Primes which contain only one odd digit

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

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


Stretch goal

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

11l

Translation of: Nim
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

F hasLastDigitOdd(=n)
   n I/= 10
   L n != 0
      I ((n % 10) [&] 1) != 0
         R 0B
      n I/= 10
   R 1B

V l = (1.<1000).step(2).filter(n -> hasLastDigitOdd(n) & is_prime(n))
print(‘Found ’l.len‘ primes with only one odd digit below 1000:’)
L(n) l
   print(‘#3’.format(n), end' I (L.index + 1) % 9 == 0 {"\n"} E ‘ ’)

V count = 0
L(n) (1.<1'000'000).step(2)
   I hasLastDigitOdd(n) & is_prime(n)
      count++
print("\nFound "count‘ primes with only one odd digit below 1000000.’)
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 1000000.

Action!

INCLUDE "H6:SIEVE.ACT"

BYTE FUNC OddDigitsCount(INT x)
  BYTE c,d

  c=0
  WHILE x#0
  DO
    d=x MOD 10
    IF (d&1)=1 THEN
      c==+1
    FI
    x==/10
  OD
RETURN (c)

PROC Main()
  DEFINE MAX="999"
  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 primes(i)=1 AND OddDigitsCount(i)=1 THEN
      PrintI(i) Put(32)
      count==+1
    FI
  OD
  PrintF("%E%EThere are %I primes",count)
RETURN
Output:

Screenshot from Atari 8-bit computer

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 45 primes

ALGOL 68

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

Arturo

onlyOneOddDigit?: function [n][
    and? -> prime? n
         -> one? select digits n => odd?
]

primesWithOnlyOneOddDigit: select 1..1000 => onlyOneOddDigit?

loop split.every: 9 primesWithOnlyOneOddDigit 'x ->
    print map x 's -> pad to :string s 4

nofPrimesBelow1M: enumerate 1..1000000 => onlyOneOddDigit?

print ""
print ["Found" nofPrimesBelow1M "primes with only one odd digit below 1000000."]
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 2560 primes with only one odd digit below 1000000.

AWK

# 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#

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)

C++

#include <vector>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <iterator>

bool isPrime( int n ) {
   int limit = static_cast<int>( std::floor( std::sqrt( static_cast<double>( n ) ) ) ) ;
   for ( int i = 2 ; i < limit + 1 ; i++ ) {
      if ( n % i == 0 ) {
         return false ;
      }
   }
   return true ;
}

bool hasOneOdd( int n ) {
   std::vector<int> digits ;
   while ( n != 0 ) {
      digits.push_back( n % 10 ) ;
      n /= 10 ;
   }
   return std::count_if( digits.begin( ) , digits.end( ) , []( int i ) { return 
         i % 2 == 1 ; } ) == 1 ;
}

bool condition( int n ) {
   return isPrime( n ) && hasOneOdd( n ) ;
}

int main( ) {
   std::vector<int> primes ;
   for ( int i = 2 ; i < 1000 ; i++ ) {
      if ( condition( i ) ) 
         primes.push_back( i ) ;
   }
   std::cout << "Primes under 1000 with only one odd digit :\n" ;
   std::copy( primes.begin( ) , primes.end( ) , std::ostream_iterator<int>( std::cout , 
            " " ) ) ;
   for ( int i = 1000 ; i < 1000000 ; i++ ) {
      if ( condition( i ) ) 
         primes.push_back( i ) ;
   }
   std::cout << "\nThe number of primes under 1000000 with only one odd digit is " <<
      primes.size( ) << " !\n " ;
   return 0 ;
}
Output:
Primes under 1000 with 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 
The number of primes under 1000000 with only one odd digit is 2560 !

Delphi

Works with: Delphi version 6.0


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 ShowOneOddDigitPrime(Memo: TMemo);
var I,Cnt1,Cnt2: integer;
var IA: TIntegerDynArray;
var S: string;

	function HasOneOddDigit(N: integer): boolean;
	var I,Odd: integer;
	begin
	Odd:=0;
	GetDigits(N,IA);
	for I:=0 to High(IA) do
	 if (IA[I] and 1)=1 then Inc(Odd);
	Result:=Odd=1;
	end;

begin
Cnt1:=0; Cnt2:=0;
S:='';
for I:=0 to 1000000-1 do
 if IsPrime(I) then
  if HasOneOddDigit(I) then
	begin
	Inc(Cnt1);
	if I<1000 then
	  	begin
	  	Inc(Cnt2);
	  	S:=S+Format('%4D',[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;
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

Count < 1,000     = 45
Count < 1,000,000 = 2560
Elapsed Time: 171.630 ms.

