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Line 5: Find and show primes p such that pq+2 is prime, where q is next prime after p and '''p < 500''' <br><br> See also: [[Special neighbor primes]] =={{header\|11l}}== Line 53 ⟶ 56: 439 443 194479 487 491 239119 </pre> =={{header\|ALGOL 68}}== {{libheader\|ALGOL 68-primes}} Very similar to [[Special_neighbor_primes#ALGOL_68\|The ALGOL 68 sample in the Special neighbor primes task]] <syntaxhighlight lang="algol68"> BEGIN # find adjacent primes p1, p2 such that p1p2 + 2 s also prime # PR read "primes.incl.a68" PR INT max prime = 500; []BOOL prime = PRIMESIEVE ( ( max prime max prime ) + 2 ); # sieve the primes to max prime ^ 2 + 2 # []INT low prime = EXTRACTPRIMESUPTO max prime FROMPRIMESIEVE prime; # get a list of the primes up to max prime # # find the adjacent primes p1, p2 such that p1p2 + 2 is prime # FOR i TO UPB low prime - 1 DO IF INT p1 p2 plus 2 = ( low prime[ i ] low prime[ i + 1 ] ) + 2; prime[ p1 p2 plus 2 ] THEN print( ( "(", whole( low prime[ i ], -3 ) , " ", whole( low prime[ i + 1 ], -3 ) , " ) + 2 = ", whole( p1 p2 plus 2, -6 ) , newline ) ) FI OD END </syntaxhighlight> {{out}} <pre> ( 3 5 ) + 2 = 17 ( 5 * 7 ) + 2 = 37 ( 7 * 11 ) + 2 = 79 ( 13 * 17 ) + 2 = 223 ( 19 * 23 ) + 2 = 439 ( 67 * 71 ) + 2 = 4759 (149 151 ) + 2 = 22501 (179 181 ) + 2 = 32401 (229 233 ) + 2 = 53359 (239 241 ) + 2 = 57601 (241 251 ) + 2 = 60493 (269 271 ) + 2 = 72901 (277 281 ) + 2 = 77839 (307 311 ) + 2 = 95479 (313 317 ) + 2 = 99223 (397 401 ) + 2 = 159199 (401 409 ) + 2 = 164011 (419 421 ) + 2 = 176401 (439 443 ) + 2 = 194479 (487 491 ) + 2 = 239119 </pre> Line 407 ⟶ 457: 17 found under 500 for " + 18 " 25 found under 500 for " + 20 "</pre> =={{header\|Delphi}}== {{works with\|Delphi\|6.0}} {{libheader\|SysUtils,StdCtrls}} <syntaxhighlight lang="Delphi"> function IsPrime(N: int64): boolean; {Fast, optimised prime test} var I,Stop: int64; begin if (N = 2) or (N=3) then Result:=true else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false else begin I:=5; Stop:=Trunc(sqrt(N+0.0)); Result:=False; while I<=Stop do begin if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit; Inc(I,6); end; Result:=True; end; end; function GetNextPrime(var Start: integer): integer; {Get the next prime number after Start} {Start is passed by "reference," so the {original variable is incremented} begin repeat Inc(Start) until IsPrime(Start); Result:=Start; end; procedure ShowNeighborPrimes(Memo: TMemo); var P1,P2,P3,Cnt: integer; var S: string; begin Memo.Lines.Add('Count P Q PQ+2'); Memo.Lines.Add('-----------------------'); Cnt:=0; P1:=1; P2:=1; S:=''; While P1< 500 do begin GetNextPrime(P2); P3:=P1 * P2 + 2; if IsPrime(P3) then begin Inc(Cnt); S:=S+Format('%5D %4D %4D %6D',[Cnt,P1,P2,P3]); S:=S+#$0D#$0A; end; P1:=P2; end; Memo.Lines.Add(S); end; </syntaxhighlight> {{out}} <pre> Count