setlength(Chkprimes,0);
end;
var
i,lmt,cnt,primeCount : NativeInt;
BEGIN
InitPrimes;
//only exception, that the index difference is greater 1
write(primes[0]:3,':',primes[2]:3,' ');
cnt := 1;
lmt := 1000;
For i := 1 to High(primes) do
Begin
if primes[i] >lmt then
break;
IF primes[i]-primes[i-1] = 4 then
Begin
write(primes[i-1]:3,':',primes[i]:3,' ');
inc(cnt);
If cnt MOD 6 = 0 then
writeln;
end;
end;
writeln;
OutCount(lmt,cnt);
writeln;
cnt := 1;
lmt *= 10;
primeCount := High(primes);
For i := 1 to primeCount do
Begin
if primes[i] >lmt then
Begin
OutCount(lmt,cnt);
lmt *= 10;
end;
inc(cnt,ORD(primes[i]-primes[i-1] = 4));
end;
OutCount(MAXNUMBER,cnt);
setlength(primes,0);
END.
- Output:
3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97:101 103:107 109:113 127:131 163:167 193:197 223:227 229:233 277:281 307:311 313:317 349:353 379:383 397:401 439:443 457:461 463:467 487:491 499:503 613:617 643:647 673:677 739:743 757:761 769:773 823:827 853:857 859:863 877:881 883:887 907:911 937:941 967:971 41 cousin primes up to 1000 203 cousin primes up to 10000 1216 cousin primes up to 100000 8144 cousin primes up to 1000000 58622 cousin primes up to 10000000 440258 cousin primes up to 100000000 real 0m0,484s
Perl
use warnings;
use feature 'say';
use ntheory 'is_prime';
my($limit, @cp) = 1000;
is_prime($_) and is_prime($_+4) and push @cp, "$_/@{[$_+4]}" for 2..$limit;
say @cp . " cousin prime pairs < $limit:\n" . (sprintf "@{['%8s' x @cp]}", @cp) =~ s/(.{56})/$1\n/gr;
- Output:
41 cousin prime pairs < 1000:
3/7 7/11 13/17 19/23 37/41 43/47 67/71
79/83 97/101 103/107 109/113 127/131 163/167 193/197
223/227 229/233 277/281 307/311 313/317 349/353 379/383
397/401 439/443 457/461 463/467 487/491 499/503 613/617
643/647 673/677 739/743 757/761 769/773 823/827 853/857
859/863 877/881 883/887 907/911 937/941 967/971
Phix
function has_cousin(integer p) return is_prime(p+4) end function for n=2 to 7 do integer tn = power(10,n) sequence res = filter(get_primes_le(tn-9),has_cousin) res = columnize({res,sq_add(res,4)}) printf(1,"%,d cousin prime pairs less than %,d found: %v\n",{length(res),tn,shorten(res,"",min(4,5-floor(n/2)))}) end for
(Uses tn-9 instead of the more obvious tn-4 since none of 96,95,94,93,92 or similar with 9..99999 prefix could ever be prime. Note that {97,101} is deliberately excluded from < 100.)
- Output:
8 cousin prime pairs less than 100 found: {{3,7},{7,11},{13,17},{19,23},{37,41},{43,47},{67,71},{79,83}}
41 cousin prime pairs less than 1,000 found: {{3,7},{7,11},{13,17},{19,23},"...",{883,887},{907,911},{937,941},{967,971}}
203 cousin prime pairs less than 10,000 found: {{3,7},{7,11},{13,17},"...",{9787,9791},{9829,9833},{9883,9887}}
1,216 cousin prime pairs less than 100,000 found: {{3,7},{7,11},{13,17},"...",{99709,99713},{99829,99833},{99877,99881}}
8,144 cousin prime pairs less than 1,000,000 found: {{3,7},{7,11},"...",{999769,999773},{999979,999983}}
58,622 cousin prime pairs less than 10,000,000 found: {{3,7},{7,11},"...",{9999217,9999221},{9999397,9999401}}
Python
'''Cousin primes'''
from itertools import chain, takewhile
# cousinPrimes :: [Int]
def cousinPrimes():
'''Non finite list of pairs of primes which differ by 4.
