Triplet of three numbers: Difference between revisions
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5654: 5653, 5657, 5659 |
5654: 5653, 5657, 5659 |
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5738: 5737, 5741, 5743</pre> |
5738: 5737, 5741, 5743</pre> |
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=={{header|Cowgol}}== |
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<lang cowgol>include "cowgol.coh"; |
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const LIMIT := 6000; |
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var prime: uint8[LIMIT+5]; |
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var i: @indexof prime; |
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var j: @indexof prime; |
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prime[0] := 0; |
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prime[1] := 0; |
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MemSet(&prime[2], 1, @bytesof prime-2); |
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i := 2; |
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while i <= @sizeof prime/2-1 loop |
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if prime[i] != 0 then |
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j := i*2; |
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while j <= @sizeof prime-1 loop |
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prime[j] := 0; |
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j := j+i; |
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end loop; |
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end if; |
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i := i+1; |
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end loop; |
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i := 2; |
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while i < LIMIT loop |
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if prime[i-1] & prime[i+3] & prime[i+5] != 0 then |
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print_i32(i as uint32); |
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print(": "); |
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print_i32(i as uint32-1); |
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print(", "); |
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print_i32(i as uint32+3); |
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print(", "); |
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print_i32(i as uint32+5); |
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print_nl(); |
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end if; |
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i := i + 1; |
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end loop;</lang> |
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{{out}} |
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<pre style='height:50ex'>8: 7, 11, 13 |
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14: 13, 17, 19 |
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38: 37, 41, 43 |
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68: 67, 71, 73 |
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98: 97, 101, 103 |
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104: 103, 107, 109 |
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194: 193, 197, 199 |
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224: 223, 227, 229 |
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278: 277, 281, 283 |
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308: 307, 311, 313 |
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458: 457, 461, 463 |
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614: 613, 617, 619 |
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824: 823, 827, 829 |
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854: 853, 857, 859 |
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878: 877, 881, 883 |
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1088: 1087, 1091, 1093 |
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1298: 1297, 1301, 1303 |
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1424: 1423, 1427, 1429 |
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1448: 1447, 1451, 1453 |
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1484: 1483, 1487, 1489 |
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1664: 1663, 1667, 1669 |
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1694: 1693, 1697, 1699 |
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1784: 1783, 1787, 1789 |
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1868: 1867, 1871, 1873 |
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1874: 1873, 1877, 1879 |
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1994: 1993, 1997, 1999 |
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2084: 2083, 2087, 2089 |
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2138: 2137, 2141, 2143 |
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2378: 2377, 2381, 2383 |
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2684: 2683, 2687, 2689 |
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2708: 2707, 2711, 2713 |
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2798: 2797, 2801, 2803 |
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3164: 3163, 3167, 3169 |
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3254: 3253, 3257, 3259 |
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3458: 3457, 3461, 3463 |
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3464: 3463, 3467, 3469 |
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3848: 3847, 3851, 3853 |
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4154: 4153, 4157, 4159 |
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4514: 4513, 4517, 4519 |
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4784: 4783, 4787, 4789 |
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5228: 5227, 5231, 5233 |
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5414: 5413, 5417, 5419 |
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5438: 5437, 5441, 5443 |
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5648: 5647, 5651, 5653 |
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5654: 5653, 5657, 5659 |
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5738: 5737, 5741, 5743</lang> |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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<lang julia>using Primes |
<lang julia>using Primes |
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Revision as of 20:43, 17 May 2021
Triplet of three numbers 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.