P Q PQ+2 ----------------------- 1 3 5 17 2 5 7 37 3 7 11 79 4 13 17 223 5 19 23 439 6 67 71 4759 7 149 151 22501 8 179 181 32401 9 229 233 53359 10 239 241 57601 11 241 251 60493 12 269 271 72901 13 277 281 77839 14 307 311 95479 15 313 317 99223 16 397 401 159199 17 401 409 164011 18 419 421 176401 19 439 443 194479 20 487 491 239119 </pre> =={{header\|F_Sharp\|F#}}== Line 518 ⟶ 660: 439 443 194479 487 491 239119 </pre> =={{header\|FutureBasic}}== <syntaxhighlight lang="futurebasic"> local fn IsPrime( n as NSUInteger ) as BOOL BOOL isPrime = YES NSUInteger i if n < 2 then exit fn = NO if n = 2 then exit fn = YES if n mod 2 == 0 then exit fn = NO for i = 3 to int(n^.5) step 2 if n mod i == 0 then exit fn = NO next end fn = isPrime local fn FindNeighborPrimes( searchLimit as long ) NSUInteger p, q printf @"p q pq+2" printf @"----------------------" for p = 2 to searchLimit if ( fn IsPrime(p) == NO ) then continue q = p + 1 while ( fn IsPrime(q) == NO ) q += 1 wend if ( fn IsPrime( p q + 2 ) == NO ) then continue printf @"%lu\t\t%-6lu\t%-6lu", p, q, p * q + 2 next end fn fn FindNeighborPrimes( 499 ) HandleEvents </syntaxhighlight> {{output}} <pre style="height:20ex;"> p q pq+2 ---------------------- 3 5 17 5 7 37 7 11 79 13 17 223 19 23 439 67 71 4759 149 151 22501 179 181 32401 229 233 53359 239 241 57601 241 251 60493 269 271 72901 277 281 77839 307 311 95479 313 317 99223 397 401 159199 401 409 164011 419 421 176401 439 443 194479 487 491 239119 </pre> =={{header\|Fōrmulæ}}== {{FormulaeEntry\|page=https://formulae.org/?script=examples/Neighbour_primes}} Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition. '''Solution''' [[File:Fōrmulæ - Neighbour primes 01.png]] Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used. [[File:Fōrmulæ - Neighbour primes 02.png]] ~~In '''[https://formulae.org/?example=Neighbour_primes this]''' page you can see the program(s) related to this task and their results.~~ =={{header\|Go}}== Line 584 ⟶ 789: [3,5,7,13,19,67,149,179,229,239,241,269,277,307,313,397,401,419,439,487] </pre> =={{header\|J}}== <syntaxhighlight lang="j"> (#~ 1 p: {:"1) 2 (, 2 + /)\ i.&.(p:inv) 500 3 5 17 5 7 37 7 11 79 13 17 223 19 23 439 67 71 4759 149 151 22501 179 181 32401 229 233 53359 239 241 57601 241 251 60493 269 271 72901 277 281 77839 307 311 95479 313 317 99223 397 401 159199 401 409 164011 419 421 176401 439 443 194479 487 491 239119</syntaxhighlight> =={{header\|jq}}== Line 833 ⟶ 1,061: </pre> =={{header\|PL/0}}== Formatted output isn't PL/0's forté, so this sample just shows each p1 of the p1, p2 neighbours. <br> This is almost identical to the [[Special neighbor primes#PL/0\|PL/0 sample in the Special Neighbor primes task]] <syntaxhighlight lang="pascal"> var n, p1, p2, prime; procedure isnprime; var p; begin prime := 1; if n < 2 then prime := 0; if n > 2 then begin prime := 0; if odd( n ) then prime := 1; p := 3; while p * p <= n * prime do begin if n - ( ( n / p ) * p ) = 0 then prime := 0; p := p + 2; end end end; begin p1 := 3; p2 := 5; while p2 < 500 do begin n := ( p1 * p2 ) + 2; call isnprime; if prime = 1 then ! p1; n := p2 + 2; call isnprime; while prime = 0 do begin n := n + 2; call isnprime; end; p1 := p2; p2 := n; end end. </syntaxhighlight> {{out}} <pre> 3 5 7 13 19 67 149 179 229 239 241 269 277 307 313 397 401 419 439 487 </pre> =={{header\|Prolog}}== for swi prolog (© 2024) <syntaxhighlight lang="prolog"> primes(2, Limit):- 2 =< Limit. primes(P, Limit):- between(3, Limit, P), P /\ 1 > 0, % odd M is floor(sqrt(P)) - 1, % reverse 2I+1 Max is M div 2, forall(between(1, Max, I), P mod (2I+1) > 0). isPrime(P):- primes(P, inf). primeProd(PList, [P1, P2]):- append([_, [P1, P2], _], PList), Prod is P1 * P2 + 2, isPrime(Prod). showList(List):- findnsols(10, _, (member(Pair, List), format('~\|~t(~d,~d)~9+ ', Pair)), _), nl, fail. showList(_). do:-Limit is 500, findall(P, primes(P, Limit), PrimeList), findall(Pair, primeProd(PrimeList, Pair), P1P2List), showList(P1P2List). </syntaxhighlight> {{out}} <pre> ?- do. (3,5) (5,7) (7,11) (13,17) (19,23) (67,71) (149,151) (179,181) (229,233) (239,241) (241,251) (269,271) (277,281) (307,311) (313,317) (397,401) (401,409) (419,421) (439,443) (487,491) true. </pre> =={{header\|Python}}== Line 879 ⟶ 1,208: 439 443 194479 487 491 239119</pre> =={{header\|Raku}}== Line 1,062 ⟶ 1,390: <pre> [3, 5, 7, 13, 19, 67, 149, 179, 229, 239, 241, 269, 277, 307, 313, 397, 401, 419, 439, 487] </pre> =={{header\|RPL}}== {{works with\|HP\|49}} ≪ → max ≪ { } 2 '''WHILE''' DUP max < '''REPEAT''' DUP NEXTPRIME '''IF''' DUP2 * 2 + ISPRIME? '''THEN''' UNROT + SWAP '''ELSE''' NIP '''END''' '''END''' DROP ≫ ≫ '<span style="color:blue">NEIGHB</span>' STO 500 <span style="color:blue">NEIGHB</span> {{out}} <pre> 1: {3 5 7 13 19 67 149 179 229 239 241 269 277 307 313 397 401 419 439 487} </pre> =={{header\|Ruby}}== <syntaxhighlight lang="ruby">require 'prime' p Prime.each(500).each_cons(2).select{\|p, q\| (p*q+2).prime? }</syntaxhighlight> {{out}} <pre> [[3, 5], [5, 7], [7, 11], [13, 17], [19, 23], [67, 71], [149, 151], [179, 181], [229, 233], [239, 241], [241, 251], [269, 271], [277, 281], [307, 311], [313, 317], [397, 401], [401, 409], [419, 421], [439, 443], [487, 491]] </pre> Line 1,073 ⟶ 1,426: =={{header\|Wren}}== {{libheader\|Wren-math}} ~~{{libheader\|Wren-seq}}~~ {{libheader\|Wren-fmt}} <syntaxhighlight lang="~~ecmascript~~wren">import "./math" for Int import "./~~seq~~fmt" for ~~Lst~~Fmt ~~import "/fmt" for Fmt~~ var primes = Int.primeSieve(504) Line 1,086 ⟶ 1,437: if (Int.isPrime(p)) nprimes.add(primes[i]) } Fmt.tprint("$3d", nprimes, 10) ~~for (chunk in Lst.chunks(nprimes, 10)) Fmt.print("$3d", chunk)~~ System.print("\nFound %(nprimes.count) such primes.")</syntaxhighlight>