I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

Primes which contain only one odd digit

From Rosetta Code
Primes which contain only one odd digit 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

Show on this page those primes under   1,000   which when expressed in decimal contains only one odd digit.


Stretch goal

Show on this page only the   count   of those primes under   1,000,000   which when expressed in decimal contains only one odd digit.

ALGOL 68[edit]

BEGIN  # find primes whose decimal representation contains only one odd digit #
# sieve the primes to 1 000 000 #
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE 1 000 000;
# show a count of primes #
PROC show total = ( INT count, INT limit, STRING name )VOID:
print( ( newline, "Found ", whole( count, 0 ), " ", name, " primes upto ", whole( limit, 0 ), newline ) );
# find the appropriate primes #
# 2 is the only even prime, so the final digit must be odd for primes > 2 #
# so we only need to check that the digits other than the last are all even #
INT show max = 1 000;
INT p1odd count := 0;
FOR n FROM 3 TO UPB prime DO
IF prime[ n ] THEN
BOOL p1odd := TRUE;
INT v := n OVER 10;
WHILE v > 0 AND ( p1odd := NOT ODD v ) DO
v OVERAB 10
OD;
IF p1odd THEN
# the prime has only 1 odd digit #
p1odd count +:= 1;
IF n <= show max THEN
print( ( whole( n, -5 ) ) );
IF p1odd count MOD 12 = 0 THEN print( ( newline ) ) FI
FI
FI
FI;
IF n = show max THEN
print( ( newline ) );
show total( p1odd count, show max, "single-odd-digit" )
FI
OD;
show total( p1odd count, UPB prime, "single-odd-digit" )
END
Output:
    3    5    7   23   29   41   43   47   61   67   83   89
  223  227  229  241  263  269  281  283  401  409  421  443
  449  461  463  467  487  601  607  641  643  647  661  683
  809  821  823  827  829  863  881  883  887

Found 45 single-odd-digit primes upto 1000

Found 2560 single-odd-digit primes upto 1000000

AWK[edit]

 
# syntax: GAWK -f PRIMES_WHICH_CONTAIN_ONLY_ONE_ODD_NUMBER.AWK
BEGIN {
start = 1
stop = 999
for (i=start; i<=stop; i++) {
if (is_prime(i)) {
if (gsub(/[13579]/,"&",i) == 1) {
rec_odd = sprintf("%s%5d%1s",rec_odd,i,++count_odd%10?"":"\n")
}
if (gsub(/[02468]/,"&",i) == 1) {
rec_even = sprintf("%s%5d%1s",rec_even,i,++count_even%10?"":"\n")
}
}
}
printf("%s\nPrimes which contain only one odd number %d-%d: %d\n\n",rec_odd,start,stop,count_odd)
printf("%s\nPrimes which contain only one even number %d-%d: %d\n\n",rec_even,start,stop,count_even)
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)
}
 
Output:
    3     5     7    23    29    41    43    47    61    67
   83    89   223   227   229   241   263   269   281   283
  401   409   421   443   449   461   463   467   487   601
  607   641   643   647   661   683   809   821   823   827
  829   863   881   883   887
Primes which contain only one odd number 1-999: 45

    2    23    29    41    43    47    61    67    83    89
  101   103   107   109   127   149   163   167   181   211
  233   239   251   257   271   277   293   307   347   349
  367   383   389   419   431   433   439   457   479   491
  499   503   509   521   523   541   547   563   569   587
  613   617   619   631   653   659   673   677   691   701
  709   727   743   761   769   787   811   839   853   857
  859   877   907   929   941   947   967   983
Primes which contain only one even number 1-999: 78

C#[edit]

Modifies a conventional prime sieve to cull the items with more than one odd digit.