EasyLang

fastfunc isprim num .
   i = 2
   while i <= sqrt num
      if num mod i = 0
         return 0
      .
      i += 1
   .
   return 1
.
fastfunc nextprim prim .
   repeat
      prim += 1
      until isprim prim = 1
   .
   return prim
.
func digodd n .
   while n > 0
      r += if n mod 2 = 1
      n = n div 10
   .
   return r
.
p = 2
repeat
   if digodd p = 1
      write p & " "
   .
   p = nextprim p
   until p >= 1000
.
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 

F#

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

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

FreeBASIC

#include "isprime.bas"

function b(j as uinteger, n as uinteger) as uinteger
     'auxiliary function for evendig below
     dim as uinteger m = int(log(n-1)/log(5))
     return int((n-1-5^m)/5^j)
end function

function evendig(n as uinteger) as uinteger
    'produces the integers with only even digits
    dim as uinteger m = int(log(n-1)/log(5)), a
    a = ((2*b(m, n)) mod 8 + 2)*10^m
    if n<=1 or m=0 then return a
    for j as uinteger = 0 to m-1
        a += ((2*b(j, n)) mod 10)*10^j
    next j
    return a
end function

dim as uinteger n=1, count = 0, p=1
while p<1000000
    p = 1 + evendig(n)   'if it's a prime the odd digit must be the last one
    if isprime(p) then
        count += 1
        if p<1000 then print p
    end if
    n+=1
wend

print "There are ";count;" such primes below one million."

Go

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     = 9999999999
        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.\n")

    primes = rcu.Primes(LIMIT2)
    count := 0
    pow := 10
    for _, prime := range primes[1:] {
        if allButOneEven(prime) {
            count++
        }
        if prime > pow {
            fmt.Printf("There are %7s such primes under %s\n", rcu.Commatize(count), rcu.Commatize(pow))
            pow *= 10
        }
    }
    fmt.Printf("There are %7s such primes under %s\n", rcu.Commatize(count), rcu.Commatize(pow))
}
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       3 such primes under 10
There are      12 such primes under 100
There are      45 such primes under 1,000
There are     171 such primes under 10,000
There are     619 such primes under 100,000
There are   2,560 such primes under 1,000,000
There are  10,774 such primes under 10,000,000
There are  46,708 such primes under 100,000,000
There are 202,635 such primes under 1,000,000,000
There are 904,603 such primes under 10,000,000,000

Haskell

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

J

   getOneOdds=. #~ 1 = (2 +/@:| "."0@":)"0
   primesTo=. i.&.(p:inv)

   _15 ]\ getOneOdds primesTo 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

   # getOneOdds primesTo 1e6
2560

jq

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

### 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

# 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

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.

Mathematica / Wolfram Language

Labeled[Cases[
  NestWhileList[NextPrime, 
   2, # < 
     1000 &], _?(Total[Mod[IntegerDigits@#, 2]] == 
      1 &)], "Primes < 1000 with one odd digit", Top]
Labeled[Length@
  Cases[NestWhileList[NextPrime, 
    2, # < 
      1000000 &], _?(Total[Mod[IntegerDigits@#, 2]] == 
       1 &)], "Number of primes < 1,000,000 with one odd digit", Top]
Output:

Primes < 1000 with 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}

Number of primes < 1,000,000 with one odd digit 2560

Nim

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(1_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

