Erdős-primes: Difference between revisions

← Older edit

Erdős-primes (view source)

Revision as of 14:16, 10 April 2024

24,339 bytes added , 1 month ago

Add APL

Not a robot

2,093

edits

Revision as of 17:36, 30 October 2021 (view source) Enter your username (talk \| contribs) m (→‎{{header\|C#\|CSharp}}: lol, ordinal, not cardinal...) ← Older edit		Latest revision as of 14:16, 10 April 2024 (view source) Not a robot (talk \| contribs) (Add APL)
(40 intermediate revisions by 15 users not shown)
Line 15: :*   the OEIS entry:   [http://oeis.org/A064152 A064152 Erdos primes]. <br><br> =={{header\|11l}}== {{trans\|Nim}} <syntaxhighlight lang="11l">F primes_upto(limit) V is_prime = [0B] * 2 [+] [1B] * (limit - 1) L(n) 0 .< Int(limit ^ 0.5 + 1.5) I is_prime[n] L(i) (n * n .. limit).step(n) is_prime[i] = 0B R is_prime V is_prime = primes_upto(1'000'000) V primeList = enumerate(is_prime).filter((i, prime) -> prime).map((i, prime) -> i) [Int] factorials L(n) 1.. I factorial(n) >= 1'000'000 L.break factorials.append(factorial(n)) F isErdosPrime(p) L(f) :factorials I f >= p L.break I :is_prime[p - f] R 0B R 1B [Int] erdosList2500 L(p) primeList I p >= 2500 L.break I isErdosPrime(p) erdosList2500.append(p) print(‘Found ’erdosList2500.len‘ Erdos primes less than 2500:’) L(prime) erdosList2500 print(‘#5’.format(prime), end' I (L.index + 1) % 10 == 0 {"\n"} E ‘ ’) print() V count = 0 L(p) primeList I isErdosPrime(p) count++ I count == 7875 print("\nThe 7875th Erdos prime is "p‘.’) L.break</syntaxhighlight> {{out}} <pre> Found 25 Erdos primes less than 2500: 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 The 7875th Erdos prime is 999721. </pre> =={{header\|ABC}}== <syntaxhighlight lang="abc">HOW TO REPORT prime n: SELECT: n < 2: FAIL n mod 2 = 0: REPORT n=2 ELSE: REPORT NO d IN {2..floor (root n)} HAS n mod d = 0 HOW TO REPORT erdos p: IF NOT prime p: FAIL PUT 1, 1 IN k, k.fac WHILE k.fac < p: IF prime (p - k.fac): FAIL PUT k+1 IN k PUT k.fack IN k.fac SUCCEED PUT 0 IN nprimes FOR n IN {1..2499}: IF erdos n: WRITE n>>6 PUT nprimes+1 IN nprimes IF nprimes mod 10 = 0: WRITE/ WRITE / WRITE "There are `nprimes` Erdos primes < 2500."/ PUT 2499 IN n WHILE nprimes < 7875: PUT n+2 IN n IF erdos n: PUT nprimes + 1 IN nprimes WRITE "The `nprimes`th Erdos prime is `n`."/</syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 There are 25 Erdos primes < 2500. The 7875th Erdos prime is 999721.</pre> =={{header\|Action!}}== {{libheader\|Action! Sieve of Eratosthenes}} <syntaxhighlight lang="action!">INCLUDE "H6:SIEVE.ACT" BYTE Func IsErdosPrime(INT x BYTE ARRAY primes) INT k,f IF primes(x)=0 THEN RETURN (0) FI k=1 f=1 WHILE f<x DO IF primes(x-f) THEN RETURN (0) FI k==+1 f==k OD RETURN (1) PROC Main() DEFINE MAX="2499" BYTE ARRAY primes(MAX+1) INT i,count=[0] Put(125) PutE() ;clear the screen Sieve(primes,MAX+1) FOR i=2 TO MAX DO IF IsErdosPrime(i,primes) THEN PrintI(i) Put(32) count==+1 FI OD PrintF("%E%EThere are %I Erdos primes",count) RETURN</syntaxhighlight> {{out}} [https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Erd%C5%91s-primes.png Screenshot from Atari 8-bit computer] <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 There are 25 Erdos primes </pre> =={{header\|ALGOL 68}}== <syntaxhighlight lang="algol68"> BEGIN # find Erdős primes - primes p where p-k! is composite for all 1<=k!<p # # returns TRUE if p is an Erdős prime # PROC is erdos prime = ( INT p )BOOL: IF NOT prime[ p ] THEN FALSE ELSE BOOL result := TRUE; FOR k WHILE factorial[ k ] < p AND result DO result := NOT prime[ p - factorial[ k ] ] OD; result FI # is erdos prime # ; INT max prime = 1 000 000; # maximum number we will consider # INT max erdos = 7 875; # maximum Erdős prime to find # # construct a table of factorials large enough for max prime # [ 1 : 12 ]INT factorial; factorial[ 1 ] := 1; FOR f FROM 2 TO UPB factorial DO factorial[ f ] := factorial[ f - 1 ] * f OD; PR read "primes.incl.a68" PR # include prime utilities # []BOOL prime = PRIMESIEVE max prime; # sieve the primes to max prime # INT max show = 2 500; # find the Erdős primes, showing the ones up to max show # INT e count := 0; IF is erdos prime( 2 ) THEN print( ( " 2" ) ); e count +:= 1 FI; INT last erdos := 0; FOR p FROM 3 BY 2 TO max show DO IF is