Primes whose first and last number is 3: Difference between revisions
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=={{header|ALGOL 68}}==
{{Trans|ALGOL W}} With added stretch goal. As with the Go and other samples, generates the candidate sequence.
<lang algol68>BEGIN # find some primes whose first and last digits are 3 #
INT max prime = 1 000 000; # largest number to consider #
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Revision as of 17:13, 24 July 2021
- Task
Find primes n (in base ten) whose first and last decimal digit is 3, and where n < 4,000.
Show all output here on this page.
- Stretch goal
Find and show only the number of these types of primes that are < 1,000,000.
ALGOL 68
With added stretch goal. As with the Go and other samples, generates the candidate sequence.
<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 # [ 1 : max prime ]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 prime ) DO IF prime[ i ] THEN FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD FI OD; INT p3count := 0; # prints n, if it is prime, handles newlines # PROC p = ( INT n )VOID: IF prime[ n ] THEN print( ( " ", whole( n, - 4 ) ) ); IF ( p3count +:= 1 ) MOD 12 = 0 THEN print( ( newline ) ) FI FI # p #; # find 1, 2, 3 and 4 digit 3x3 primes # p( 3 ); p( 33 ); FOR i FROM 0 BY 10 TO 90 DO p( 303 + i ) OD; FOR i FROM 0 BY 10 TO 990 DO p( 3003 + i ) OD; # 5 and 6 digit 3x3 primes # FOR i FROM 0 BY 10 TO 9 990 DO IF prime[ 30 003 + i ] THEN p3count +:= 1 FI OD; 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</lang>
- Output:
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 "3x3" primes below 1000000
ALGOL W
As with the Go and oher samples, finds the numbers by generating the candidate seuence. <lang algolw>begin % find some primes whose first and last digits are 3 %
integer MAX_PRIME; MAX_PRIME := 4000; begin logical array isPrime ( 1 :: MAX_PRIME ); integer p3Count; % increments n by 1 % integer procedure inc( integer value result n ) ; begin n := n + 1; n end; % prints n, if it is prime, handles newlines % procedure p ( integer value n ) ; if isPrime( n ) then begin writeon( i_w := 4, s_w := 0, " ", n ); if inc( p3Count ) rem 12 = 0 then write() end; % sieve the primes to MAX_PRIME % isPrime( 1 ) := false; isPrime( 2 ) := true; for i := 3 step 2 until MAX_PRIME do isPrime( i ) := true; for i := 4 step 2 until MAX_PRIME do isPrime( i ) := false; for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin integer ii; ii := i + i; if isPrime( i ) then for pr := i * i step ii until MAX_PRIME do isPrime( pr ) := false end for_i ; % find the 3x3 primes % p3Count := 0; % 1, 2 and 3 digit 3x3 primes % p( 3 ); p( 33 ); for i := 0 step 10 until 90 do p( 303 + i ); % 4 digit 3x3 primes % for i := 0 step 10 until 990 do p( 3003 + i ); end
end.</lang>
- Output:
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
Go
<lang go>package main
import (
"fmt" "rcu"
)
func main() {
var primes []int candidates := []int{3, 33} for i := 303; i <= 393; i += 10 { candidates = append(candidates, i) } for i := 3003; i <= 3993; i += 10 { candidates = append(candidates, i) } for _, cand := range candidates { if rcu.IsPrime(cand) { primes = append(primes, cand) } } fmt.Println("Primes under 4,000 which begin and end in 3:") for i, p := range primes { fmt.Printf("%5s ", rcu.Commatize(p)) if (i+1)%11 == 0 { fmt.Println() } } fmt.Println("\nFound", len(primes), "Such primes.") pc := len(primes) for i := 30003; i <= 39993; i += 10 { if rcu.IsPrime(i) { pc++ } } for i := 300003; i <= 399993; i += 10 { if rcu.IsPrime(i) { pc++ } } pcc := rcu.Commatize(pc) fmt.Println("\nFound", pcc, "primes under 1,000,000 which begin and end with 3.")
}</lang>
- Output:
Primes under 4,000 which begin and end in 3: 3 313 353 373 383 3,023 3,083 3,163 3,203 3,253 3,313 3,323 3,343 3,373 3,413 3,433 3,463 3,533 3,583 3,593 3,613 3,623 3,643 3,673 3,733 3,793 3,803 3,823 3,833 3,853 3,863 3,923 3,943 Found 33 Such primes. Found 2,251 primes under 1,000,000 which begin and end with 3.