- Task
Numbers n such that the three numbers n-1, n+3 and n+5 are all prime. where n < 6000
BASIC
<lang basic>10 DEFINT A-Z: N=6000 20 DIM P(N+5) 30 FOR I=2 TO SQR(N) 40 IF NOT P(I) THEN FOR J=I*2 TO N STEP I: P(J)=1: NEXT 50 NEXT 60 FOR I=3 TO N 70 IF P(I-1) OR P(I+3) OR P(I+5) GOTO 90 80 PRINT USING "####,: ####, ####, ####,";I;I-1;I+3;I+5 90 NEXT</lang>
- Output:
8: 7 11 13 14: 13 17 19 38: 37 41 43 68: 67 71 73 98: 97 101 103 104: 103 107 109 194: 193 197 199 224: 223 227 229 278: 277 281 283 308: 307 311 313 458: 457 461 463 614: 613 617 619 824: 823 827 829 854: 853 857 859 878: 877 881 883 1,088: 1,087 1,091 1,093 1,298: 1,297 1,301 1,303 1,424: 1,423 1,427 1,429 1,448: 1,447 1,451 1,453 1,484: 1,483 1,487 1,489 1,664: 1,663 1,667 1,669 1,694: 1,693 1,697 1,699 1,784: 1,783 1,787 1,789 1,868: 1,867 1,871 1,873 1,874: 1,873 1,877 1,879 1,994: 1,993 1,997 1,999 2,084: 2,083 2,087 2,089 2,138: 2,137 2,141 2,143 2,378: 2,377 2,381 2,383 2,684: 2,683 2,687 2,689 2,708: 2,707 2,711 2,713 2,798: 2,797 2,801 2,803 3,164: 3,163 3,167 3,169 3,254: 3,253 3,257 3,259 3,458: 3,457 3,461 3,463 3,464: 3,463 3,467 3,469 3,848: 3,847 3,851 3,853 4,154: 4,153 4,157 4,159 4,514: 4,513 4,517 4,519 4,784: 4,783 4,787 4,789 5,228: 5,227 5,231 5,233 5,414: 5,413 5,417 5,419 5,438: 5,437 5,441 5,443 5,648: 5,647 5,651 5,653 5,654: 5,653 5,657 5,659 5,738: 5,737 5,741 5,743
BCPL
<lang bcpl>get "libhdr" manifest $( limit = 6000 $)
let sieve(p, n) be $( p!0 := false
p!1 := false
for i=2 to n do p!i := true
for i=2 to n/2
if p!i
$( let j = i*2
while j <= n
$( p!j := false
j := j+i
$)
$)
$)
let triplet(p, n) = n>=2 & p!(n-1) & p!(n+3) & p!(n+5)
let start() be $( let prime = getvec(limit)
sieve(prime, limit)
for i=2 to limit
if triplet(prime, i) do
writef("%I4: %I4, %I4, %I4*N", i, i-1, i+3, i+5)
freevec(prime)
$)</lang>
- Output:
8: 7, 11, 13 14: 13, 17, 19 38: 37, 41, 43 68: 67, 71, 73 98: 97, 101, 103 104: 103, 107, 109 194: 193, 197, 199 224: 223, 227, 229 278: 277, 281, 283 308: 307, 311, 313 458: 457, 461, 463 614: 613, 617, 619 824: 823, 827, 829 854: 853, 857, 859 878: 877, 881, 883 1088: 1087, 1091, 1093 1298: 1297, 1301, 1303 1424: 1423, 1427, 1429 1448: 1447, 1451, 1453 1484: 1483, 1487, 1489 1664: 1663, 1667, 1669 1694: 1693, 1697, 1699 1784: 1783, 1787, 1789 1868: 1867, 1871, 1873 1874: 1873, 1877, 1879 1994: 1993, 1997, 1999 2084: 2083, 2087, 2089 2138: 2137, 2141, 2143 2378: 2377, 2381, 2383 2684: 2683, 2687, 2689 2708: 2707, 2711, 2713 2798: 2797, 2801, 2803 3164: 3163, 3167, 3169 3254: 3253, 3257, 3259 3458: 3457, 3461, 3463 3464: 3463, 3467, 3469 3848: 3847, 3851, 3853 4154: 4153, 4157, 4159 4514: 4513, 4517, 4519 4784: 4783, 4787, 4789 5228: 5227, 5231, 5233 5414: 5413, 5417, 5419 5438: 5437, 5441, 5443 5648: 5647, 5651, 5653 5654: 5653, 5657, 5659 5738: 5737, 5741, 5743
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- include <math.h>
- define LIMIT 6000
char *primes(unsigned int limit) {
char *p = malloc(limit + 1);