using System;
using System.Collections.Generic;
 
class Program
{
// starts as an ordinary odds-only prime sieve, but becomes
// extraordinary after the else statement...
static List<uint> sieve(uint max, bool ordinary = false)
{
uint k = ((max - 3) >> 1) + 1,
lmt = ((uint)(Math.Sqrt(max++) - 3) >> 1) + 1;
var pl = new List<uint> { };
var ic = new bool[k];
for (uint i = 0, p = 3; i < lmt; i++, p += 2) if (!ic[i])
for (uint j = (p * p - 3) >> 1; j < k; j += p) ic[j] = true;
if (ordinary)
{
pl.Add(2);
for (uint i = 0, j = 3; i < k; i++, j += 2)
if (!ic[i]) pl.Add(j);
}
else
for (uint i = 0, j = 3, t = j; i < k; i++, t = j += 2)
if (!ic[i])
{
while ((t /= 10) > 0)
if (((t % 10) & 1) == 1) goto skip;
pl.Add(j);
skip:;
}
return pl;
}
 
static void Main(string[] args)
{
var pl = sieve((uint)1e9);
uint c = 0, l = 10, p = 1;
Console.WriteLine("List of one-odd-digit primes < 1,000:");
for (int i = 0; pl[i] < 1000; i++)
Console.Write("{0,3}{1}", pl[i], i % 9 == 8 ? "\n" : " ");
string fmt = "\nFound {0:n0} one-odd-digit primes < 10^{1} ({2:n0})";
foreach (var itm in pl)
if (itm < l) c++;
else Console.Write(fmt, c++, p++, l, l *= 10);
Console.Write(fmt, c++, p++, l);
}
}
 
Output:
List of one-odd-digit primes < 1,000:
  3    5    7   23   29   41   43   47   61
 67   83   89  223  227  229  241  263  269
281  283  401  409  421  443  449  461  463
467  487  601  607  641  643  647  661  683
809  821  823  827  829  863  881  883  887

Found 3 one-odd-digit primes < 10^1 (10)
Found 12 one-odd-digit primes < 10^2 (100)
Found 45 one-odd-digit primes < 10^3 (1,000)
Found 171 one-odd-digit primes < 10^4 (10,000)
Found 619 one-odd-digit primes < 10^5 (100,000)
Found 2,560 one-odd-digit primes < 10^6 (1,000,000)
Found 10,774 one-odd-digit primes < 10^7 (10,000,000)
Found 46,708 one-odd-digit primes < 10^8 (100,000,000)
Found 202,635 one-odd-digit primes < 10^9 (1,000,000,000)

F#[edit]

This task uses Extensible Prime Generator (F#)

 
// Primes which contain only one odd number. Nigel Galloway: July 28th., 2021
let rec fN g=function 2->false |n when g=0->n=1 |n->fN (g/10) (n+g%2)
primes32()|>Seq.takeWhile((>)1000)|>Seq.filter(fun g->fN g 0)|>Seq.iter(printf "%d "); printfn ""
 
Output:
3 5 7 23 29 41 43 47 61 67 83 89 223 227 229 241 263 269 281 283 401 409 421 443 449 461 463 467 487 601 607 641 643 647 661 683 809 821 823 827 829 863 881 883 887

Factor[edit]

Works with: Factor version 0.99 2021-06-02
USING: grouping io lists lists.lazy literals math math.primes
numspec prettyprint ;
 
<<
DIGIT: o 357
DIGIT: q 1379
DIGIT: e 2468
DIGIT: E 02468
 
NUMSPEC: one-odd-candidates o eq eEq ... ;
>>
 
CONSTANT: p $[ one-odd-candidates [ prime? ] lfilter ]
 
"Primes with one odd digit under 1,000:" print
p [ 1000 < ] lwhile list>array 9 group simple-table.
 
"\nCount of such primes under 1,000,000:" print
p [ 1,000,000 < ] lwhile llength .
 
"\nCount of such primes under 1,000,000,000:" print
p [ 1,000,000,000 < ] lwhile llength .
Output:
Primes with one odd digit under 1,000:
3   5   7   23  29  41  43  47  61
67  83  89  223 227 229 241 263 269
281 283 401 409 421 443 449 461 463
467 487 601 607 641 643 647 661 683
809 821 823 827 829 863 881 883 887

Count of such primes under 1,000,000:
2560

Count of such primes under 1,000,000,000:
202635

Go[edit]

