Cousin primes
- 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 less than 1,000.
Optionally, show the number of such pairs.
Pascal
Sieving only odd numbers.
<lang pascal>program CousinPrimes; //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
MAXZAHL = 1000;// > 3 MAXLIMIT = (MAXZAHL-1) DIV 2; //estimate CountOfPrimes = trunc(MAXZAHL/(ln(MAXZAHL)-1.08))+100;
type
tChkprimes = array[0..MAXLIMIT] of byte;//prime == 1 , nonprime == 0
var
Chkprimes:tChkprimes; primes : array[0..CountOfPrimes]of Uint32;//here starting with 3 primeCount:NativeInt;
procedure InitPrimes; //sieve of eratothenes var
i,j : NativeInt;
begin
// i = 2*j+1
fillchar(Chkprimes,SizeOf(tChkprimes),#1);
Chkprimes[0] := 0;
i := 1;
repeat
if Chkprimes[(i-1) DIV 2] <> 0 then
Begin
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);
end;
// writeln('prime count ',j+1,' til ',MAXZAHL); //count "2"
primeCount := j-1;
IF CountOfPrimes-primeCount < 0 then
begin
writeln(' Need more space for primes ', primeCount-CountOfPrimes);
HALT(-243);
end;
end; var
i,cnt : NativeInt;
BEGIN
InitPrimes;
//only exception, that the index difference is greater 1
write(primes[0]:3,':',primes[2]:3,' ');
cnt := 1;
For i := 1 to primeCount do
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;
writeln;
writeln(cnt,' cousin primes found');
END. </lang>
- 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 found
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl see "cousin primes are:" + nl
ind = 0 row = 0 limit = 1000
for n = 1 to limit
if isprime(n) and isprime(n+4)
row = row + 1
see "(" + n + ", " + (n+4) + ") "
if row%5 = 0
see nl
ok
ok
next
see nl + "done..." + nl </lang>
- 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) done...
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt
var c = Int.primeSieve(999, false) var count = 0 System.print("Cousin primes under 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")</lang>
- Output:
Cousin primes 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