int i, j, sqr = sqrt(limit);
p[0] = p[1] = 0;
memset(p+2, 1, limit-1);
for (i=2; i<=sqr; i++)
if (p[i])
for (j=i*2; j<=limit; j+=i)
p[j] = 0;
return p;
}
int triplet(const char *p, unsigned int n) {
return n >= 2 && p[n-1] && p[n+3] && p[n+5];
}
int main() {
char *p = primes(LIMIT+5);
int i;
for (i=2; i<LIMIT; i++)
if (triplet(p, i))
printf("%4d: %4d, %4d, %4d\n", i, i-1, i+3, i+5);
free(p);
return 0;
}</lang>
- Output:
8: 7, 11, 13 14: 13, 17, 19 38: 37, 41, 43 68: 67, 71, 73 98: 97, 101, 103 104: 103, 107, 109 194: 193, 197, 199 224: 223, 227, 229 278: 277, 281, 283 308: 307, 311, 313 458: 457, 461, 463 614: 613, 617, 619 824: 823, 827, 829 854: 853, 857, 859 878: 877, 881, 883 1088: 1087, 1091, 1093 1298: 1297, 1301, 1303 1424: 1423, 1427, 1429 1448: 1447, 1451, 1453 1484: 1483, 1487, 1489 1664: 1663, 1667, 1669 1694: 1693, 1697, 1699 1784: 1783, 1787, 1789 1868: 1867, 1871, 1873 1874: 1873, 1877, 1879 1994: 1993, 1997, 1999 2084: 2083, 2087, 2089 2138: 2137, 2141, 2143 2378: 2377, 2381, 2383 2684: 2683, 2687, 2689 2708: 2707, 2711, 2713 2798: 2797, 2801, 2803 3164: 3163, 3167, 3169 3254: 3253, 3257, 3259 3458: 3457, 3461, 3463 3464: 3463, 3467, 3469 3848: 3847, 3851, 3853 4154: 4153, 4157, 4159 4514: 4513, 4517, 4519 4784: 4783, 4787, 4789 5228: 5227, 5231, 5233 5414: 5413, 5417, 5419 5438: 5437, 5441, 5443 5648: 5647, 5651, 5653 5654: 5653, 5657, 5659 5738: 5737, 5741, 5743
Cowgol
<lang cowgol>include "cowgol.coh";
const LIMIT := 6000;
var prime: uint8[LIMIT+5]; var i: @indexof prime; var j: @indexof prime;
prime[0] := 0; prime[1] := 0; MemSet(&prime[2], 1, @bytesof prime-2); i := 2; while i <= @sizeof prime/2-1 loop
if prime[i] != 0 then
j := i*2;
while j <= @sizeof prime-1 loop
prime[j] := 0;
j := j+i;
end loop;
end if;
i := i+1;
end loop;
i := 2; while i < LIMIT loop
if prime[i-1] & prime[i+3] & prime[i+5] != 0 then
print_i32(i as uint32);
print(": ");
print_i32(i as uint32-1);
print(", ");
print_i32(i as uint32+3);
print(", ");
print_i32(i as uint32+5);
print_nl();
end if;
i := i + 1;
end loop;</lang>
- Output:
8: 7, 11, 13
14: 13, 17, 19
38: 37, 41, 43
68: 67, 71, 73
98: 97, 101, 103
104: 103, 107, 109
194: 193, 197, 199
224: 223, 227, 229
278: 277, 281, 283
308: 307, 311, 313
458: 457, 461, 463
614: 613, 617, 619
824: 823, 827, 829
854: 853, 857, 859
878: 877, 881, 883
1088: 1087, 1091, 1093
1298: 1297, 1301, 1303
1424: 1423, 1427, 1429
1448: 1447, 1451, 1453
1484: 1483, 1487, 1489
1664: 1663, 1667, 1669
1694: 1693, 1697, 1699
1784: 1783, 1787, 1789
1868: 1867, 1871, 1873
1874: 1873, 1877, 1879
1994: 1993, 1997, 1999
2084: 2083, 2087, 2089
2138: 2137, 2141, 2143
2378: 2377, 2381, 2383
2684: 2683, 2687, 2689
2708: 2707, 2711, 2713
2798: 2797, 2801, 2803
3164: 3163, 3167, 3169
3254: 3253, 3257, 3259
3458: 3457, 3461, 3463
3464: 3463, 3467, 3469
3848: 3847, 3851, 3853
4154: 4153, 4157, 4159
4514: 4513, 4517, 4519
4784: 4783, 4787, 4789
5228: 5227, 5231, 5233
5414: 5413, 5417, 5419
5438: 5437, 5441, 5443
5648: 5647, 5651, 5653