erdos prime( p ) THEN print( ( " ", whole( p, 0 ) ) ); last erdos := p; e count +:= 1 FI OD; print( ( newline, "Found ", whole( e count, 0 ) , " Erdos primes up to ", whole( max show, 0 ), newline ) ); # find the max erdos'th Erdős prime # FOR p FROM max show WHILE e count < max erdos DO IF is erdos prime( p ) THEN last erdos := p; e count +:= 1 FI OD; print( ( whole( last erdos, 0 ), " is Erdos prime ", whole( e count, 0 ), newline ) ) END </syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 Found 25 Erdos primes up to 2500 999721 is Erdos prime 7875 </pre> =={{header\|APL}}== <syntaxhighlight lang="apl">erdos_primes←{ prime ← {(⍵≥2) ∧ 0∧.≠(1↓⍳⌊⍵÷2)\|⍵} erdos ← {(prime ⍵) ∧ ∧/~prime¨ ⍵-!⍳⌊(!⍣¯1)⍵} e2500 ← (erdos¨e)/e←⍳2500 ⎕←e2500 ⎕←'There are ',(⍕⍴e2500),' Erdős numbers ≤ 2500' }</syntaxhighlight> {{out}} <pre>2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 There are 25 Erdős numbers ≤ 2500</pre> =={{header\|Arturo}}== <~~lang~~syntaxhighlight lang="rebol">factorials: map 1..20 => [product 1..&] erdos?: function [x][ if not? prime? x -> return false Line 30 ⟶ 243: loop split.every:10 select 2..2500 => erdos? 'a -> print map a => [pad to :string & 5]</~~lang~~syntaxhighlight> {{out}} Line 39 ⟶ 252: =={{header\|AWK}}== {{trans\|FreeBASIC}} ~~<lang AWK>~~ <syntaxhighlight lang="awk"> # syntax: GAWK -f ERDOS-PRIMES.AWK # converted from FreeBASIC Line 77 ⟶ 291: return(1) } </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 85 ⟶ 299: </pre> =={{header\|~~C#\|CSharp~~BASIC}}== ==={{header\|FreeBASIC}}=== ~~<lang csharp>using System; using static System.Console;~~ I won't bother reproducing a primality-testing function; use the one from [[Primality_by_trial_division#FreeBASIC]]. <syntaxhighlight lang="freebasic">#include "isprime.bas" function is_erdos_prime( p as uinteger ) as boolean if not isprime(p) then return false dim as uinteger kf=1, m=1 while kf < p kf=m : m+=1 if isprime(p - kf) then return false wend return true end function dim as integer c = 0, i = 1 while c<7875 i+=1 if is_erdos_prime(i) then c+=1 if i<2500 or c=7875 then print c, i end if wend</syntaxhighlight> {{out}}<pre>1 2 2 101 3 211 4 367 5 409 6 419 7 461 8 557 9 673 10 709 11 769 12 937 13 967 14 1009 15 1201 16 1259 17 1709 18 1831 19 1889 20 2141 21 2221 22 2309 23 2351 24 2411 25 2437 7875 999721 </pre> ==={{header\|Palo Alto Tiny BASIC}}=== {{trans\|Tiny BASIC\|Removed overlapping loops.}} Without the stretch goal because numbers are limited to signed 16-bit integers. <syntaxhighlight lang="basic"> 10 REM ERDOS-PRIMES 20 LET P=2,C=1 30 PRINT C," ",P 40 FOR P=3 TO 2500 STEP 2 50 LET Z=P;GOSUB 1000 60 IF A=0 GOTO 160 70 REM F = K! 80 LET K=1,F=1,Z=P-F 90 IF Z<0 GOTO 150 100 GOSUB 1000 110 IF A=1 GOTO 150 120 LET K=K+1,F=FK,Z=P-F 130 IF Z<0 GOTO 150 140 GOTO 100 150 IF Z<0 LET C=C+1;PRINT C," ",P 160 NEXT P 170 STOP 980 REM PRIMALITY OF Z BY TRIAL DIVISION 990 REM RESULT IS IN A 1000 LET A=0 1010 IF Z=2 LET A=1;RETURN 1020 IF Z<3 RETURN 1030 LET Y=2 1040 IF (Z/Y)Y=Z RETURN 1050 IF YY>=Z LET A=1;RETURN 1060 LET Y=Y+1 1070 GOTO 1040 1080 RETURN </syntaxhighlight> {{out}} <pre> 1 2 2 101 3 211 4 367 5 409 6 419 7 461 8 557 9 673 10 709 11 769 12 937 13 967 14 1009 15 1201 16 1259 17 1709 18 1831 19 1889 20 2141 21 2221 22 2309 23 2351 24 2411 25 2437 </pre> ==={{header\|Tiny BASIC}}=== Can't manage the stretch goal because integers are limited to signed 16 bit. {{works with\|TinyBasic}} Tiny BASICs other than Tom Pittman's TinyBasic use <code>,</code> instead of <code>;</code> for string concatenation in <code>PRINT</code>. <syntaxhighlight lang="basic">10 REM Erdős-primes 20 LET P = 1 30 LET C = 0 40 IF P > 2 THEN LET P = P + 2 50 IF P < 3 THEN LET P = P + 1 60 LET Z = P 70 GOSUB 1000 80 IF A = 0 THEN GOTO 40 90 LET K = 0 100 LET F = 1 110 LET K = K + 1 120 REM F = K! 130 LET F = F K 140 LET Z = P - F 150 IF Z < 0 THEN GOTO 190 160 GOSUB 1000 170 IF A = 1 THEN GOTO 40 180 GOTO 110 190 LET C = C + 1 200 IF P < 2500 THEN PRINT C; " "; P 210 IF P > 2500 THEN END 220 GOTO 40 990 REM primality of Z by trial division, result is in A 1000 LET Y = 1 1010 LET A = 0 1020 IF Z = 2 THEN LET A = 1 1030 IF Z < 3 THEN RETURN 1040 LET Y = Y + 1 1050 IF (Z / Y) * Y = Z THEN RETURN 1060 IF Y * Y < Z THEN GOTO 1040 1070 LET