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Primes whose first and last number is 3: Difference between revisions

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Primes whose first and last number is 3 (view source)

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Find and show only the   ''number''   of these types of primes   that are   '''<   1,000,000'''.
<br><br>
 
=={{header|11l}}==
{{trans|Nim}}
 
<syntaxhighlight lang="11l">F is_prime(n)
I n == 2
R 1B
I n < 2 | n % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(n))).step(2)
I n % i == 0
R 0B
R 1B
 
V lim = 1'000'000
V primes3x3 = [3]
V m = 100
V count = 1
L m * 3 < lim
L(n) (3 * m + 3 .. 4 * m - 7).step(10)
I n > lim
L.break
I is_prime(n)
count++
I n < 4000
primes3x3.append(n)
m *= 10
 
print(‘Found ’primes3x3.len‘ primes starting and ending with 3 below 4000:’)
L(n) primes3x3
print(‘#4’.format(n), end' I (L.index + 1) % 11 == 0 {"\n"} E ‘ ’)
 
print("\nFound "count‘ primes starting and ending with 3 below 1000000.’)</syntaxhighlight>
 
{{out}}
<pre>
Found 33 primes starting and ending with 3 below 4000:
3 313 353 373 383 3023 3083 3163 3203 3253 3313
3323 3343 3373 3413 3433 3463 3533 3583 3593 3613 3623
3643 3673 3733 3793 3803 3823 3833 3853 3863 3923 3943
 
Found 2251 primes starting and ending with 3 below 1000000.
</pre>
 
=={{header|Action!}}==
{{libheader|Action! Sieve of Eratosthenes}}
<langsyntaxhighlight Actionlang="action!">INCLUDE "H6:SIEVE.ACT"
 
BYTE Func IsSpecialPrime(INT i BYTE ARRAY primes)
Line 53 ⟶ 96:
OD
PrintF("%E%EThere are %I primes",count)
RETURN</langsyntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Primes_whose_first_and_last_number_is_3.png Screenshot from Atari 8-bit computer]
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{{Trans|ALGOL W}} With added stretch goal. As with the Go and other samples, generates the candidate sequence.
{{libheader|ALGOL 68-primes}}
<langsyntaxhighlight lang="algol68">BEGIN # find some primes whose first and last digits are 3 #
INT max prime = 1 000 000; # largest number to consider #
# sieve the primes to max prime #
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FOR i FROM 0 BY 10 TO 99 990 DO IF prime[ 300 003 + i ] THEN p3count +:= 1 FI OD;
print( ( newline, "Found ", whole( p3count, 0 ), " ""3x3"" primes below 1000000", newline ) )
END</langsyntaxhighlight>
{{out}}
<pre>
Line 97 ⟶ 140:
=={{header|ALGOL W}}==
As with the Go and oher samples, finds the numbers by generating the candidate seuence.
<langsyntaxhighlight lang="algolw">begin % find some primes whose first and last digits are 3 %
integer MAX_PRIME;
MAX_PRIME := 4000;
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for i := 0 step 10 until 990 do p( 3003 + i );
end
end.</langsyntaxhighlight>
{{out}}
<pre>
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3733 3793 3803 3823 3833 3853 3863 3923 3943
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">firstAndLastIs3?: function [n][
if not? prime? n -> return false
return and? -> 3 = first digits n
-> 3 = last digits n
]
 
primesWithFirstAndLast3: select 1..4000 => firstAndLastIs3?
 
loop split.every: 11 primesWithFirstAndLast3 'x ->
print map x 's -> pad to :string s 5
 
nofPrimesBelow1M: enumerate 1..1000000 => firstAndLastIs3?
 
print ""
print ["Found" nofPrimesBelow1M "primes starting and ending with 3 below 1000000."]</syntaxhighlight>
 
{{out}}
 
<pre> 3 313 353 373 383 3023 3083 3163 3203 3253 3313
3323 3343 3373 3413 3433 3463 3533 3583 3593 3613 3623
3643 3673 3733 3793 3803 3823 3833 3853 3863 3923 3943
 
