Triplet of three numbers
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.
ALGOL 68
<lang algol68>BEGIN # find numbers n where n-1, n+3 and n+5 are prime #
INT max number = 6000;
# sieve the primes up to max number #
[ 1 : max number ]BOOL prime;
prime[ 1 ] := FALSE; prime[ 2 ] := TRUE;
FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( max number ) DO
IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI
OD;
# returns a string represention of n #
OP TOSTRING = ( INT n )STRING: whole( n, 0 );
# look for suitable numbers #
# 2 is clearly not a member of the required numbers, so we start at 3 #
INT n count := 0;
FOR n FROM 3 TO max number - 5 DO
IF prime[ n - 1 ] AND prime[ n + 3 ] AND prime[ n + 5 ] THEN
print( ( " (", TOSTRING n, " | ", TOSTRING ( n - 1 ), ", ", TOSTRING ( n + 3 ), ", ", TOSTRING ( n + 5 ), ")" ) );
n count +:= 1;
IF n count MOD 4 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline, "Found ", TOSTRING n count, " triplets", newline ) )
END</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) Found 46 triplets
AWK
<lang AWK>
- syntax: GAWK -f TRIPLET_OF_THREE_NUMBERS.AWK
BEGIN {
start = 1
stop = 6000
print(" N N-1 N+3 N+5")
print("----- ---- ---- ----")
for (i=start; i<=stop; i++) {
if (is_prime(i-1) && is_prime(i+3) && is_prime(i+5)) {
printf("%4d: %4d %4d %4d\n",i,i-1,i+3,i+5)
count++
}
}
printf("Triplet of three numbers %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)
} </lang>
- Output:
N N-1 N+3 N+5 ----- ---- ---- ---- 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 Triplet of three numbers 1-6000: 46
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
C#
How about some upper limits above 6000? <lang csharp>using System; using System.Collections.Generic; using System.Linq; using T3 = System.Tuple<int, int, int>; using static System.Console; class Program { static void Main() {
WriteLine(" \"N\": Prime Triplet Adjacent (to previous)\n" +
" ---- ----------------- -----------------------");
foreach(var lmt in new double[]{6e3, 1e5, 1e6, 1e7, 1e8}) {
var pr = PG.Primes((int)lmt); int l = 0, c = 0; bool a;
foreach (var t in pr) { c += (a = l == t.Item1) ? 1 : 0;
if (lmt < 1e5) WriteLine("{0,4}: {1,-18} {2}",
t.Item1 + 1, t, a ? " *" : ""); l = t.Item3; }
Console.WriteLine ("Up to {0:n0} there are {1:n0} prime triples, " +
"of which {2:n0} were found to be adjacent.", lmt, pr.Count(), c); } } }
class PG { static bool[] f; static bool isPrT(int x, int y, int z) {
if (x < 7) return false; return !f[x] && !f[y] && !f[z]; }
public static IEnumerable<T3> Primes(int l) { f = new bool[l += 6];
int j, lj, llj, lllj; j = lj = llj = lllj = 3;
for (int d = 8, s = 9; s < l; lllj = llj, llj = lj, lj = j, j += 2, s += d += 8)
if (!f[j]) { if (isPrT(lllj, lj, j)) yield return new T3(lllj, lj, j);
for (int k = s, i = j << 1; k < l; k += i) f[k] = true; }
for (; j < l; lllj = llj, llj = lj, lj = j, j += 2)
if (isPrT(lllj, lj, j)) yield return new T3(lllj, lj, j); } }</lang>
- Output:
"N": Prime Triplet Adjacent (to previous) ---- ----------------- ----------------------- 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) Up to 6,000 there are 46 prime triples, of which 5 were found to be adjacent. Up to 100,000 there are 248 prime triples, of which 11 were found to be adjacent. Up to 1,000,000 there are 1,444 prime triples, of which 31 were found to be adjacent. Up to 10,000,000 there are 8,677 prime triples, of which 161 were found to be adjacent. Up to 100,000,000 there are 55,556 prime triples, of which 686 were found to be adjacent.