A = 1 1080 RETURN</syntaxhighlight> {{out}} <pre>1 2 2 101 3 211 4 367 5 409 6 419 7 461 8 557 9 673 10 709 11 769 12 937 13 967 14 1009 15 1201 16 1259 17 1709 18 1831 19 1889 20 2141 21 2221 22 2309 23 2351 24 2411 25 2437 </pre> =={{header\|C}}== {{trans\|Wren}} <syntaxhighlight lang="c">#include <stdio.h> #include <stdlib.h> #include <stdbool.h> #include <locale.h> #define LIMIT 1000000 #define LOWER_LIMIT 2500 bool sieve(int limit) { int i, p; limit++; // True denotes composite, false denotes prime. bool c = calloc(limit, sizeof(bool)); // all false by default c[0] = true; c[1] = true; for (i = 4; i < limit; i += 2) c[i] = true; p = 3; // Start from 3. while (true) { int p2 = p * p; if (p2 >= limit) break; for (i = p2; i < limit; i += 2 * p) c[i] = true; while (true) { p += 2; if (!c[p]) break; } } return c; } int main() { int i, j, fact, ec = 0, ec2 = 0, lastErdos = 0; bool found; bool c = sieve(LIMIT-1); int erdos[30]; for (i = 2; i < LIMIT;) { if (!c[i]) { j = 1; fact = 1; found = true; while (fact < i) { if (!c[i-fact]) { found = false; break; } ++j; fact = j; } if (found) { if (i < LOWER_LIMIT) erdos[ec2++] = i; lastErdos = i; ++ec; } } i = (i > 2) ? i + 2 : i + 1; } setlocale(LC_NUMERIC, ""); printf("The %'d Erdős primes under %'d are:\n", ec2, LOWER_LIMIT); for (i = 0; i < ec2; ++i) { printf("%6d ", erdos[i]); if (!((i+1)%10)) printf("\n"); } printf("\n\nThe %'dth Erdős prime is %'d.\n", ec, lastErdos); free(c); return 0; }</syntaxhighlight> {{out}} <pre> The 25 Erdős primes under 2,500 are: 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 The 7,875th Erdős prime is 999,721. </pre> =={{header\|C sharp\|C#}}== <syntaxhighlight lang="csharp">using System; using static System.Console; class Program { const int lmt = (int)1e6, first = 2500; static int[] f = new int[10]; Line 108 ⟶ 577: if (x < 4) return x > 1; if ((x & 1) == 0) return false; for (int i = 3; i * i <= x; i += 2) if (x % i == 0) return false; return true; } } }</~~lang~~syntaxhighlight> {{out}} <pre> 2 101 211 367 409 Line 121 ⟶ 590: =={{header\|C++}}== {{libheader\|Primesieve}} <~~lang~~syntaxhighlight lang="cpp">#include <cstdint> #include <iomanip> #include <iostream> Line 170 ⟶ 639: std::wcout << L"\n\nThe " << max_count << L"th Erd\x151s prime is " << p << L".\n"; return 0; }</~~lang~~syntaxhighlight> {{out}} Line 180 ⟶ 649: The 7,875th Erdős prime is 999,721. </pre> =={{header\|Delphi}}== {{works with\|Delphi\|6.0}} {{libheader\|SysUtils,StdCtrls}} Executes in 225 ms. It could be faster with a Factorial lookup table. <syntaxhighlight lang="Delphi"> function IsPrime(N: integer): boolean; {Optimised prime test - about 40% faster than the naive approach} var I,Stop: integer; 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)); 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 Factorial(N: Word): int64; var I: integer; begin Result:= 1; for I := 2 to N do Result:=Result * I; end; function IsErdosPrime(P: integer): boolean; {Test if specified Primes is Erdos} {i.e. all p-k! for 1<=k!<p are composite.} var K: integer; var F: int64; begin K:=1; Result:=False; while True do begin F:=Factorial(K); if F>=P then break; if IsPrime(P-F) then exit; Inc(K); end; Result:=True; end; procedure FindErdosPrimes(Memo: TMemo); {Collect and display Erdos primes} var P,I,Cnt: integer; var Erdos: array of integer; var S: string; begin {Collect all Erdos Primes<1,000,000} for P:=2 to 1000000 do if IsPrime(P) then if IsErdosPrime(P) then begin SetLength(Erdos,Length(Erdos)+1); Erdos[High(Erdos)]:=P; end; {Display the data in several different ways} Memo.Lines.Add('25 Erdos primes less than 2500'); S:=''; for I:=0 to 24 do begin S:=S+Format('%8d',[Erdos[I]]); if (((I+1) mod 5)=0) or (I=24) then begin Memo.Lines.Add(S); S:=''; end; end; Memo.Lines.Add('Summary:'); Memo.Lines.Add('Number of Erdos Primes < 1-million: '+IntToStr(Length(Erdos))); Memo.Lines.Add('Last Erdos Prime < 1-million: '+IntToStr(Erdos[High(Erdos)])); end; </syntaxhighlight> {{out}} <pre> 25 Erdos primes less than 2500 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 Summary: Number of Erdos Primes < 1-million: 7875 Last Erdos Prime < 1-million: 999721 </pre> =={{header\|EasyLang}}== {{trans\|Action!