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Primes_whose_first_and_last_number_is_3 use warnings; use ntheory qw( primes );
my @n33 = grep /^3/ && /3$/, @{ primes( 4000 ) }; 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";</lang>
- Output:
33 under 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 2251 under 1000000
Raku
<lang perl6>my $upto = 1e4;
for 1,3,5,7,9 -> $bracket {
print "\nPrimes up to $upto bracketed by $bracket - "; say display ^$upto .grep: { .starts-with($bracket) && .ends-with($bracket) && .is-prime }
}
sub display ($list, :$cols = 10, :$fmt = '%6d', :$title = "{+$list} matching:\n" ) {
cache $list; $title ~ $list.batch($cols)».fmt($fmt).join: "\n"
}</lang>
- Output:
Primes up to 10000 bracketed by 1 - 39 matching: 11 101 131 151 181 191 1021 1031 1051 1061 1091 1151 1171 1181 1201 1231 1291 1301 1321 1361 1381 1451 1471 1481 1511 1531 1571 1601 1621 1721 1741 1801 1811 1831 1861 1871 1901 1931 1951 Primes up to 10000 bracketed by 3 - 33 matching: 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 Primes up to 10000 bracketed by 5 - 1 matching: 5 Primes up to 10000 bracketed by 7 - 35 matching: 7 727 757 787 797 7027 7057 7127 7177 7187 7207 7237 7247 7297 7307 7417 7457 7477 7487 7507 7517 7537 7547 7577 7607 7687 7717 7727 7757 7817 7867 7877 7907 7927 7937 Primes up to 10000 bracketed by 9 - 29 matching: 919 929 9029 9049 9059 9109 9199 9209 9239 9319 9349 9419 9439 9479 9539 9619 9629 9649 9679 9689 9719 9739 9749 9769 9829 9839 9859 9929 9949
REXX
This REXX version allows the specification of the limit to search for these types of primes (in base ten), and it also
allows the specification of what (both) the leading and trailing decimal digit must be.
Also, if a negative cols is specified, only the count of primes found is shown. <lang ring>/*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.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ if dig== | dig=="," then dig= 3 /* " " " " " " */ call genP /*build array of semaphores for primes.*/ w= 10 /*width of a number in any column. */ title= ' primes N (in base ten) that have a leading and trailing digit of ' dig ,
" where N < " commas(hi)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') found= 0; idx= 1 /*initialize # of primes found; IDX. */ $= /*list of primes that contain a string.*/
do j=1 for # /*find primes with leading/trailing dig*/ parse var @.j Ld 2 -1 Td /*obtain the leading and trailing digit*/ if Ld\==dig then iterate /*does prime contain a leading DIG ? */ /* ◄■■■■■■■ a filter.*/ if Td\==dig then iterate /* " " " " trailing ? ? */ /* ◄■■■■■■■ a filter.*/ found= found + 1 /*bump the number of primes found. */ if cols<=0 then iterate /*Build the list (to be shown later)? */ c= commas(@.j) /*maybe add commas to the number. */ $= $ right(c, max(w, length(c) ) ) /*add a prime ──► $ list, allow big #*/ if found//cols\==0 then iterate /*have we populated a line of output? */ say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */ idx= idx + cols /*bump the index count for the output*/ end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(found) title 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 ? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " semaphores. */ #=5; sq.#= @.# **2 /*number of primes so far; prime². */ do j=@.#+2 by 2 to hi-1 /*find odd primes from here on. */ parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/ if j// 3==0 then iterate /*" " " 3? */ if j// 7==0 then iterate /*" " " 7? */ do k=5 while sq.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; sq.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */ end /*j*/; return</lang>
- output when using the default inputs:
index │ primes N (in base ten) that have a leading and trailing digit of 3 where N < 4,000 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 3 313 353 373 383 3,023 3,083 3,163 3,203 3,253 11 │ 3,313 3,323 3,343 3,373 3,413 3,433 3,463 3,533 3,583 3,593 21 │ 3,613 3,623 3,643 3,673 3,733 3,793 3,803 3,823 3,833 3,853 31 │ 3,863 3,923 3,943 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 33 primes N (in base ten) that have a leading and trailing digit of 3 where N < 4,000
- output when using the default inputs of: 1000000 -1
Found 2,251 primes N (in base ten) that have a leading and trailing digit of 3 where N < 1,000,000
Ring
<lang ring> load "stdlib.ring" see "working..." + nl see "Primes whose first and last number is 3" + nl row = 0
for n = 1 to 4000
strn = string(n) if left(strn,1) = "3" and right(strn,1) = "3" and isprime(n) see "" + n + " " row++ if row%10 = 0 see nl ok ok
next
see nl + "Found " + row + " numbers" + nl see "done..." + nl </lang>
- Output:
working... Primes whose first and last number is 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 Found 33 numbers done...