Translation of: Wren
Library: Go-rcu
package main
 
import (
"fmt"
"rcu"
)
 
func allButOneEven(prime int) bool {
digits := rcu.Digits(prime, 10)
digits = digits[:len(digits)-1]
allEven := true
for _, d := range digits {
if d&1 == 1 {
allEven = false
break
}
}
return allEven
}
 
func main() {
const (
LIMIT = 999
LIMIT2 = 999999
MAX_DIGITS = 3
)
primes := rcu.Primes(LIMIT)
var results []int
for _, prime := range primes[1:] {
if allButOneEven(prime) {
results = append(results, prime)
}
}
fmt.Println("Primes under", rcu.Commatize(LIMIT+1), "which contain only one odd digit:")
for i, p := range results {
fmt.Printf("%*s ", MAX_DIGITS, rcu.Commatize(p))
if (i+1)%9 == 0 {
fmt.Println()
}
}
fmt.Println("\nFound", len(results), "such primes.")
 
primes = rcu.Primes(LIMIT2)
count := 0
for _, prime := range primes[1:] {
if allButOneEven(prime) {
count = count + 1
}
}
cs := rcu.Commatize(count)
ls := rcu.Commatize(LIMIT2 + 1)
fmt.Println("\nThere are", cs, "primes under", ls, "which contain only one odd digit.")
}
Output:
Primes under 1,000 which contain only one odd digit:
  3   5   7  23  29  41  43  47  61 
 67  83  89 223 227 229 241 263 269 
281 283 401 409 421 443 449 461 463 
467 487 601 607 641 643 647 661 683 
809 821 823 827 829 863 881 883 887 

Found 45 such primes.

There are 2,560 primes under 1,000,000 which contain only one odd digit.

Haskell[edit]

import Data.List (intercalate, maximum, transpose)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (primes)
import Text.Printf (printf)
 
 
------------------ ONE ODD DECIMAL DIGIT -----------------
 
oneOddDecimalDigit :: Int -> Bool
oneOddDecimalDigit =
(1 ==) . length . filter odd . digits
 
digits :: Int -> [Int]
digits = fmap (read . return) . show
 
 
--------------------------- TEST -------------------------
main :: IO ()
main = do
putStrLn "Below 1000:"
(putStrLn . table " " . chunksOf 10 . fmap show) $
sampleBelow 1000
 
putStrLn "Count of matches below 10E6:"
(print . length) $
sampleBelow 1000000
 
sampleBelow :: Int -> [Int]
sampleBelow =
filter oneOddDecimalDigit
. flip takeWhile primes
. (>)
 
------------------------- DISPLAY ------------------------
 
table :: String -> [[String]] -> String
table gap rows =
let ws = maximum . fmap length <$> transpose rows
pw = printf . flip intercalate ["%", "s"] . show
in unlines $ intercalate gap . zipWith pw ws <$> rows
Output:
Below 1000:
  3   5   7  23  29  41  43  47  61  67
 83  89 223 227 229 241 263 269 281 283
401 409 421 443 449 461 463 467 487 601
607 641 643 647 661 683 809 821 823 827
829 863 881 883 887

Count of matches below 10E6:
2560

jq[edit]

Works with: jq

Works with gojq, the Go implementation of jq

As noted in the Julia entry, if only one digit of a prime is odd, then that digit is in the ones place. The first solution presented here uses this observation to generate plausible candidates. The second solution is more brutish and slower but simpler.

See e.g. Erdős-primes#jq for a suitable implementation of `is_prime`.

Fast solution[edit]

### Preliminaries
 
def count(s): reduce s as $x (null; .+1);
 
def emit_until(cond; stream):
label $out | stream | if cond then break $out else . end;
 
# Output: an unbounded stream
def primes_with_exactly_one_odd_digit:
# Output: a stream of candidate strings, in ascending numerical order
def candidates:
# input is $width
def evens:
. as $width
| if $width == 0 then ""
else ("0","2","4","6","8") as $i
| ((.-1)|evens) as $j
| "\($i)\($j)"
end;
("2","4","6","8") as $leading
| evens as $even
| ("1","3","5","7","9") as $odd
| "\($leading)\($even)\($odd)";
 
(3,5,7),
(range(0; infinite)
| candidates | tonumber
| select(is_prime)) ;
 
### The Task
emit_until(. > 1000; primes_with_exactly_one_odd_digit),
 
"\nThe number of primes less than 1000000 with exactly one odd digits is \(count(emit_until(. > 1000000; primes_with_exactly_one_odd_digit)))."
Output:
3
5
7
23
29
41
43
47
61
67
83
89
223
227
229
241
263
269
281
283
401
409
421
443
449
461
463
467
487
601
607
641
643
647
661
683
809
821
823
827
829
863
881
883
887

The number of primes less than 1000000 with exactly one odd digits is 2560.