}} <syntaxhighlight> fastfunc isprim num . if num < 2 return 0 . i = 2 while i <= sqrt num if num mod i = 0 return 0 . i += 1 . return 1 . func iserdosprim p . if isprim p = 0 return 0 . k = 1 f = 1 while f < p if isprim (p - f) = 1 return 0 . k += 1 f = k . return 1 . for p = 2 to 2499 if iserdosprim p = 1 write p & " " . . </syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 </pre> =={{header\|F_Sharp\|F#}}== This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)] <~~lang~~syntaxhighlight lang="fsharp"> // Erdős Primes. Nigel Galloway: March 22nd., 2021 let rec fN g=function 1->g \|n->fN(gn)(n-1) Line 190 ⟶ 804: let eP()=primes32()\|>Seq.filter(fG 1>>Seq.forall id) eP()\|>Seq.takeWhile((>)2500)\|>Seq.iter(printf "%d "); printfn "\n\n7875th Erdős prime is %d" (eP()\|>Seq.item 7874) </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 197 ⟶ 811: 7875th Erdos prime is 999721 </pre> =={{header\|Factor}}== {{works with\|Factor\|0.99 2021-02-05}} <syntaxhighlight lang="text">USING: formatting io kernel lists lists.lazy math math.factorials math.primes math.primes.lists math.vectors prettyprint sequences tools.memory.private ; Line 216 ⟶ 831: 7874 erdős lnth commas "The 7,875th Erdős prime is %s.\n" printf</~~lang~~syntaxhighlight> {{out}} <pre> Line 227 ⟶ 842: =={{header\|Forth}}== {{works with\|Gforth}} <~~lang~~syntaxhighlight lang="forth">: prime? ( n -- ? ) here + c@ 0= ; : notprime! ( n -- ) here + 1 swap c! ; Line 278 ⟶ 893: 2500 print_erdos_primes bye</~~lang~~syntaxhighlight> {{out}} Line 288 ⟶ 903: Count: 25 </pre> ~~=={{header\|FreeBASIC}}==~~ ~~I won't bother reproducing a primality-testing function; use the one from [[Primality_by_trial_division#FreeBASIC]].~~ ~~<lang freebasic>#include "isprime.bas"~~ ~~function is_erdos_prime( p as uinteger ) as boolean~~ ~~if not isprime(p) then return false~~ ~~dim as uinteger kf=1, m=1~~ ~~while kf < p~~ ~~kf=m : m+=1~~ ~~if isprime(p - kf) then return false~~ ~~wend~~ ~~return true~~ ~~end function~~ ~~dim as integer c = 0, i = 1~~ ~~while c<7875~~ ~~i+=1~~ ~~if is_erdos_prime(i) then~~ ~~c+=1~~ ~~if i<2500 or c=7875 then print c, i~~ ~~end if~~ ~~wend</lang>~~ ~~{{out}}<pre>1 2~~ ~~2 101~~ ~~3 211~~ ~~4 367~~ ~~5 409~~ ~~6 419~~ ~~7 461~~ ~~8 557~~ ~~9 673~~ ~~10 709~~ ~~11 769~~ ~~12 937~~ ~~13 967~~ ~~14 1009~~ ~~15 1201~~ ~~16 1259~~ ~~17 1709~~ ~~18 1831~~ ~~19 1889~~ ~~20 2141~~ ~~21 2221~~ ~~22 2309~~ ~~23 2351~~ ~~24 2411~~ ~~25 2437~~ ~~7875 999721~~ ~~</pre>~~ =={{header\|Go}}== {{trans\|Wren}} {{libheader\|Go-rcu}} ~~<lang go>package main~~ <syntaxhighlight lang="go">package main import ~~"fmt"~~( "fmt" "rcu" ~~func sieve(limit int) []bool {~~ ) ~~limit++~~ ~~// True denotes composite, false denotes prime.~~ ~~c := make([]bool, limit) // all false by default~~ ~~c[0] = true~~ ~~c[1] = true~~ ~~for i := 4; i < limit; i += 2 {~~ ~~c[i] = true~~ } ~~p := 3 // Start from 3.~~ ~~for {~~ ~~p2 := p p~~ ~~if p2 >= limit {~~ ~~break~~ } ~~for i := p2; i < limit; i += 2 * p {~~ ~~c[i] = true~~ } ~~for {~~ ~~p += 2~~ ~~if !c[p] {~~ ~~break~~ } } } ~~return c~~ } ~~func commatize(n int) string {~~ ~~s := fmt.Sprintf("%d", n)~~ ~~if n < 0 {~~ ~~s = s[1:]~~ } ~~le := len(s)~~ ~~for i := le - 3; i >= 1; i -= 3 {~~ ~~s = s[0:i] + "," + s[i:]~~ } ~~if n >= 0 {~~ ~~return s~~ } ~~return "-" + s~~ } func main() { limit := int(1e6) clowerLimit := ~~sieve(limit - 1)~~2500 c := rcu.PrimeSieve(limit-1, true) var erdos []int lastErdos := 0 ec := 0 for i := 2; i < limit; { if !c[i] { Line 405 ⟶ 933: } if found { ~~erdos~~if =i ~~append(erdos,~~< i)lowerLimit { erdos = append(erdos, i) } lastErdos = i ec++ } } Line 414 ⟶ 946: } } fmt.Printf("The %d Erdős primes under %s are\n", len(erdos), rcu.Commatize(lowerLimit)) ~~lowerLimit := 2500~~ rcu.PrintTable(erdos, 10, 6, false) ~~var erdosLower []int~~ fmt.Printf("\nThe %s Erdős prime is %s.\n", rcu.Commatize(ec), rcu.Commatize(lastErdos)) ~~for _, e := range erdos {~~ }</syntaxhighlight> ~~if e < lowerLimit {~~ ~~erdosLower = append(erdosLower, e)~~ ~~} else {~~ ~~break~~ } } ~~fmt.Printf("The %d Erdős primes under %s are\n", len(erdosLower), commatize(lowerLimit))~~ ~~for i, e := range erdosLower {~~ ~~fmt.Printf("%6d", e)~~ ~~if (i+1)%10 == 0 {~~ ~~fmt.Println()~~ } } ~~show := 7875~~ ~~fmt.Printf("\n\nThe %s Erdős prime is %s.