'''
def go(x):
n = 4 + x
return [(x, n)] if isPrime(n) else []
return chain.from_iterable(
map(go, primes())
)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Cousin pairs where each value is below 1000'''
pairs = list(
takewhile(
lambda ab: 1000 > ab[1],
cousinPrimes()
)
)
print(f'{len(pairs)} cousin pairs below 1000:\n')
print(
spacedTable(list(
chunksOf(4)([
repr(x) for x in pairs
])
))
)
# ----------------------- GENERIC ------------------------
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
'''
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go
# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
def p(x):
return 0 == n % x or 0 == n % (2 + x)
return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))
# primes :: [Int]
def primes():
''' Non finite sequence of prime numbers.
'''
n = 2
dct = {}
while True:
if n in dct:
for p in dct[n]:
dct.setdefault(n + p, []).append(p)
del dct[n]
else:
yield n
dct[n * n] = [n]
n = 1 + n
# listTranspose :: [[a]] -> [[a]]
def listTranspose(xss):
'''Transposition of a list of lists
'''
def go(xss):
if xss:
h, *t = xss
return (
[[h[0]] + [xs[0] for xs in t if xs]] + (
go([h[1:]] + [xs[1:] for xs in t])
)
) if h and isinstance(h, list) else go(t)
else:
return []
return go(xss)
# spacedTable :: [[String]] -> String
def spacedTable(rows):
'''Tabulation with right-aligned cells'''
columnWidths = [
len(str(row[-1])) for row in listTranspose(rows)
]
return '\n'.join([
' '.join(
map(
lambda w, s: s.rjust(w, ' '),
columnWidths, row
)
) for row in rows
])
# MAIN ---
if __name__ == '__main__':
main()
- Output:
41 cousin pairs below 1000:
(3, 7) (7, 11) (13, 17) (19, 23)
(37, 41) (43, 47) (67, 71) (79, 83)
(97, 101) (103, 107) (109, 113) (127, 131)
(163, 167) (193, 197) (223, 227) (229, 233)
(277, 281) (307, 311) (313, 317) (349, 353)
(379, 383) (397, 401) (439, 443) (457, 461)
(463, 467) (487, 491) (499, 503) (613, 617)
(643, 647) (673, 677) (739, 743) (757, 761)
(769, 773) (823, 827) (853, 857) (859, 863)
(877, 881) (883, 887) (907, 911) (937, 941)
(967, 971)
Quackery
eratosthenes and isprime are defined at Sieve of Eratosthenes#Quackery.
1000 eratosthenes
[] 1000 4 - times
[ i^ isprime
i^ 4 + isprime
and if
[ i^ dup 4 + join
nested join ] ]
dup echo cr cr
size echo- Output:
[ [ 3 7 ] [ 7 11 ] [ 13 17 ] [ 19 23 ] [ 37 41 ] [ 43 47 ] [ 67 71 ] [ 79 83 ] [ 97 101 ] [ 103 107 ] [ 109 113 ] [ 127 131 ] [ 163 167 ] [ 193 197 ] [ 223 227 ] [ 229 233 ] [ 277 281 ] [ 307 311 ] [ 313 317 ] [ 349 353 ] [ 379 383 ] [ 397 401 ] [ 439 443 ] [ 457 461 ] [ 463 467 ] [ 487 491 ] [ 499 503 ] [ 613 617 ] [ 643 647 ] [ 673 677 ] [ 739 743 ] [ 757 761 ] [ 769 773 ] [ 823 827 ] [ 853 857 ] [ 859 863 ] [ 877 881 ] [ 883 887 ] [ 907 911 ] [ 937 941 ] [ 967 971 ] ] 41
REXX
This REXX version allows the limit to be specified, as well as the number of cousin prime pairs to be shown per line.