Found 2251 primes starting and ending with 3 below 1000000. </pre>
 
=={{header|AWK}}==
<syntaxhighlight lang="awk">
<lang AWK>
# syntax: GAWK -f PRIMES_WHOSE_FIRST_AND_LAST_NUMBER_IS_3.AWK
BEGIN {
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return(1)
}
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|C}}==
{{trans|FreeBASIC}}
<langsyntaxhighlight lang="c">#include<stdio.h>
#include<stdlib.h>
#include<math.h>
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printf( "\n\nThere were %d primes of the form 3x3 below one million.\n", np );
return 0;
}</langsyntaxhighlight>
{{out}}<pre>
3 313 353 373 383 3023 3083 3163 3203 3253
Line 215 ⟶ 283:
 
There were 2251 primes of the form 3x3 below one million.</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;
 
 
 
 
procedure GetDigits(N: integer; var IA: TIntegerDynArray);
{Get an array of the integers in a number}
var T: integer;
begin
SetLength(IA,0);
repeat
begin
T:=N mod 10;
N:=N div 10;
SetLength(IA,Length(IA)+1);
IA[High(IA)]:=T;
end
until N<1;
end;
 
 
 
procedure ShowFirstLast3Prime(Memo: TMemo);
var I,Cnt1,Cnt2: integer;
var IA: TIntegerDynArray;
var S: string;
 
function FirstLast3(N: integer): boolean;
var I: integer;
begin
GetDigits(N,IA);
Result:=(IA[0]=3) and (IA[High(IA)]=3);
end;
 
begin
Cnt1:=0; Cnt2:=0;
S:='';
for I:=0 to 1000000-1 do
if IsPrime(I) then
if FirstLast3(I) then
begin
Inc(Cnt1);
if I<4000 then
begin
Inc(Cnt2);
S:=S+Format('%5D',[I]);
If (Cnt2 mod 5)=0 then S:=S+CRLF;
end;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Count < 1,000 = '+IntToStr(Cnt2));
Memo.Lines.Add('Count < 1,000,000 = '+IntToStr(Cnt1));
end;
 
 
</syntaxhighlight>
{{out}}
<pre>
3 313 353 373 383
3023 3083 3163 3203 3253
3313 3323 3343 3373 3413
3433 3463 3533 3583 3593
3613 3623 3643 3673 3733
3793 3803 3823 3833 3853
3863 3923 3943
Count < 1,000 = 33
Count < 1,000,000 = 2251
Elapsed Time: 181.797 ms.
 
</pre>
 
 
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)]
<langsyntaxhighlight lang="fsharp">
//3 Sandwich Primes. Nigel Galloway: July 25th., 2021
primes32()|>Seq.takeWhile((>)4000)|>Seq.filter(fun n->n%10=3 && (n=3||(n>29 && n<40)||(n>299 && n<400)||n>2999))|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|Factor}}==
{{works with|Factor|0.99 2021-06-02}}
<langsyntaxhighlight lang="factor">USING: formatting grouping io kernel lists lists.lazy math
math.functions math.primes sequences ;
 
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3 1,000,000 surrounded llength
"Found %d primes beginning and ending with 3 under 1,000,000.\n" printf</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Fermat}}==
<langsyntaxhighlight lang="fermat">np := 1;
!(3,' ');
for d = 1 to 5 do
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!!;
!!('There were ',np,' primes of the form 3...3 below 1,000,000');
</syntaxhighlight>
</lang>
{{out}}<pre>
3 313 353 373 383 3023 3083 3163 3203 3253
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=={{header|FreeBASIC}}==
<langsyntaxhighlight lang="freebasic">#include "isprime.bas"
 
dim as integer np = 1, d, n, i
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next d
print : print
print "There were ";np;" 3...3 primes below 1000000"</langsyntaxhighlight>
{{out}}<pre>
3 313 353 373 383 3023 3083 3163 3203 3253
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=={{header|Go}}==
{{libheader|Go-rcu}}
<langsyntaxhighlight lang="go">package main
 
import (
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pcc := rcu.Commatize(pc)
fmt.Println("\nFound", pcc, "primes under 1,000,000 which begin and end with 3.")
}</langsyntaxhighlight>
 
{{out}}
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Found 2,251 primes under 1,000,000 which begin and end with 3.
</pre>
 