\n", commatize(show), commatize(erdos[show-1]))~~ ~~}</lang>~~ {{out}} <pre> The 25 Erdős primes under 2,500 are 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 The 7,875 Erdős prime is 999,721. </pre> =={{header\|J}}== Implementation: <syntaxhighlight lang="j">NB. erdos primes greater than !k and less than or equal to !k+1 (where !k is the factorial of k) erdospr=: {{ k=. y f=. !k+0 1 p=. (#~ 1= f&I.) p:(+i.)/0 1+p:inv f p#~/\|:0=1 p:p-/!i.1+k }} NB. erdos primes less than j erdosprs=: {{ (#~ j&>);erdospr&.>i.>.!inv j=. y }}</syntaxhighlight> Task examples: <syntaxhighlight lang="j"> erdosprs 2500 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 (#,{:) erdosprs 1e6 7875 999721</syntaxhighlight> =={{header\|Java}}== <~~lang~~syntaxhighlight lang="java">import java.util.; public class ErdosPrimes { Line 498 ⟶ 1,035: return sieve; } }</~~lang~~syntaxhighlight> {{out}} Line 509 ⟶ 1,046: The 7875th Erdős prime is 999721. </pre> =={{header\|jq}}== Line 517 ⟶ 1,053: '''Preliminaries''' <~~lang~~syntaxhighlight lang="jq">def emit_until(cond; stream): label $out \| stream \| if cond then break $out else . end; def is_prime: Line 534 ⟶ 1,070: \| . * . > $n end; </syntaxhighlight> ~~</lang>~~ '''Erdős-primes''' <~~lang~~syntaxhighlight lang="jq"> def is_Erdos: . as $p Line 551 ⟶ 1,087: # emit the Erdos primes def Erdos: range(2; infinite) \| select(is_Erdos); </syntaxhighlight> ~~</lang>~~ '''The tasks''' <~~lang~~syntaxhighlight lang="jq">"The Erdős primes less than 2500 are:", emit_until(. >= 2500; Erdos), "\nThe 7875th Erdős prime is \(nth(7874; Erdos))." </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 590 ⟶ 1,126: =={{header\|Julia}}== <~~lang~~syntaxhighlight lang="julia">using Primes, Formatting function isErdős(p::Integer) Line 607 ⟶ 1,143: println(length(E2500), " Erdős primes < 2500: ", E2500) println("The 7875th Erdős prime is ", format(Erdőslist[7875], commas=true)) </~~lang~~syntaxhighlight>{{out}} <pre> 25 Erdős primes < 2500: [2, 101, 211, 367, 409, 419, 461, 557, 673, 709, 769, 937, 967, 1009, 1201, 1259, 1709, 1831, 1889, 2141, 2221, 2309, 2351, 2411, 2437] The 7875th Erdős prime is 999,721 </pre> =={{header\|Lua}}== <syntaxhighlight lang="lua">function isPrime (x) if x < 2 then return false end if x < 4 then return true end if x % 2 == 0 then return false end for d = 3, math.sqrt(x), 2 do if x % d == 0 then return false end end return true end function primes () local x, maxInt = 3, 2^53 local function yieldPrimes () coroutine.yield(2) repeat if isPrime(x) then coroutine.yield(x) end x = x + 2 until x == maxInt end return coroutine.wrap(function() yieldPrimes() end) end function factorial (n) local f = 1 for i = 2, n do f = f * i end return f end function isErdos (p) local k, factK = 1 repeat factK = factorial(k) if isPrime(p - factK) then return false end k = k + 1 until factK >= p return true end local nextPrime, count, prime = primes(), 0 while count < 7875 do prime = nextPrime() if isErdos(prime) then if prime < 2500 then io.write(prime .. " ") end count = count + 1 end end print("\n\nThe 7875th Erdos prime is " .. prime)</syntaxhighlight> {{out}} <pre>2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 The 7875th Erdos prime is 999721</pre> =={{header\|Mathematica}}/{{header\|Wolfram Language}}== <syntaxhighlight lang="mathematica">ClearAll[ErdosPrimeQ] ErdosPrimeQ[p_Integer] := Module[{k}, If[PrimeQ[p], k = 1; While[k! < p, If[PrimeQ[p - k!], Return[False]]; k++; ]; True , False ] ] sel = Select[Range[2500], ErdosPrimeQ] Length[sel] sel = Select[Range[999999], ErdosPrimeQ]; {Length[sel], Last[sel]}</syntaxhighlight> {{out}} <pre>{2, 101, 211, 367, 409, 419, 461, 557, 673, 709, 769, 937, 967, 1009, 1201, 1259, 1709, 1831, 1889, 2141, 2221, 2309, 2351, 2411, 2437} 25 {7875, 999721}</pre> =={{header\|Miranda}}== <syntaxhighlight lang="miranda">main :: [sys_message] main = [Stdout (lay (map show erdos2500)), Stdout ("There are " ++ show (#erdos2500) ++ " Erdos numbers <2500\n")] where erdos2500 = filter erdos [1..2499] erdos :: num->bool erdos p = prime p & ~or [prime (p-k) \| k <- takewhile (<p) (scan () 1 [2..])] prime :: num->bool prime n = n=2 \/ n=3, if n<=4 prime n = False, if n mod 2=0 prime n = and [n mod d ~= 0 \| d <- [2..entier (sqrt