/*REXX program counts/shows the number of cousin prime pairs under a specified number N.*/
parse arg hi cols . /*get optional number of primes to find*/
if hi=='' | hi=="," then hi= 1000 /*Not specified? Then assume default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " .*/
Ocols= cols; cols= abs(cols) /*Use the absolute value of cols. */
call genP hi-1 /*generate all primes under N. */
pairs= 0; dups= 0 /*initialize # cousin prime pairs; dups*/
$= /*a list of cousin prime pairs (so far)*/
do j=1 while @.j\==.; c= @.j - 4 /*lets hunt for cousin prime pairs. */
if \!.c then iterate /*Not a lowe cousin pair? Then skip it.*/
pairs= pairs + 1 /*bump the count of cousin prime pairs.*/
if @.j==11 then dups= dups + 1 /*take care to note if there is a dup. */
if Ocols<1 then iterate /*Build the list (to be shown later)? */
$= $ ' ('@.j-4","@.j')' /*add the cousin pair to the $ list. */
if pairs//cols\==0 then iterate /*have we populated a line of output? */
say strip($); $= /*display what we have so far (cols). */
end /*j*/
if $\=='' then say strip($) /*possible display some residual output*/
say
say 'found ' pairs " cousin prime pairs."
say 'found ' pairs*2-dups " unique cousin primes."
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: parse arg n; @.=.; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; #= 7
!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1
do j=@.7+2 by 2 while j<=hi /*continue on with the next odd prime. */
parse var j '' -1 _ /*obtain the last digit of the J var.*/
if _ ==5 then iterate /*is this integer a multiple of five? */
if j // 3 ==0 then iterate /* " " " " " " three? */
/* [↓] divide by the primes. ___ */
do k=4 to # while k*k<=j /*divide J by other primes ≤ √ J */
if j//@.k == 0 then iterate j /*÷ by prev. prime? ¬prime ___ */
end /*k*/ /* [↑] only divide up to √ J */
#= # + 1; @.#= j; !.j= 1 /*bump prime count; assign prime & flag*/
end /*j*/
return
- output when using the default inputs:
(3,7) (7,11) (13,17) (19,23) (37,41) (43,47) (67,71) (79,83) (97,101) (103,107) (109,113) (127,131) (163,167) (193,197) (223,227) (229,233) (277,281) (307,311) (313,317) (349,353) (379,383) (397,401) (439,443) (457,461) (463,467) (487,491) (499,503) (613,617) (643,647) (673,677) (739,743) (757,761) (769,773) (823,827) (853,857) (859,863) (877,881) (883,887) (907,911) (937,941) (967,971) found 41 cousin prime pairs. found 81 unique cousin primes.
Raku
Filter
Favoring brevity over efficiency due to the small range of n, the most concise solution is:
say grep *.all.is-prime, map { $_, $_+4 }, 2..999;
- Output:
((3 7) (7 11) (13 17) (19 23) (37 41) (43 47) (67 71) (79 83) (97 101) (103 107) (109 113) (127 131) (163 167) (193 197) (223 227) (229 233) (277 281) (307 311) (313 317) (349 353) (379 383) (397 401) (439 443) (457 461) (463 467) (487 491) (499 503) (613 617) (643 647) (673 677) (739 743) (757 761) (769 773) (823 827) (853 857) (859 863) (877 881) (883 887) (907 911) (937 941) (967 971))
Infinite List
A more efficient and versatile approach is to generate an infinite list of cousin primes, using this info from https://oeis.org/A023200 :
- Apart from the first term, all terms are of the form 6n + 1.
constant @cousins = (3, 7, *+6 … *).map: -> \n { (n, n+4) if (n & n+4).is-prime };
my $count = @cousins.first: :k, *.[0] > 1000;
.say for @cousins.head($count).batch(9);
- Output:
((3 7) (7 11) (13 17) (19 23) (37 41) (43 47) (67 71) (79 83) (97 101)) ((103 107) (109 113) (127 131) (163 167) (193 197) (223 227) (229 233) (277 281) (307 311)) ((313 317) (349 353) (379 383) (397 401) (439 443) (457 461) (463 467) (487 491) (499 503)) ((613 617) (643 647) (673 677) (739 743) (757 761) (769 773) (823 827) (853 857) (859 863)) ((877 881) (883 887) (907 911) (937 941) (967 971))
Ring
load "stdlib.ring"
see "working..." + nl
see "cousin primes are:" + nl
ind = 0
row = 0
limit = 1000
cousin = []
for n = 1 to limit
if isprime(n) and isprime(n+4)
row = row + 1
ind1 = find(cousin,n)
ind2 = find(cousin,n+4)
if ind1 < 1
add(cousin,n)
ok
if ind2 < 1
add(cousin,n+4)
ok
see "(" + n + ", " + (n+4) + ") "
if row%5 = 0
see nl
ok
ok
next
lencousin = len(cousin)
see nl + "found " + row + " cousin prime pairs." + nl
see "found " + lencousin + " unique cousin primes." + nl
see "done..." + nl- Output:
working... cousin primes are: (3, 7) (7, 11) (13, 17) (19, 23) (37, 41) (43, 47) (67, 71) (79, 83) (97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971) found 41 cousin prime pairs. found 81 unique cousin primes. done...