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
F#
This task uses Extensible Prime Generator (F#) <lang fsharp> // Prime triplets: Nigel Galloway. May 18th., 2021 primes32()|>Seq.takeWhile((>)6000)|>Seq.filter(fun n->isPrime(n+4)&&isPrime(n+6))|>Seq.iter((+)1>>printf "%d "); printfn "" </lang>
- Output:
8 14 38 68 98 104 194 224 278 308 458 614 824 854 878 1088 1298 1424 1448 1484 1664 1694 1784 1868 1874 1994 2084 2138 2378 2684 2708 2798 3164 3254 3458 3464 3848 4154 4514 4784 5228 5414 5438 5648 5654 5738
Factor
<lang factor>USING: combinators formatting grouping kernel math math.primes math.statistics sequences ;
- 4,2-gaps ( upto -- seq )
4 + primes-upto 3 <clumps>
[ differences { 4 2 } sequence= ] filter ;
- triplet. ( 1 n 2 3 -- )
"..., %4d, [%4d], __, __, %4d, __, %4d, ...\n" printf ;
6000 4,2-gaps [ first3 [ dup 1 + ] 2dip triplet. ] each</lang>
- Output:
..., 7, [ 8], __, __, 11, __, 13, ... ..., 13, [ 14], __, __, 17, __, 19, ... ..., 37, [ 38], __, __, 41, __, 43, ... ..., 67, [ 68], __, __, 71, __, 73, ... ..., 97, [ 98], __, __, 101, __, 103, ... ..., 103, [ 104], __, __, 107, __, 109, ... ..., 193, [ 194], __, __, 197, __, 199, ... ..., 223, [ 224], __, __, 227, __, 229, ... ..., 277, [ 278], __, __, 281, __, 283, ... ..., 307, [ 308], __, __, 311, __, 313, ... ..., 457, [ 458], __, __, 461, __, 463, ... ..., 613, [ 614], __, __, 617, __, 619, ... ..., 823, [ 824], __, __, 827, __, 829, ... ..., 853, [ 854], __, __, 857, __, 859, ... ..., 877, [ 878], __, __, 881, __, 883, ... ..., 1087, [1088], __, __, 1091, __, 1093, ... ..., 1297, [1298], __, __, 1301, __, 1303, ... ..., 1423, [1424], __, __, 1427, __, 1429, ... ..., 1447, [1448], __, __, 1451, __, 1453, ... ..., 1483, [1484], __, __, 1487, __, 1489, ... ..., 1663, [1664], __, __, 1667, __, 1669, ... ..., 1693, [1694], __, __, 1697, __, 1699, ... ..., 1783, [1784], __, __, 1787, __, 1789, ... ..., 1867, [1868], __, __, 1871, __, 1873, ... ..., 1873, [1874], __, __, 1877, __, 1879, ... ..., 1993, [1994], __, __, 1997, __, 1999, ... ..., 2083, [2084], __, __, 2087, __, 2089, ... ..., 2137, [2138], __, __, 2141, __, 2143, ... ..., 2377, [2378], __, __, 2381, __, 2383, ... ..., 2683, [2684], __, __, 2687, __, 2689, ... ..., 2707, [2708], __, __, 2711, __, 2713, ... ..., 2797, [2798], __, __, 2801, __, 2803, ... ..., 3163, [3164], __, __, 3167, __, 3169, ... ..., 3253, [3254], __, __, 3257, __, 3259, ... ..., 3457, [3458], __, __, 3461, __, 3463, ... ..., 3463, [3464], __, __, 3467, __, 3469, ... ..., 3847, [3848], __, __, 3851, __, 3853, ... ..., 4153, [4154], __, __, 4157, __, 4159, ... ..., 4513, [4514], __, __, 4517, __, 4519, ... ..., 4783, [4784], __, __, 4787, __, 4789, ... ..., 5227, [5228], __, __, 5231, __, 5233, ... ..., 5413, [5414], __, __, 5417, __, 5419, ... ..., 5437, [5438], __, __, 5441, __, 5443, ... ..., 5647, [5648], __, __, 5651, __, 5653, ... ..., 5653, [5654], __, __, 5657, __, 5659, ... ..., 5737, [5738], __, __, 5741, __, 5743, ...