A simpler but slower solution[edit]

# Input is assumed to be prime.
# So we only need check the other digits are all even.
def prime_has_exactly_one_odd_digit:
if . == 2 then false
# The codepoints for the odd digits are also odd: [49,51,53,55,57]
else all(tostring | explode[:-1][]; . % 2 == 0)
end;
 
def primes_with_exactly_one_odd_digit_crudely:
# It is much faster to check for primality afterwards.
range(3; infinite; 2)
| select(prime_has_exactly_one_odd_digit and is_prime);

Julia[edit]

If only one digit of a prime is odd, then that odd digit is the ones place digit. We don't actually need to check for an odd first digit once we exclude 2.

using Primes
 
function isoneoddprime(n, base = 10)
d = digits(n ÷ base, base = base)
return n != 2 && all(iseven, d)
end
 
found = filter(isoneoddprime, primes(1000))
println("Found $(length(found)) primes with one odd digit in base 10:")
foreach(p -> print(rpad(last(p), 5), first(p) % 9 == 0 ? "\n" : ""), enumerate(found))
 
println("\nThere are ", count(isoneoddprime, primes(1_000_000)),
" primes with only one odd digit in base 10 between 1 and 1,000,000.")
 
Output:
Found 45 primes with one odd digit in base 10:
3    5    7    23   29   41   43   47   61
67   83   89   223  227  229  241  263  269
281  283  401  409  421  443  449  461  463
467  487  601  607  641  643  647  661  683
809  821  823  827  829  863  881  883  887

There are 2560 primes with only one odd digit in base 10 between 1 and 1,000,000.

Nim[edit]

import sequtils, strutils
 
func isPrime(n: Positive): bool =
if n == 1: return false
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0:
return false
inc d, 2
if n mod d == 0:
return false
inc d, 4
result = true
 
func hasLastDigitOdd(n: Natural): bool =
var n = n
n = n div 10
while n != 0:
if (n mod 10 and 1) != 0: return false
n = n div 10
result = true
 
iterator primesOneOdd(lim: Positive): int =
var n = 1
while n <= lim:
if n.hasLastDigitOdd and n.isPrime:
yield n
inc n, 2
 
 
let list = toSeq(primesOneOdd(1000))
echo "Found $# primes with only one odd digit below 1000:".format(list.len)
for i, n in list:
stdout.write ($n).align(3), if (i + 1) mod 9 == 0: '\n' else: ' '
 
var count = 0
for _ in primesOneOdd(100_000_000):
inc count
echo "\nFound $# primes with only one odd digit below 1_000_000.".format(count)
Output:
Found 45 primes with only one odd digit below 1000:
  3   5   7  23  29  41  43  47  61
 67  83  89 223 227 229 241 263 269
281 283 401 409 421 443 449 461 463
467 487 601 607 641 643 647 661 683
809 821 823 827 829 863 881 883 887

Found 2560 primes with only one odd digit below 1_000_000.

Perl[edit]

#!/usr/bin/perl
 
use strict;
use warnings;
use ntheory qw( primes );
 
my @singleodd = grep tr/13579// == 1, @{ primes(1e3) };
my $million = grep tr/13579// == 1, @{ primes(1e6) };
print "found " . @singleodd .
"\n\n@singleodd\n\nfound $million in 1000000\n" =~ s/.{60}\K /\n/gr;
Output:
found 45

3 5 7 23 29 41 43 47 61 67 83 89 223 227 229 241 263 269 281
283 401 409 421 443 449 461 463 467 487 601 607 641 643 647 661
683 809 821 823 827 829 863 881 883 887

found 2560 in 1000000

Phix[edit]

Relies on the fact that '0', '1', '2', etc are just as odd/even as 0, 1, 2, etc.