RPL
≪ { } → cousins
≪ 2 3 5
DO
ROT DROP DUP NEXTPRIME
CASE
DUP 4 PICK - 4 == THEN PICK3 OVER R→C 'cousins' SWAP STO+ END
DUP2 - -4 == THEN DUP2 R→C 'cousins' SWAP STO+ END
END
UNTIL DUP 1000 ≥ END
3 DROPN
cousins DUP SIZE
≫ ≫ 'TASK' STO
- Output:
2: { (3., 7.) (7., 11.) (13., 17.) (19., 23.) (37., 41.) (43., 47.) (67., 71.) (79., 83.) (97., 101.) (103., 107.) (109., 113.) (127., 131.) (163., 167.) (193., 197.) (223., 227.) (229., 233.) (277., 281.) (307., 311.) (313., 317.) (349., 353.) (379., 383.) (397., 401.) (439., 443.) (457., 461.) (463., 467.) (487., 491.) (499., 503.) (613., 617.) (643., 647.) (673., 677.) (739., 743.) (757., 761.) (769., 773.) (823., 827.) (853., 857.) (859., 863.) (877., 881.) (883., 887.) (907., 911.) (937., 941.) (967., 971.) }
1: 41
Ruby
require 'prime'
primes = Prime.each(1000).to_a
p cousins = primes.filter_map{|pr| [pr, pr+4] if primes.include?(pr+4) }
puts "#{cousins.size} cousins found."
- Output:
[[3, 7], [7, 11], [13, 17], [19, 23], [37, 41], [43, 47], [67, 71], [79, 83], [97, 101], [103, 107], [109, 113], [127, 131], [163, 167], [193, 197], [223, 227], [229, 233], [277, 281], [307, 311], [313, 317], [349, 353], [379, 383], [397, 401], [439, 443], [457, 461], [463, 467], [487, 491], [499, 503], [613, 617], [643, 647], [673, 677], [739, 743], [757, 761], [769, 773], [823, 827], [853, 857], [859, 863], [877, 881], [883, 887], [907, 911], [937, 941], [967, 971]] 41 cousins found.
Seed7
$ include "seed7_05.s7i";
const func boolean: isPrime (in integer: number) is func
result
var boolean: prime is FALSE;
local
var integer: upTo is 0;
var integer: testNum is 3;
begin
if number = 2 then
prime := TRUE;
elsif odd(number) and number > 2 then
upTo := sqrt(number);
while number rem testNum <> 0 and testNum <= upTo do
testNum +:= 2;
end while;
prime := testNum > upTo;
end if;
end func;
const proc: main is func
local
var integer: n is 0;
var integer: count is 0;
begin
for n range 7 to 999 step 2 do
if isPrime(n) and isPrime(n - 4) then
writeln(n - 4 lpad 3 <& ", " <& n lpad 3);
incr(count);
end if;
end for;
writeln("\n" <& count <& " cousin prime pairs found < 1000.");
end func;- Output:
3, 7 7, 11 13, 17 19, 23 37, 41 43, 47 67, 71 79, 83 97, 101 103, 107 109, 113 127, 131 163, 167 193, 197 223, 227 229, 233 277, 281 307, 311 313, 317 349, 353 379, 383 397, 401 439, 443 457, 461 463, 467 487, 491 499, 503 613, 617 643, 647 673, 677 739, 743 757, 761 769, 773 823, 827 853, 857 859, 863 877, 881 883, 887 907, 911 937, 941 967, 971 41 cousin prime pairs found < 1000.