n)]]</syntaxhighlight> {{out}} <pre>2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 There are 25 Erdos numbers <2500</pre> =={{header\|Nim}}== <~~lang~~syntaxhighlight ~~Nim~~lang="nim">import math, sets, strutils, sugar const N = 1_000_000 Line 665 ⟶ 1,320: erdös7875 = p break echo "\nThe 7875th Erdös prime is $#.".format(erdös7875)</~~lang~~syntaxhighlight> {{out}} Line 677 ⟶ 1,332: =={{header\|Perl}}== {{libheader\|ntheory}} <~~lang~~syntaxhighlight lang="perl">use strict; use warnings; use feature 'say'; Line 697 ⟶ 1,352: say 'Erdős primes < ' . (my $max = 2500) . ':'; say join ' ', before { $_ > 2500 } @Erdős; say "\nErdős prime #" . @Erdős . ' is ' . $Erdős[-1];</~~lang~~syntaxhighlight> {{out}} <pre>Erdős primes < 2500: Line 705 ⟶ 1,360: =={{header\|Phix}}== <!--<~~lang~~syntaxhighlight ~~Phix~~lang="phix">--> <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">facts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> Line 725 ⟶ 1,380: <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"The %,d%s Erdos prime is %,d (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ord</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[$],</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span> <!--</~~lang~~syntaxhighlight>--> {{out}} <pre> Line 732 ⟶ 1,387: The 7,875th Erdos prime is 999,721 (1.2s) </pre> =={{header\|PL/0}}== Without stretch goal. <syntaxhighlight lang="pascal"> var p, c, z, k, isprime, factk, iskchecked; procedure checkprimality; var i, isichecked; begin isprime := 0; if z = 2 then isprime := 1; if z >= 3 then begin i := 2; isichecked := 0; while isichecked = 0 do begin if (z / i) i = z then isichecked := 1; if isichecked = 0 then if i * i >= z then begin isprime := 1; isichecked := 1 end; i := i + 1 end end end; begin p := 2; c := 1; ! p; p := 3; while p <= 2500 do begin z := p; call checkprimality; if isprime = 1 then begin k := 1; factk := 1; z := p - factk; iskchecked := 1; if z >= 0 then iskchecked := 0; while iskchecked = 0 do begin call checkprimality; if isprime = 1 then iskchecked := 1; if isprime <> 1 then begin k := k + 1; factk := factk * k; z := p - factk; iskchecked := 1; if z >= 0 then iskchecked := 0 end end; if z < 0 then begin c := c + 1; ! p end end; p := p + 2 end end. </syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 </pre> =={{header\|PL/M}}== {{works with\|8080 PL/M Compiler}} ... under CP/M (or an emulator) Basic task only as PL/M integers are 8/16 bit unsigned. <syntaxhighlight lang="plm"> 100H: /* FIND ERDOS PRIMES: PRIMES P WHERE P-K! IS COMPOSITE FOR ALL 1<=K!<P / / CP/M SYSTEM CALL AND I/O ROUTINES / BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END; PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END; PR$NUMBER: PROCEDURE( N ); / PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH / DECLARE N ADDRESS; DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE; V = N; W = LAST( N$STR ); N$STR( W ) = '$'; N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); DO WHILE( ( V := V / 10 ) > 0 ); N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); END; CALL PR$STRING( .N$STR( W ) ); END PR$NUMBER; / TASK / DECLARE MAX$NUMBER LITERALLY '2500' , FALSE LITERALLY '0' , TRUE LITERALLY '0FFH' ; DECLARE PRIME ( MAX$NUMBER )BYTE; / SIEVE THE PRIMES TO MAX$NUMBER - 1 / DECLARE I ADDRESS; PRIME( 0 ), PRIME( 1 ) = FALSE; PRIME( 2 ) = TRUE; DO I = 3 TO LAST( PRIME ) BY 2; PRIME( I ) = TRUE; END; DO I = 4 TO LAST( PRIME ) BY 2; PRIME( I ) = FALSE; END; DO I = 3 TO LAST( PRIME ) BY 2; IF PRIME( I ) THEN DO; DECLARE S ADDRESS; DO S = I + I TO LAST( PRIME ) BY I; PRIME( S ) = FALSE; END; END; END; / TABLE OF FACTORIALS / DECLARE FACTORIAL ( 8 )ADDRESS INITIAL( 1, 1, 2, 6, 24, 120, 720, 5040 ); / RETURNS TRUE IF P IS AN ERDOS PRIME, FALSE OTHERWISE / IS$ERDOS$PRIME: PROCEDURE( P )BYTE; DECLARE P ADDRESS; DECLARE RESULT BYTE; RESULT = PRIME( P ); IF RESULT THEN DO; DECLARE K BYTE; K = 1; DO WHILE FACTORIAL( K ) < P AND RESULT; RESULT = NOT PRIME( P - FACTORIAL( K ) ); K = K + 1; END; END; RETURN RESULT; END IS$ERDOS$PRIME ; / FIND THE ERDOS PRIMES / DECLARE ( P, COUNT ) ADDRESS; COUNT = 0; IF IS$ERDOS$PRIME( 2 ) THEN DO; COUNT = COUNT + 1; CALL PR$STRING( .' 