with javascript_semantics
function oneodddigit(integer n) return sum(apply(sprint(n),odd))=1 end function
sequence res = filter(get_primes_le(1_000),oneodddigit)
printf(1,"Found %d one odd digit primes < 1,000: %V\n",{length(res),shorten(res,"",5)})
Output:
Found 45 one odd digit primes < 1,000: {3,5,7,23,29,"...",829,863,881,883,887}

stretch[edit]

Fast skip from 11 direct to 20+, from 101 direct to 200+, etc. Around forty times faster than the above would be, but less than twice as fast as it would be without such skipping.
Of course the last digit must/will be odd for all primes (other than 2 which has no odd digit anyway), and all digits prior to that must be even, eg 223 or 241, and not 257 or 743.

with javascript_semantics
for m=1 to iff(platform()=JS?8:9) do
    integer m10 = power(10,m)
    sequence primes = get_primes_le(m10)
    integer n = 2, count = 0
    while n<=length(primes) do
        integer p = primes[n], skip = 10
        while true do
            p = floor(p/10)
            if odd(p) then
                p = (p+1)*skip
                n = abs(binary_search(p,primes))
                exit
            end if
            if p=0 then
                count += 1
                n += 1
                exit
            end if
            skip *=10
        end while
    end while
    printf(1,"Found %,d one odd digit primes < %,d\n",{count,m10})
end for
Output:
Found 3 one odd digit primes < 10
Found 12 one odd digit primes < 100
Found 45 one odd digit primes < 1,000
Found 171 one odd digit primes < 10,000
Found 619 one odd digit primes < 100,000
Found 2,560 one odd digit primes < 1,000,000
Found 10,774 one odd digit primes < 10,000,000
Found 46,708 one odd digit primes < 100,000,000
Found 202,635 one odd digit primes < 1,000,000,000

Raku[edit]

put display ^1000 .grep: { ($_ % 2) && .is-prime && (.comb[^(*-1)].all %% 2) }
 
sub display ($list, :$cols = 10, :$fmt = '%6d', :$title = "{+$list} matching:\n" ) {
cache $list;
$title ~ $list.batch($cols)».fmt($fmt).join: "\n"
}
Output:
45 matching:
     3      5      7     23     29     41     43     47     61     67
    83     89    223    227    229    241    263    269    281    283
   401    409    421    443    449    461    463    467    487    601
   607    641    643    647    661    683    809    821    823    827
   829    863    881    883    887

REXX[edit]

/*REXX pgm finds & displays primes (base ten) that contain only one odd digit (< 1,000).*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 1000 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
title= ' primes N (in base ten) that only contain one odd digit, 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=2 for #-1; p= @.j; L= length(p) /*find primes with leading/trailing dig*/
z= 0
do k=L by -1 for L
if verify(substr(p, k, 1), 13579, 'M')>0 then do; z= z+1; if z>1 then iterate j /* ◄■■■■■■■ the filter.*/
end
end /*k*/
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. */
#=5; sq.#= @.# **2 /*number of primes so far; prime square*/
do [email protected].#+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 /*bump # of Ps; assign next P; P square*/
end /*j*/; return
output   when using the default inputs:
 index │                   primes  N  (in base ten)  that only contain one odd digit, where N < 1,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          3          5          7         23         29         41         43         47         61         67
  11   │         83         89        223        227        229        241        263        269        281        283
  21   │        401        409        421        443        449        461        463        467        487        601
  31   │        607        641        643        647        661        683        809        821        823        827
  41   │        829        863        881        883        887
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  45  primes  N  (in base ten)  that only contain one odd digit, where N < 1,000
output   when using the inputs of:     1000000   -1
Found  2,560  primes  N  (in base ten)  that only contain one odd digit, where N < 1,000,000

Ring[edit]

 
load "stdlib.ring"
see "working..." + nl
see "Primes which contain only one odd number:" + nl
row = 0
 
for n = 1 to 1000
odd = 0
str = string(n)
for m = 1 to len(str)
if number(str[m])%2 = 1
odd++
ok
next
if odd = 1 and isprime(n)
see "" + n + " "
row++
if row%5 = 0
see nl
ok
ok
next
 
see "Found " + row + " prime numbers" + nl
see "done..." + nl
 
Output:
working...
Primes which contain only one odd number:
3 5 7 23 29 
41 43 47 61 67 
83 89 223 227 229 
241 263 269 281 283 
401 409 421 443 449 
461 463 467 487 601 
607 641 643 647 661 
683 809 821 823 827 
829 863 881 883 887 
Found 45 prime numbers
done...