J
<lang j>triplet=: (1 *./@p: _1 3 5+])"0 echo (0 _1 3 5+])"0 (triplet#]) i.6000 exit </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
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 + 3, n + 5]), filter(makesprimetriplet, 2:6005))
</lang>
- Output:
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, 196, 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]
MAD
<lang MAD> NORMAL MODE IS INTEGER
BOOLEAN PRIME
DIMENSION PRIME(6005)
LIMIT = 6000
PRIME(0) = 0B
PRIME(1) = 0B
THROUGH SET, FOR I=2, 1, I.G.LIMIT+5
SET PRIME(I) = 1B
LAST = SQRT.(LIMIT+5)
THROUGH SIEVE, FOR I=2, 1, I.G.LAST
WHENEVER PRIME(I)
THROUGH UNSET, FOR J=I*2, I, J.G.LIMIT+5
UNSET PRIME(J) = 0B
END OF CONDITIONAL
SIEVE CONTINUE
THROUGH TEST, FOR I=2, 1, I.G.LIMIT
WHENEVER PRIME(I-1).AND.PRIME(I+3).AND.PRIME(I+5)
PRINT FORMAT FMT, I, I-1, I+3, I+5
END OF CONDITIONAL
TEST CONTINUE
VECTOR VALUES FMT = $I4,3H =,3(I5)*$
END OF PROGRAM </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
Nim
<lang Nim>import strformat
const
N = 5999 Max = 6003 # 5998 + 5.
- Sieve of Erathosthenes: false (default) is composite.
var composite: array[3..Max, bool] # Ignore 2 as all primes should be odd. var n = 3 while true:
let n2 = n * n
if n2 > Max: break
if not composite[n]:
for k in countup(n2, Max, 2 * n):
composite[k] = true
inc n, 2
template isPrime(n: int): bool = not composite[n]
echo " n n-1 n+3 n+5" var count = 0 for n in countup(4, N, 2):
if (n - 1). isPrime and (n + 3).isPrime and (n + 5).isPrime:
echo &"{n:4}: {n-1:4} {n+3:4} {n+5:4}"
inc count
echo &"\nFound {count} triplets for n < {N+1}."</lang>
- Output:
n n-1 n+3 n+5 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 triplets for n < 6000.
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Triplet_of_three_numbers use warnings;
my %cache; sub isprime { $cache{$_[0]} //= (1 x $_[0]) =~ /^(11+)\1+$/ ? 0 : 1 }
for ( 3 .. 6000 )
{
$_ & 1 and isprime($_+6) and isprime($_+4) and isprime($_) and
printf "%6d" x 4 . "\n", $_ + 1, $_, $_ + 4, $_ + 6;
}</lang>
- Output:
8 7 11 13
14 13 17 19
38 37 41 43
68 67 71 73
98 97 101 103
104 103 107 109
194 193 197 199
224 223 227 229
278 277 281 283
308 307 311 313
458 457 461 463
614 613 617 619
824 823 827 829
854 853 857 859
878 877 881 883
1088 1087 1091 1093
1298 1297 1301 1303
1424 1423 1427 1429
1448 1447 1451 1453
1484 1483 1487 1489
1664 1663 1667 1669
1694 1693 1697 1699
1784 1783 1787 1789
1868 1867 1871 1873
1874 1873 1877 1879
1994 1993 1997 1999
2084 2083 2087 2089
2138 2137 2141 2143
2378 2377 2381 2383
2684 2683 2687 2689
2708 2707 2711 2713
2798 2797 2801 2803
3164 3163 3167 3169
3254 3253 3257 3259
3458 3457 3461 3463
3464 3463 3467 3469
3848 3847 3851 3853
4154 4153 4157 4159
4514 4513 4517 4519
4784 4783 4787 4789
5228 5227 5231 5233
5414 5413 5417 5419
5438 5437 5441 5443
5648 5647 5651 5653
5654 5653 5657 5659
5738 5737 5741 5743
Phix
function trio(integer n) return sum(apply({n-1,n+3,n+5},is_prime))=3 end function sequence res = filter(tagset(6000),trio) printf(1,"%d found: %V\n",{length(res),shorten(res,"",5)})
- Output:
(assumes you can add {-1,3,5} to each number in your head easily enough)
46 found: {8,14,38,68,98,"...",5414,5438,5648,5654,5738}
PL/M
<lang plm>100H: BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS; EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT; PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9, S); END PRINT;
DECLARE LIMIT LITERALLY '6000';
PRINT$NUMBER: PROCEDURE (N);
DECLARE S (6) BYTE INITIAL ('.....$');
DECLARE (N, P) ADDRESS, C BASED P BYTE;
P = .S(5);
DIGIT:
P = P-1; C = N MOD 10 + '0'; N = N/10; IF N>0 THEN GO TO DIGIT; CALL PRINT(P);
END PRINT$NUMBER;
SIEVE: PROCEDURE (PX, N);
DECLARE (PX, N, P BASED PX) ADDRESS;
DECLARE (I, J) ADDRESS;
P(0) = 0;
P(1) = 0;
DO I=2 TO N;
P(I) = 1;
END;
DO I=2 TO N/2;
IF P(I) THEN
DO J=I*2 TO N BY I;
P(J) = 0;
END;
END;
END SIEVE;
IS$TRIPLE: PROCEDURE (PX, N) BYTE;
DECLARE (PX, N, P BASED PX) ADDRESS; IF N < 2 THEN RETURN 0; RETURN P(N-1) AND P(N+3) AND P(N+5);
END IS$TRIPLE;
PRINT$TRIPLE: PROCEDURE (N);
DECLARE COMMA DATA (', $');
DECLARE N ADDRESS;
CALL PRINT$NUMBER(N);
CALL PRINT(.': $');
CALL PRINT$NUMBER(N-1);
CALL PRINT(.COMMA);
CALL PRINT$NUMBER(N+3);
CALL PRINT(.COMMA);
CALL PRINT$NUMBER(N+5);
CALL PRINT(.(13,10,'$'));
END PRINT$TRIPLE;
DECLARE I ADDRESS; CALL SIEVE(.MEMORY, LIMIT+5); DO I=2 TO LIMIT;
IF IS$TRIPLE(.MEMORY, I) THEN CALL PRINT$TRIPLE(I);
END; CALL EXIT; EOF</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
Quackery
<lang Quackery> [ 1 swap times [ i 1+ * ] ] is ! ( n --> n )
[ dup 2 < iff
[ drop false ] done
dup 1 - ! 1+
swap mod 0 = ] is prime ( n --> b )
[] 3000 times
[ i^ 2 *
dup 1 - prime iff
[ dup 3 + prime iff
[ dup 5 + prime iff
join else drop ]
else drop ]
else drop ]
echo</lang>
- Output:
[ 8 14 38 68 98 104 194 224 278 308 458 614 824 854 878 1088 1298 1424 1448 1484 1664 1694 1784 1868 1874 1994 2084 2138 2378 2684 2708 2798 3164 3254 3458 3464 3848 4154 4514 4784 5228 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)
REXX
<lang rexx>/*REXX pgm finds prime triplets (Alabama primes) such that P, P-1, and P+2 are primes.*/ parse arg hi . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 6000 /*Not specified? Then use the default.*/ call genP /*build array of semaphores for primes.*/ w= length( commas(hi) ) /*the width of the largest number. */ ow= 70; pad= left(, w + 1) /*the width of the data column. */ @primTrip= ' prime triplets such that N-1, N+3, N+5 are prime, N < ' commas(hi) say ' N │'center(@primTrip, 1 + (ow+1) ) /*display the title for the output grid*/ say '───────┼'center("" , 1 + (ow+1), '─') /* " " header " " " " */ found= 0 /*initialize # of prime triplets. */
do j=1 for hi-1 /*find some prime triplets < HI. */
if \isPrime(j-1) | \isPrime(j+3) | \isPrime(j+5) then iterate /*¬ prime? */
found= found + 1 /*bump the number of prime triplets. */
say center(commas(j), 7)'│' pad "(N-1)=" right( commas(j-1), w) ,
pad '(N+3)=' right( commas(j+3), w) ,
pad "(N+5)=" right( commas(j+5), w)
end /*j*/