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">
isPrime :: Int -> Bool
isPrime n
|n == 2 = True
|n == 1 = False
|otherwise = null $ filter (\i -> mod n i == 0 ) [2 .. root]
where
root :: Int
root = floor $ sqrt $ fromIntegral n
 
condition :: Int -> Bool
condition n = isPrime n && head numstr == '3' && last numstr == '3'
where
numstr :: String
numstr = show n
 
solution :: [Int]
solution = filter condition [1..3999]
 
main :: IO ( )
main = do
print solution
putStrLn ( "There are " ++ ( show $ length $ filter condition [1..999999]
) ++ " 3 x 3 primes below 1000000!" )
</syntaxhighlight>
{{out}}
<pre>
[3,313,353,373,383,3023,3083,3163,3203,3253,3313,3323,3343,3373,3413,3433,3463,3533,3583,3593,3613,3623,3643,3673,3733,3793,3803,3823,3833,3853,3863,3923,3943]
There are 2251 3 x 3 primes below 1000000!
</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j"> primes3x3=. 3 ;@; 10 <@(#~ 1&p:)@(30&* + 3 + 10 * i.)@^ i.
 
primes3x3 3
3 313 353 373 383 3023 3083 3163 3203 3253 3313 3323 3343 3373 3413 3433 3463 3533 3583 3593 3613 3623 3643 3673 3733 3793 3803 3823 3833 3853 3863 3923 3943
 
# primes3x3 5
2251</syntaxhighlight>
 
=={{header|jq}}==
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See e.g. [[Erd%C5%91s-primes#jq]] for a suitable implementation of `is_prime`.
<langsyntaxhighlight lang="jq"># For the stretch goal:
def count(s): reduce s as $x (null; .+1);
 
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task(2),
"\nStretch goal: \(count( task(4) ))"</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Julia}}==
<langsyntaxhighlight lang="julia">using Primes
 
isxbyx(n, base=10, dig=3) = n ÷ prevpow(base, n) == dig && n % base == dig
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println("\nTotal $(d)x$d primes less than 1,000,000: ", length(p3x3(1_000_000, 10, d)), ".")
end
</langsyntaxhighlight>{{out}}
<pre>
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</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<langsyntaxhighlight Mathematicalang="mathematica">Cases[NestWhileList[NextPrime,
2, # < 4000 &], _?(IntegerDigits[#][[{1, -1}]] === {3, 3} &)]</langsyntaxhighlight>
 
{{out}}<pre>
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=={{header|Nim}}==
<langsyntaxhighlight Nimlang="nim">import strformat
 
func isPrime(n: Positive): bool =
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stdout.write &"{n:4}", if (i + 1) mod 11 == 0: '\n' else: ' '
 
echo &"\nFound {count} primes starting and ending with 3 below 1_000_000."</langsyntaxhighlight>
 
{{out}}
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=={{header|Perl}}==
{{libheader|ntheory}}
<langsyntaxhighlight lang="perl">#!/usr/bin/perl
 
use strict; # https://rosettacode.org/wiki/Primes_whose_first_and_last_number_is_3
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my $n33 = grep /^3/ && /3$/, @{ primes( 1_000_000 ) };
print @n33 . " under 4000\n\n@n33" =~ s/.{75}\K /\n/gr,
"\n\n$n33 under 1000000\n";</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Phix}}==
Works for any digit, partly inspired by the Wren entry.
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">primes_with_first_and_last_digit</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p10</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">primes_with_first_and_last_digit</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</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;">"There are %d primes under 1,000,000 which begin and end in 3\n"</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>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
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=={{header|Raku}}==
<syntaxhighlight lang="raku" perl6line>my $upto = 1e4;
 
for 1,3,5,7,9 -> $bracket {
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cache $list;
$title ~ $list.batch($cols)».fmt($fmt).join: "\n"
}</langsyntaxhighlight>
{{out}}
<pre>Primes up to 10000 bracketed by 1 - 39 matching:
Line 656 ⟶ 861:
 