Sidef[edit]

func primes_with_one_odd_digit(upto, base = 10) {
 
var list = []
var digits = @(^base)
 
var even_digits = digits.grep { .is_even }
var odd_digits = digits.grep { .is_odd && .is_coprime(base) }
 
list << digits.grep { .is_odd && .is_prime && !.is_coprime(base) }...
 
for k in (0 .. upto.len(base)-1) {
even_digits.variations_with_repetition(k, {|*a|
next if (a.last == 0)
break if ([1, a...].digits2num(base) > upto)
odd_digits.each {|d|
var n = [d, a...].digits2num(base)
list << n if n.is_prime
}
})
}
 
list.sort
}
 
with (1e3) {|n|
var list = primes_with_one_odd_digit(n)
say "There are #{list.len} primes under #{n.commify} which contain only one odd digit:"
list.each_slice(9, {|*a| say a.map { '%3s' % _ }.join(' ') })
}
 
say ''
 
for k in (1..8) {
var count = primes_with_one_odd_digit(10**k).len
say "There are #{'%6s' % count.commify} such primes <= 10^#{k}"
}
Output:
There are 45 primes under 1,000 which contain only one odd digit:
  3   5   7  23  29  41  43  47  61
 67  83  89 223 227 229 241 263 269
281 283 401 409 421 443 449 461 463
467 487 601 607 641 643 647 661 683
809 821 823 827 829 863 881 883 887

There are      3 such primes <= 10^1
There are     12 such primes <= 10^2
There are     45 such primes <= 10^3
There are    171 such primes <= 10^4
There are    619 such primes <= 10^5
There are  2,560 such primes <= 10^6
There are 10,774 such primes <= 10^7
There are 46,708 such primes <= 10^8

Wren[edit]

Library: Wren-math
Library: Wren-fmt
Library: Wren-seq
import "/math" for Int
import "/fmt" for Fmt
import "/seq" for Lst
 
var limit = 999
var maxDigits = 3
var primes = Int.primeSieve(limit)
var results = []
for (prime in primes.skip(1)) {
if (Int.digits(prime)[0...-1].all { |d| d & 1 == 0 }) results.add(prime)
}
Fmt.print("Primes under $,d which contain only one odd digit:", limit + 1)
for (chunk in Lst.chunks(results, 9)) Fmt.print("$,%(maxDigits)d", chunk)
System.print("\nFound %(results.count) such primes.")
 
limit = 999999
primes = Int.primeSieve(limit)
var count = 0
for (prime in primes.skip(1)) {
if (Int.digits(prime)[0...-1].all { |d| d & 1 == 0 }) count = count + 1
}
Fmt.print("\nThere are $,d primes under $,d which contain only one odd digit.", count, limit + 1)
Output:
Primes under 1,000 which contain only one odd digit:
  3   5   7  23  29  41  43  47  61
 67  83  89 223 227 229 241 263 269
281 283 401 409 421 443 449 461 463
467 487 601 607 641 643 647 661 683
809 821 823 827 829 863 881 883 887

Found 45 such primes.

There are 2,560 primes under 1,000,000 which contain only one odd digit.

XPL0[edit]

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;
];
 
int Count, N, Hun, Ten, One;
[Count:= 0;
for Hun:= 0 to 4 do
for Ten:= 0 to 4 do
for One:= 0 to 4 do
[N:= Hun*200 + Ten*20 + One*2 + 1;
if IsPrime(N) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
];
CrLf(0);
IntOut(0, Count);
Text(0, " such numbers found.
");
]
Output:
3       5       7       23      29      41      43      47      61      67
83      89      223     227     229     241     263     269     281     283
401     409     421     443     449     461     463     467     487     601
607     641     643     647     661     683     809     821     823     827
829     863     881     883     887     
45 such numbers found.