5654: 5653, 5657, 5659
5738: 5737, 5741, 5743</lang>
=={{header|Julia}}==
<lang julia>using Primes
makesprimetriplet(n) = all(isprime, [n - 1, n + 3, n + 5])
println(" N Prime Triplet\n--------------------------")
foreach(n -> println(rpad(n, 6), [n - 1, n + 1, n + 5]), filter(makesprimetriplet, 2:6005))
</lang>{{out}}
<pre>
N Prime Triplet
--------------------------
8 [7, 9, 13]
14 [13, 15, 19]
38 [37, 39, 43]
68 [67, 69, 73]
98 [97, 99, 103]
104 [103, 105, 109]
194 [193, 195, 199]
224 [223, 225, 229]
278 [277, 279, 283]
308 [307, 309, 313]
458 [457, 459, 463]
614 [613, 615, 619]
824 [823, 825, 829]
854 [853, 855, 859]
878 [877, 879, 883]
1088 [1087, 1089, 1093]
1298 [1297, 1299, 1303]
1424 [1423, 1425, 1429]
1448 [1447, 1449, 1453]
1484 [1483, 1485, 1489]
1664 [1663, 1665, 1669]
1694 [1693, 1695, 1699]
1784 [1783, 1785, 1789]
1868 [1867, 1869, 1873]
1874 [1873, 1875, 1879]
1994 [1993, 1995, 1999]
2084 [2083, 2085, 2089]
2138 [2137, 2139, 2143]
2378 [2377, 2379, 2383]
2684 [2683, 2685, 2689]
2708 [2707, 2709, 2713]
2798 [2797, 2799, 2803]
3164 [3163, 3165, 3169]
3254 [3253, 3255, 3259]
3458 [3457, 3459, 3463]
3464 [3463, 3465, 3469]
3848 [3847, 3849, 3853]
4154 [4153, 4155, 4159]
4514 [4513, 4515, 4519]
4784 [4783, 4785, 4789]
5228 [5227, 5229, 5233]
5414 [5413, 5415, 5419]
5438 [5437, 5439, 5443]
5648 [5647, 5649, 5653]
5654 [5653, 5655, 5659]
5738 [5737, 5739, 5743]
Phix
function trio(integer n) return sum(apply({n-1,n+3,n+5},is_prime))=3 end function sequence res = filter(tagset(6000),trio) printf(1,"%d found: %V\n",{length(res),shorten(res,"",5)})
- Output:
46 found: {8,14,38,68,98,"...",5414,5438,5648,5654,5738}
Raku
A weird combination of Cousin primes and Twin primes that are siblings, but known by their neighbor.... I shall dub these Alabama primes.
<lang perl6>say "{.[0]+1}: ",$_ for grep *.all.is-prime, ^6000 .race.map: { $_-1, $_+3, $_+5 };</lang>
- Output:
8: (7 11 13) 14: (13 17 19) 38: (37 41 43) 68: (67 71 73) 98: (97 101 103) 104: (103 107 109) 194: (193 197 199) 224: (223 227 229) 278: (277 281 283) 308: (307 311 313) 458: (457 461 463) 614: (613 617 619) 824: (823 827 829) 854: (853 857 859) 878: (877 881 883) 1088: (1087 1091 1093) 1298: (1297 1301 1303) 1424: (1423 1427 1429) 1448: (1447 1451 1453) 1484: (1483 1487 1489) 1664: (1663 1667 1669) 1694: (1693 1697 1699) 1784: (1783 1787 1789) 1868: (1867 1871 1873) 1874: (1873 1877 1879) 1994: (1993 1997 1999) 2084: (2083 2087 2089) 2138: (2137 2141 2143) 2378: (2377 2381 2383) 2684: (2683 2687 2689) 2708: (2707 2711 2713) 2798: (2797 2801 2803) 3164: (3163 3167 3169) 3254: (3253 3257 3259) 3458: (3457 3461 3463) 3464: (3463 3467 3469) 3848: (3847 3851 3853) 4154: (4153 4157 4159) 4514: (4513 4517 4519) 4784: (4783 4787 4789) 5228: (5227 5231 5233) 5414: (5413 5417 5419) 5438: (5437 5441 5443) 5648: (5647 5651 5653) 5654: (5653 5657 5659) 5738: (5737 5741 5743)
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "n prime triplet" + nl see "----------------" + nl row = 0