2$' ); END; P = 1; DO WHILE COUNT < 25; P = P + 2; IF IS$ERDOS$PRIME( P ) THEN DO; COUNT = COUNT + 1; CALL PR$CHAR( ' ' ); IF P < 1000 THEN CALL PR$CHAR( ' ' ); CALL PR$NUMBER( P ); IF COUNT MOD 5 = 0 THEN CALL PR$NL; END; END; EOF </syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 </pre> =={{header\|Raku}}== <syntaxhighlight lang="raku" ~~perl6~~line>use Lingua::EN::Numbers; my @factorial = 1, \|[\] 1..; Line 743 ⟶ 1,581: put 'Erdős primes < 2500:'; put @Erdős[^(@Erdős.first: > 2500, :k)]»., put "\nThe 7,875th Erdős prime is: " ~ @Erdős[7874].,</~~lang~~syntaxhighlight> {{out}} <pre>Erdős primes < 2500: Line 749 ⟶ 1,587: The 7,875th Erdős prime is: 999,721</pre> Alternately, using fewer hard coded values: <syntaxhighlight lang="raku" line>use Lingua::EN::Numbers; use List::Divvy; my @factorial = 1, \|[\] 1..; my @Erdős = ^∞ .grep: { .is-prime and none($_ «-« @factorial.&upto: $_).is-prime } put "Erdős primes < 2500:\n" ~ @Erdős.&before(2500)».&comma.batch(8)».fmt("%5s").join: "\n"; put "\nThe largest Erdős prime less than {comma 1e6.Int} is {comma .[-1]} in {.&ordinal-digit} position." given @Erdős.&before(1e6);</syntaxhighlight> {{out}} <pre>Erdős primes < 2500: 2 101 211 367 409 419 461 557 673 709 769 937 967 1,009 1,201 1,259 1,709 1,831 1,889 2,141 2,221 2,309 2,351 2,411 2,437 The largest Erdős prime less than 1,000,000 is 999,721 in 7875th position.</pre> =={{header\|REXX}}== <~~lang~~syntaxhighlight lang="rexx">/REXX program counts/displays the number of Erdos primes under a specified number N. / parse arg n cols . /get optional number of primes to find/ if n=='' \| n=="," then n= 2500 /Not specified? Then assume default./ Line 801 ⟶ 1,660: end /k/ / [↑] only divide up to √ J / #= # + 1; @.#= j; !.j= 1 /bump prime count; assign prime & flag/ end /j/; return</~~lang~~syntaxhighlight> {{out\|output\|text=  when using the default inputs:}} <pre> Line 819 ⟶ 1,678: 999,721 is the 7,875th Erdos prime. </pre> =={{header\|Ring}}== <syntaxhighlight lang="ring"> load "stdlibcore.ring" see "working..." + nl row = 0 limit = 2500 for p = 1 to limit flag = 1 if isprime(p) for k = 1 to p if factorial(k) < p temp = p - factorial(k) if not isprime(temp) flag = 1 else flag = 0 exit ok else exit ok next else flag = 0 ok if flag = 1 row++ see "" + p + " " if row % 5 = 0 see nl ok ok next see nl + "Found " + row + " Erdos primes less than 2500" + nl see "done..." + nl </syntaxhighlight> {{out}} <pre> working... 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 Found 25 Erdos primes less than 2500 done... </pre> =={{header\|RPL}}== {{works with\|HP\|49}} « 0 → p k « 1 SF '''WHILE''' p 'k' INCR FACT - DUP 0 > 1 FS? AND '''REPEAT''' '''IF''' ISPRIME? '''THEN''' 1 CF '''END''' '''END''' DROP 1 FS? » » '<span style="color:blue">ERDOS?</span>' STO <span style="color:grey">@ ( n → erdös(n) )</span> « { } 2 '''WHILE''' DUP 2500 < '''REPEAT''' '''IF''' DUP <span style="color:blue">ERDOS?</span> '''THEN''' SWAP OVER + SWAP '''END''' NEXTPRIME '''END''' DROP DUP SIZE "count" →TAG » '<span style="color:blue">TASK</span>' STO <span style="color:grey">@ ( → results )</span> {{out}} <pre> 2: { 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 } 1: count: 25. </pre> =={{header\|Rust}}== <~~lang~~syntaxhighlight lang="rust">// [dependencies] // primal = "0.3" Line 863 ⟶ 1,797: println!("\nThe 7875th Erd\u{151}s prime is {}.", p); } }</~~lang~~syntaxhighlight> {{out}} Line 875 ⟶ 1,809: </pre> =={{header\|SETL}}== <syntaxhighlight lang="setl">program erdos_primes; loop for e in [1..2499] \| erdos e do nprint(lpad(str e, 6)); if (n +:= 1) mod 10=0 then print; end if; end loop; print; print("There are " + str n + " Erdos numbers < 2500"); e := 2499; loop while n < 7875 do loop until erdos e do e +:= 2; end loop; n +:= 1; end loop; print("The " + str n + "th Erdos number is " + str e); op erdos(p); return prime p and not exists k in faclist p \| prime (p-k); end erdos; op faclist(n); f := 1; return [[i+:=1, f:=i](2) : until n<f](..i-1); end op; op prime(n); if n<=4 then return n in [2,3]; end if; return odd n and not exists d in [3, 5..floor (sqrt n)] \| n mod d=0; end op; end program;</syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 There are 25 Erdos numbers < 2500 The 7875th Erdos number is 999721</pre> =={{header\|Sidef}}== <~~lang~~syntaxhighlight lang="ruby">func is_erdos_prime(p) { return true if p==2 Line 892 ⟶ 1,868: say ("Erdős primes <= 2500: ", 1..2500 -> grep(is_erdos_prime)) say ("The 7875th Erdős prime is: ", is_erdos_prime.nth(7875))</~~lang~~syntaxhighlight> {{out}} <pre> Erdős primes <= 2500: [2, 101, 211, 367, 409, 419, 461, 557, 673, 709, 769, 937, 967, 1009, 1201, 1259, 1709, 1831, 1889, 2141, 2221, 2309, 2351, 2411, 2437] The 7875th Erdős prime is: 999721 ~~</pre>~~ ~~=={{header\|Tiny BASIC}}==~~ ~~Can't manage the stretch goal because integers are limited to signed 16 bit.