say '───────┴'center("" , 1 + (ow+1), '─') /*display foot header for output grid. */ say say 'Found ' commas(found) @primTrip exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? isPrime: parse arg ?; return !.? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: @.1=2; @.2=3; @.3=5; @.4=7 /*define some low primes. */
!.=0; !.2=1; !.3=1; !.5=1; !.7=1 /* " " " " semaphores. */
#=4; s.#= @.# **2 /*number of primes so far; prime². */
do j=@.#+2 by 2 to hi /*find odd primes where P < hi. */
parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
do k=4 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</lang>
- output when using the default inputs:
N │ prime triplets such that N-1, N+3, N+5 are prime, N < 6,000 ───────┼──────────────────────────────────────────────────────────────────────── 8 │ (N-1)= 7 (N+3)= 11 (N+5)= 13 14 │ (N-1)= 13 (N+3)= 17 (N+5)= 19 38 │ (N-1)= 37 (N+3)= 41 (N+5)= 43 68 │ (N-1)= 67 (N+3)= 71 (N+5)= 73 98 │ (N-1)= 97 (N+3)= 101 (N+5)= 103 104 │ (N-1)= 103 (N+3)= 107 (N+5)= 109 194 │ (N-1)= 193 (N+3)= 197 (N+5)= 199 224 │ (N-1)= 223 (N+3)= 227 (N+5)= 229 278 │ (N-1)= 277 (N+3)= 281 (N+5)= 283 308 │ (N-1)= 307 (N+3)= 311 (N+5)= 313 458 │ (N-1)= 457 (N+3)= 461 (N+5)= 463 614 │ (N-1)= 613 (N+3)= 617 (N+5)= 619 824 │ (N-1)= 823 (N+3)= 827 (N+5)= 829 854 │ (N-1)= 853 (N+3)= 857 (N+5)= 859 878 │ (N-1)= 877 (N+3)= 881 (N+5)= 883 1,088 │ (N-1)= 1,087 (N+3)= 1,091 (N+5)= 1,093 1,298 │ (N-1)= 1,297 (N+3)= 1,301 (N+5)= 1,303 1,424 │ (N-1)= 1,423 (N+3)= 1,427 (N+5)= 1,429 1,448 │ (N-1)= 1,447 (N+3)= 1,451 (N+5)= 1,453 1,484 │ (N-1)= 1,483 (N+3)= 1,487 (N+5)= 1,489 1,664 │ (N-1)= 1,663 (N+3)= 1,667 (N+5)= 1,669 1,694 │ (N-1)= 1,693 (N+3)= 1,697 (N+5)= 1,699 1,784 │ (N-1)= 1,783 (N+3)= 1,787 (N+5)= 1,789 1,868 │ (N-1)= 1,867 (N+3)= 1,871 (N+5)= 1,873 1,874 │ (N-1)= 1,873 (N+3)= 1,877 (N+5)= 1,879 1,994 │ (N-1)= 1,993 (N+3)= 1,997 (N+5)= 1,999 2,084 │ (N-1)= 2,083 (N+3)= 2,087 (N+5)= 2,089 2,138 │ (N-1)= 2,137 (N+3)= 2,141 (N+5)= 2,143 2,378 │ (N-1)= 2,377 (N+3)= 2,381 (N+5)= 2,383 2,684 │ (N-1)= 2,683 (N+3)= 2,687 (N+5)= 2,689 2,708 │ (N-1)= 2,707 (N+3)= 2,711 (N+5)= 2,713 2,798 │ (N-1)= 2,797 (N+3)= 2,801 (N+5)= 2,803 3,164 │ (N-1)= 3,163 (N+3)= 3,167 (N+5)= 3,169 3,254 │ (N-1)= 3,253 (N+3)= 3,257 (N+5)= 3,259 3,458 │ (N-1)= 3,457 (N+3)= 3,461 (N+5)= 3,463 3,464 │ (N-1)= 3,463 (N+3)= 3,467 (N+5)= 3,469 3,848 │ (N-1)= 3,847 (N+3)= 3,851 (N+5)= 3,853 4,154 │ (N-1)= 4,153 (N+3)= 4,157 (N+5)= 4,159 4,514 │ (N-1)= 4,513 (N+3)= 4,517 (N+5)= 4,519 4,784 │ (N-1)= 4,783 (N+3)= 4,787 (N+5)= 4,789 5,228 │ (N-1)= 5,227 (N+3)= 5,231 (N+5)= 5,233 5,414 │ (N-1)= 5,413 (N+3)= 5,417 (N+5)= 5,419 5,438 │ (N-1)= 5,437 (N+3)= 5,441 (N+5)= 5,443 5,648 │ (N-1)= 5,647 (N+3)= 5,651 (N+5)= 5,653 5,654 │ (N-1)= 5,653 (N+3)= 5,657 (N+5)= 5,659 5,738 │ (N-1)= 5,737 (N+3)= 5,741 (N+5)= 5,743 ───────┴──────────────────────────────────────────────────────────────────────── Found 46 prime triplets such that N-1, N+3, N+5 are prime, N < 6,000
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 + " prime triplets" + 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 prime triplets 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.