Also, &nbsp; if a negative &nbsp; '''cols''' &nbsp; is specified, &nbsp; only the &nbsp; ''count'' &nbsp; of primes found is shown.
<langsyntaxhighlight lang="rexx">/*REXX pgm finds and displays primes (base ten) that contain a leading and trailing 3. */
parse arg hi cols dig . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 4000 /*Not specified? Then use the default.*/
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end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; sq.#= j*j /*bump # of Ps; assign next P; P square*/
end /*j*/; return</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
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=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
load "stdlib.ring"
see "working..." + nl
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see nl + "Found " + row + " numbers" + nl
see "done..." + nl
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 749 ⟶ 954:
Found 33 numbers
done...
</pre>
 
=={{header|RPL}}==
Uses a candidate numbers generator to speed up execution.
{{works with|HP|49}}
≪ { } 3
'''WHILE''' DUP 4000 < '''REPEAT'''
'''IF''' DUP ISPRIME? '''THEN''' SWAP OVER + SWAP '''END'''
10 +
'''IF''' DUP MANT IP 3 ≠ '''THEN''' XPON 1 + ALOG 3 * 3 + '''END'''
'''END''' DROP
≫ '<span style="color:blue">33PRIMES</span>' STO
{{out}}
<pre>
1: { 3 313 353 373 383 3023 3083 3163 3203 3253 3313 3323 3343 3373 3413 3433 3463 3533 3583 3593 3613 3623 3643 3673 3733 3793 3803 3823 3833 3853 3863 3923 3943 }
</pre>
 
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
 
puts "Primes below #{n=4000} which start and end with #{d=3}: "
p Prime.each(n).select{|pr| p_d = pr.digits; p_d.first == d && p_d.last == d}
 
print "\nCount of primes below #{n=1_000_000} which start and en with #{d=3}: "
puts Prime.each(n).count{|pr| p_d = pr.digits; p_d.first == d && p_d.last == d}
</syntaxhighlight>
{{out}}
<pre>Primes below 4000 which start and end with 3:
[3, 313, 353, 373, 383, 3023, 3083, 3163, 3203, 3253, 3313, 3323, 3343, 3373, 3413, 3433, 3463, 3533, 3583, 3593, 3613, 3623, 3643, 3673, 3733, 3793, 3803, 3823, 3833, 3853, 3863, 3923, 3943]
 
Count of primes below 1000000 which start and en with 3: 2251
</pre>
 
=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby">func numbers_with_edges(upto, base = 10, s = [3]) {
Enumerator({|callback|
callback(s.digits2num(base))
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var count = numbers_with_edges(n).grep{.is_prime}.len
say "\nThere are #{count} primes <= #{n.commify} which begin and end in 3"
}</langsyntaxhighlight>
{{out}}
<pre>
Line 793 ⟶ 1,029:
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-traititerate}}
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
 
===Basic task===
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Int
import "./traititerate" for Stepped
import "./seqfmt" for LstFmt
import "/fmt" for Fmt
 
var primes = []
Line 808 ⟶ 1,042:
}
System.print("Primes under 4,000 which begin and end in 3:")
for (chunk in Lst.chunks(primes, 11)) Fmt.printtprint("$,5d", chunkprimes, 11)
System.print("\nFound %(primes.count) such primes.")</langsyntaxhighlight>
 
{{out}}
Line 823 ⟶ 1,057:
===More general===
This version deals with primes (in base 10) beginning and ending with any specified digit and with up to a given number of digits.
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Int
import "./traititerate" for Stepped
import "./seqfmt" for LstFmt
import "/fmt" for Fmt
 
var getQualifyingPrimes = Fn.new { |x, d|
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var len = d + ((d-1)/3).floor
Fmt.print("Primes under $,%(len)d which begin and end in $d:", 10.pow(d), x)
for (chunk in Lst.chunks(primes, 10)) Fmt.printtprint("$,%(len)d", chunkprimes, 10)
System.print("\nFound %(primes.count) such primes.\n")
}
Line 856 ⟶ 1,089:
var primes = getQualifyingPrimes.call(x, d)
Fmt.print("Found $,d primes under $,d which begin and end with $d.\n", primes.count, 10.pow(d), x)
}</langsyntaxhighlight>
 
{{out}}
Line 911 ⟶ 1,144:
 
=={{header|XPL0}}==
<langsyntaxhighlight XPL0lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
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Text(0, " such primes found below 1,000,000.
");
]</langsyntaxhighlight>
 
{{out}}
PureFox
9,487

edits

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