~~ ~~<lang tinybasic> LET P = 1~~ ~~10 IF P > 2 THEN LET P = P + 2~~ ~~IF P < 3 THEN LET P = P + 1~~ ~~LET Z = P~~ ~~GOSUB 1000~~ ~~IF A = 0 THEN GOTO 10~~ ~~LET K = 0~~ ~~20 LET K = K + 1~~ ~~GOSUB 2000~~ ~~LET Z = P - F~~ ~~IF Z < 0 THEN GOTO 30~~ ~~GOSUB 1000~~ ~~IF A = 1 THEN LET E = 0~~ ~~IF A = 1 THEN GOTO 10~~ ~~GOTO 20~~ ~~30 LET C = C + 1~~ ~~IF P < 2500 THEN PRINT C," ",P~~ ~~IF P > 2500 THEN END~~ ~~GOTO 10~~ ~~1000 REM primality of Z by trial division, result is in A~~ ~~LET Y = 1~~ ~~LET A = 0~~ ~~IF Z = 2 THEN LET A = 1~~ ~~IF Z < 3 THEN RETURN~~ ~~1010 LET Y = Y + 2~~ ~~IF (Z/Y)Y = Z THEN RETURN~~ ~~IF YY < Z THEN GOTO 1010~~ ~~LET A = 1~~ ~~RETURN~~ ~~2000 REM factorial of K, result is in F~~ ~~LET A = 1~~ ~~LET F = 1~~ ~~2010 LET F = FA~~ ~~IF A=K THEN RETURN~~ ~~LET A = A + 1~~ ~~GOTO 2010</lang>~~ ~~{{out}}<pre>1 2~~ ~~2 101~~ ~~3 211~~ ~~4 367~~ ~~5 409~~ ~~6 419~~ ~~7 461~~ ~~8 673~~ ~~9 709~~ ~~10 769~~ ~~11 937~~ ~~12 967~~ ~~13 1009~~ ~~14 1201~~ ~~15 1259~~ ~~16 1709~~ ~~17 1831~~ ~~18 2141~~ ~~19 2221~~ ~~20 2351~~ ~~21 2411~~ ~~22 2437~~ </pre> =={{header\|Wren}}== {{libheader\|Wren-math}} ~~{{libheader\|Wren-seq}}~~ {{libheader\|Wren-fmt}} <~~lang~~syntaxhighlight ~~ecmascript~~lang="wren">import "./math" for Int import "./~~seq~~fmt" for ~~Lst~~Fmt ~~import "/fmt" for Fmt~~ var limit = 1e6 var lowerLimit = 2500 ~~var primes = Int.primeSieve(limit - 1, true)~~ var c = Int.primeSieve(limit - 1, false) var erdos = [] var lastErdos = 0 ~~for (p in primes) {~~ var iec = 10 var ~~fact~~i = 12 while (i < limit) { ~~var found = true~~ ~~while~~if (~~fact < p~~!c[i]) { ifvar ~~(Int.isPrime(p~~j -= ~~fact)) {~~1 var ~~found~~fact = ~~false~~1 var found = ~~break~~true while (fact < i) { if (!c[i - fact]) { found = false break } j = j + 1 fact = fact j } if (found) { if (i < lowerLimit) erdos.add(i) lastErdos = i ec = ec + 1 } ~~i = i + 1~~ ~~fact = fact * i~~ } i = (i > 2) ? i + 2 : i + 1 ~~if (found) erdos.add(p)~~ } ~~var lowerLimit = 2500~~ Fmt.print("The $,d Erdős primes under $,d are:", erdos.count, lowerLimit) ~~var erdosLower = erdos.where { \|e\| e < lowerLimit}.toList~~ Fmt.tprint("$6d", erdos, 10) ~~Fmt.print("The $,d Erdős primes under $,d are:", erdosLower.count, lowerLimit)~~ Fmt.print("\nThe $,r Erdős prime is $,d.", ec, lastErdos)</syntaxhighlight> ~~for (chunk in Lst.chunks(erdosLower, 10)) Fmt.print("$6d", chunk)~~ ~~var show = 7875~~ ~~Fmt.print("\nThe $,r Erdős prime is $,d.", show, erdos[show-1])</lang>~~ {{out}} <pre> The 25 Erdős primes under 2,500 are: 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 The 7,875th Erdős prime is 999,721. </pre> =={{header\|XPL0}}== <syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if N is prime int N, I; [if N <= 2 then return N = 2; if (N&1) = 0 then \even >2\ return false; for I:= 3 to sqrt(N) do [if rem(N/I) = 0 then return false; I:= I+1; ]; return true; ]; func Erdos(N); \Return 'true' if N is an Erdos prime int N, F, K; [if not IsPrime(N) then return false; F:= 1; K:= 1; while F < N do [if IsPrime(N-F) then return false; K:= K+1; F:= F*K; ]; return true; ]; int Cnt, N, SN; [Format(5, 0); Cnt:= 0; N:= 2; repeat if Erdos(N) then [RlOut(0, float(N)); Cnt:= Cnt+1; if rem(Cnt/10) = 0 then CrLf(0); ]; N:= N+1; until N >= 2500; CrLf(0); Text(0, "Found "); IntOut(0, Cnt); Text(0, " Erdos primes^m^j"); Cnt:= 1; N:= 3; repeat if Erdos(N) then [Cnt:= Cnt+1; SN:= N]; N:= N+2; until N >= 1_000_000; Text(0, "The "); IntOut(0, Cnt); Text(0, "th Erdos prime is indeed "); IntOut(0, SN); CrLf(0); ]</syntaxhighlight> {{out}} <pre> 2 101 211 367 409 419 461 557 673 709 769 937 967 1009 1201 1259 1709 1831 1889 2141 2221 2309 2351 2411 2437 Found 25 Erdos primes The 7875th Erdos prime is indeed 999721 </pre>