limit = 6000
for n = 2 to limit-2
bool1 = isprime(n-1)
bool2 = isprime(n+3)
bool3 = isprime(n+5)
bool = bool1 and bool2 and bool3
if bool
row = row + 1
see "" + n + ": (" + (n-1) + " " + (n+3) + " " + (n+5) + ")" + nl
ok
next
see "Found " + row + " primes" + nl see "done..." + nl </lang>
- Output:
working... n prime triplet ---------------- 8: (7 11 13) 14: (13 17 19) 38: (37 41 43) 68: (67 71 73) 98: (97 101 103) 104: (103 107 109) 194: (193 197 199) 224: (223 227 229) 278: (277 281 283) 308: (307 311 313) 458: (457 461 463) 614: (613 617 619) 824: (823 827 829) 854: (853 857 859) 878: (877 881 883) 1088: (1087 1091 1093) 1298: (1297 1301 1303) 1424: (1423 1427 1429) 1448: (1447 1451 1453) 1484: (1483 1487 1489) 1664: (1663 1667 1669) 1694: (1693 1697 1699) 1784: (1783 1787 1789) 1868: (1867 1871 1873) 1874: (1873 1877 1879) 1994: (1993 1997 1999) 2084: (2083 2087 2089) 2138: (2137 2141 2143) 2378: (2377 2381 2383) 2684: (2683 2687 2689) 2708: (2707 2711 2713) 2798: (2797 2801 2803) 3164: (3163 3167 3169) 3254: (3253 3257 3259) 3458: (3457 3461 3463) 3464: (3463 3467 3469) 3848: (3847 3851 3853) 4154: (4153 4157 4159) 4514: (4513 4517 4519) 4784: (4783 4787 4789) 5228: (5227 5231 5233) 5414: (5413 5417 5419) 5438: (5437 5441 5443) 5648: (5647 5651 5653) 5654: (5653 5657 5659) 5738: (5737 5741 5743) Found 46 primes done...
Wren
<lang ecmascript>import "/math" for Int import "/fmt" for Fmt
var c = Int.primeSieve(6003, false) var numbers = [] System.print("Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:") var n = 4 while (n < 6000) {
if (!c[n-1] && !c[n+3] && !c[n+5]) numbers.add(n) n = n + 2
} for (n in numbers) Fmt.print("$,6d => $,6d", n, [n-1, n+3, n+5]) System.print("\nFound %(numbers.count) such numbers.")</lang>
- Output:
Numbers n < 6000 where: n - 1, n + 3, n + 5 are all primes:
8 => 7 11 13
14 => 13 17 19
38 => 37 41 43
68 => 67 71 73
98 => 97 101 103
104 => 103 107 109
194 => 193 197 199
224 => 223 227 229
278 => 277 281 283
308 => 307 311 313
458 => 457 461 463
614 => 613 617 619
824 => 823 827 829
854 => 853 857 859
878 => 877 881 883
1,088 => 1,087 1,091 1,093
1,298 => 1,297 1,301 1,303
1,424 => 1,423 1,427 1,429
1,448 => 1,447 1,451 1,453
1,484 => 1,483 1,487 1,489
1,664 => 1,663 1,667 1,669
1,694 => 1,693 1,697 1,699
1,784 => 1,783 1,787 1,789
1,868 => 1,867 1,871 1,873
1,874 => 1,873 1,877 1,879
1,994 => 1,993 1,997 1,999
2,084 => 2,083 2,087 2,089
2,138 => 2,137 2,141 2,143
2,378 => 2,377 2,381 2,383
2,684 => 2,683 2,687 2,689
2,708 => 2,707 2,711 2,713
2,798 => 2,797 2,801 2,803
3,164 => 3,163 3,167 3,169
3,254 => 3,253 3,257 3,259
3,458 => 3,457 3,461 3,463
3,464 => 3,463 3,467 3,469
3,848 => 3,847 3,851 3,853
4,154 => 4,153 4,157 4,159
4,514 => 4,513 4,517 4,519
4,784 => 4,783 4,787 4,789
5,228 => 5,227 5,231 5,233
5,414 => 5,413 5,417 5,419
5,438 => 5,437 5,441 5,443
5,648 => 5,647 5,651 5,653
5,654 => 5,653 5,657 5,659
5,738 => 5,737 5,741 5,743
Found 46 such numbers.