Wren
Basic task
<lang ecmascript>import "/math" for Int import "/trait" for Stepped import "/seq" for Lst import "/fmt" for Fmt
var primes = [] for (seq in [ 3..3, 33..33, Stepped.new(303..393, 10), Stepped.new(3003..3993, 10) ]) {
for (e in seq) if (Int.isPrime(e)) primes.add(e)
} System.print("Primes under 4,000 which begin and end in 3:") for (chunk in Lst.chunks(primes, 11)) Fmt.print("$,5d", chunk) System.print("\nFound %(primes.count) such primes.")</lang>
- Output:
Primes under 4,000 which begin and end in 3: 3 313 353 373 383 3,023 3,083 3,163 3,203 3,253 3,313 3,323 3,343 3,373 3,413 3,433 3,463 3,533 3,583 3,593 3,613 3,623 3,643 3,673 3,733 3,793 3,803 3,823 3,833 3,853 3,863 3,923 3,943 Found 33 such primes.
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. <lang ecmascript>import "/math" for Int import "/trait" for Stepped import "/seq" for Lst import "/fmt" for Fmt
var getQualifyingPrimes = Fn.new { |x, d|
if (d.type != Num || !d.isInteger || d < 1) Fiber.abort("Invalid number of digits.") if (x == 2 || x == 5) return [x] if (x % 2 == 0) return [] var primes = [] var candidates = [x] for (i in 1...d) { var pow = 10.pow(i) var start = x * (pow + 1) var end = start + pow - 10 candidates.addAll(Stepped.new(start..end, 10).toList) } return candidates.where { |cand| Int.isPrime(cand) }.toList
}
var d = 4 // up to 'd' digits for (x in [1, 2, 3, 5, 7, 9]) { // begins and ends with 'x'
var primes = getQualifyingPrimes.call(x, d) var len = d + ((d-1)/3).floor Fmt.print("Primes under $,%(len)d which begin and end in $d:", 10.pow(d), x) for (chunk in Lst.chunks(primes, 10)) Fmt.print("$,%(len)d", chunk) System.print("\nFound %(primes.count) such primes.\n")
}
d = 6 for (x in [1, 3, 7, 9]) {
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)
}</lang>
- Output:
Primes under 10,000 which begin and end in 1: 11 101 131 151 181 191 1,021 1,031 1,051 1,061 1,091 1,151 1,171 1,181 1,201 1,231 1,291 1,301 1,321 1,361 1,381 1,451 1,471 1,481 1,511 1,531 1,571 1,601 1,621 1,721 1,741 1,801 1,811 1,831 1,861 1,871 1,901 1,931 1,951 Found 39 such primes. Primes under 10,000 which begin and end in 2: 2 Found 1 such primes. Primes under 10,000 which begin and end in 3: 3 313 353 373 383 3,023 3,083 3,163 3,203 3,253 3,313 3,323 3,343 3,373 3,413 3,433 3,463 3,533 3,583 3,593 3,613 3,623 3,643 3,673 3,733 3,793 3,803 3,823 3,833 3,853 3,863 3,923 3,943 Found 33 such primes. Primes under 10,000 which begin and end in 5: 5 Found 1 such primes. Primes under 10,000 which begin and end in 7: 7 727 757 787 797 7,027 7,057 7,127 7,177 7,187 7,207 7,237 7,247 7,297 7,307 7,417 7,457 7,477 7,487 7,507 7,517 7,537 7,547 7,577 7,607 7,687 7,717 7,727 7,757 7,817 7,867 7,877 7,907 7,927 7,937 Found 35 such primes. Primes under 10,000 which begin and end in 9: 919 929 9,029 9,049 9,059 9,109 9,199 9,209 9,239 9,319 9,349 9,419 9,439 9,479 9,539 9,619 9,629 9,649 9,679 9,689 9,719 9,739 9,749 9,769 9,829 9,839 9,859 9,929 9,949 Found 29 such primes. Found 2,387 primes under 1,000,000 which begin and end with 1. Found 2,251 primes under 1,000,000 which begin and end with 3. Found 2,104 primes under 1,000,000 which begin and end with 7. Found 2,053 primes under 1,000,000 which begin and end with 9.
XPL0
<lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number int N, I; [if N <= 1 then return false; for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true; ];
func Starts3(N); \Return 'true' if most significant digit is 3 int N; [repeat N:= N/10; until N = 0; return rem(0) = 3; ];
int Count, N; [Count:= 0; N:= 3; repeat if Starts3(N) then
if IsPrime(N) then [Count:= Count+1; if N < 4000 then [IntOut(0, N); if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\); ]; ]; N:= N+10; if N = 4003 then [CrLf(0); IntOut(0, Count); Text(0, " such primes found below 4000."); ];
until N >= 1_000_000; CrLf(0); IntOut(0, Count); Text(0, " such primes found below 1,000,000. "); ]</lang>
- Output:
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 33 such primes found below 4000. 2251 such primes found below 1,000,000.