Sidef
var limit = 1000
var pairs = (limit-5).primes.map { [_, _+4] }.grep { .tail.is_prime }
say "Cousin prime pairs whose elements are less than #{limit.commify}:"
say pairs
say "\n#{pairs.len} pairs found"
- Output:
Cousin prime pairs whose elements are less than 1,000: [[3, 7], [7, 11], [13, 17], [19, 23], [37, 41], [43, 47], [67, 71], [79, 83], [97, 101], [103, 107], [109, 113], [127, 131], [163, 167], [193, 197], [223, 227], [229, 233], [277, 281], [307, 311], [313, 317], [349, 353], [379, 383], [397, 401], [439, 443], [457, 461], [463, 467], [487, 491], [499, 503], [613, 617], [643, 647], [673, 677], [739, 743], [757, 761], [769, 773], [823, 827], [853, 857], [859, 863], [877, 881], [883, 887], [907, 911], [937, 941], [967, 971]] 41 pairs found
Swift
import Foundation
func primeSieve(limit: Int) -> [Bool] {
guard limit > 0 else {
return []
}
var sieve = Array(repeating: true, count: limit)
sieve[0] = false
if limit > 1 {
sieve[1] = false
}
if limit > 4 {
for i in stride(from: 4, to: limit, by: 2) {
sieve[i] = false
}
}
var p = 3
var sq = p * p
while sq < limit {
if sieve[p] {
for i in stride(from: sq, to: limit, by: p * 2) {
sieve[i] = false
}
}
sq += (p + 1) * 4;
p += 2
}
return sieve
}
func toString(_ number: Int) -> String {
return String(format: "%3d", number)
}
let limit = 1000
let sieve = primeSieve(limit: limit)
var count = 0
for p in 0..<limit - 4 {
if sieve[p] && sieve[p + 4] {
print("(\(toString(p)), \(toString(p + 4)))", terminator: "")
count += 1
print(count % 5 == 0 ? "\n" : " ", terminator: "")
}
}
print("\nNumber of cousin prime pairs < \(limit): \(count)")
- Output:
( 3, 7) ( 7, 11) ( 13, 17) ( 19, 23) ( 37, 41) ( 43, 47) ( 67, 71) ( 79, 83) ( 97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971) Number of cousin prime pairs < 1000: 41
Wren
import "./math" for Int
import "./fmt" for Fmt
var c = Int.primeSieve(999, false)
var count = 0
System.print("Cousin prime pairs whose elements are less than 1,000:")
var i = 3
while (i <= 995) {
if (!c[i] && !c[i + 4]) {
Fmt.write("$3d:$3d ", i, i + 4)
count = count + 1
if ((count % 7) == 0) System.print()
i = (i != 3) ? i + 4 : i + 2
}
i = i + 2
}
System.print("\n\n%(count) pairs found")
- Output:
Cousin prime pairs whose elements are less than 1,000: 3: 7 7: 11 13: 17 19: 23 37: 41 43: 47 67: 71 79: 83 97:101 103:107 109:113 127:131 163:167 193:197 223:227 229:233 277:281 307:311 313:317 349:353 379:383 397:401 439:443 457:461 463:467 487:491 499:503 613:617 643:647 673:677 739:743 757:761 769:773 823:827 853:857 859:863 877:881 883:887 907:911 937:941 967:971 41 pairs found
XPL0
include xpllib; \For IsPrime and Print
int N, C;
[C:= 0;
for N:= 2 to 1000-1-4 do
[if IsPrime(N) then
if IsPrime(N+4) then
[Print("(%3.0f, %3.0f) ", float(N), float(N+4));
C:= C+1;
if rem(C/6) = 0 then CrLf(0);
];
];
Print("\nThere are %d cousin primes less than 1000.\n", C);
]- Output:
( 3, 7) ( 7, 11) ( 13, 17) ( 19, 23) ( 37, 41) ( 43, 47) ( 67, 71) ( 79, 83) ( 97, 101) (103, 107) (109, 113) (127, 131) (163, 167) (193, 197) (223, 227) (229, 233) (277, 281) (307, 311) (313, 317) (349, 353) (379, 383) (397, 401) (439, 443) (457, 461) (463, 467) (487, 491) (499, 503) (613, 617) (643, 647) (673, 677) (739, 743) (757, 761) (769, 773) (823, 827) (853, 857) (859, 863) (877, 881) (883, 887) (907, 911) (937, 941) (967, 971) There are 41 cousin primes less than 1000.
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