#!/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

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

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

Python

def prime(n):
    if n == 1:
        return False
    if n == 2:
        p.append(n)
        return True
    for y in p:
        if n % y == 0:
            return False
        if y > int(n ** 0.5):
            p.append(n)
            return True


p = []
x = 1
stopper = 0
lis = []

for i in range(0, 1000000):
    x += 1
    if prime(x) == True:
        str_x = str(x)
        if str(x).count("1") + str(x).count("3") + str(x).count("5") + str(x).count("7") + str(x).count("9") == 1:
                lis.append(x)
    if int(x) == 1000 and stopper == 0:
        print(f'There are {len(lis)} primes with one odd digit less than 1000')
        for i in lis:
            print(i)

print(f'There are {len(lis)} primes with one odd digit less than 1000000')
Output:
There are 45 primes with one odd digit less than 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
...
881
883
887
There are 2560 primes with one odd digit less than 1000000

Quackery

isprime is defined at Primality by trial division#Quackery.

evendigits returns the nth number which has only even digits and ends with zero. There are self-evidently 5^5 of them less than 1000000.

We know that the only prime ending with a 5 is 5. So we can omit generating candidate numbers that end with a 5, and stuff the 5 into the right place in the nest (i.e. as item #1; item #0 will be 3) afterwards. This explains the lines ' [ 1 3 7 9 ] witheach and 5 swap 1 stuff.

  [ [] swap
    [ 5 /mod
      rot join swap
      dup 0 = until ]
    drop
    0 swap witheach
      [ swap 10 * + ]
    20 * ]                is evendigits ( n --> n )

  []
  5 5 ** times
   [ i^ evendigits
     ' [ 1 3 7 9 ] witheach
       [ over +
         dup isprime iff
           [ swap dip join ]
         else drop ]
     drop ]
  5 swap 1 stuff
  dup say "Qualifying primes < 1000:"
  dup findwith [ 999 > ] [ ]
  split drop unbuild
  1 split nip -1 split drop
  nest$ 44 wrap$ cr cr
  say "Number of qualifying primes < 1000000: "
  size echo
Output:
Qualifying primes < 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

Number of qualifying primes < 1000000: 2560

Raku

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

/*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 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          /*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

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...

RPL

Works with: HP version 49g
≪ 
   →STR 0 
   1 3 PICK SIZE FOR j
      OVER j DUP SUB NUM 2 MOD + NEXT 
   NIP
≫ ≫ 'ODDCNT' STO

≪ 
   { } 1
   DO
      NEXTPRIME
      IF DUP ODDCNT 1 == THEN SWAP OVER + SWAP END
   UNTIL DUP 1000 ≥ END
   DROP
≫ ≫ 'TASK' STO
Output:
1: {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}

Ruby

require 'prime'

def single_odd?(pr)
  d = pr.digits
  d.first.odd? && d[1..].all?(&:even?)
end

res = Prime.each(1000).select {|pr| single_odd?(pr)}
res.each_slice(10){|s| puts "%4d"*s.size % s}

n = 1_000_000
count = Prime.each(n).count{|pr| single_odd?(pr)}
puts "\nFound #{count} single-odd-digit primes upto #{n}."
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 2560 single-odd-digit primes upto 1000000.

Rust

fn is_prime( number : u32 ) -> bool {
   let limit : u32 = (number as f32).sqrt( ).floor( ) as u32 ;
   (2..=limit).all( | i | number % i != 0 ) 
}

fn has_one_odd( mut number : u32 ) -> bool {
   let mut digits : Vec<u32> = Vec::new( ) ;
   while number != 0 {
      digits.push( number % 10 ) ;
      number /= 10 ;
   }
   digits.into_iter( ).filter( | &d | d % 2 == 1 ).count( ) == 1
}

fn main() {
   let mut solution_primes : Vec<u32> = Vec::new( ) ;
   (2..1000).filter( | &d | is_prime( d ) && has_one_odd( d )).for_each( | n | {
            solution_primes.push( n ) ;
            } ) ;
   println!("Prime numbers under 1000 with only one odd digit:") ;
   println!("{:?}" , solution_primes ) ;
   println!("Number of primes under 1000000 with only one odd digit : {}" ,
         (2..1000000).filter( | &d  | is_prime( d ) && has_one_odd( d ) ).count( ) ) ;
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]
Number of primes under 1000000 with only one odd digit : 2560

Sidef

func primes_with_one_odd_digit(upto, base = 10) {

    upto = prev_prime(upto+1)

    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.ilog(base)) {
        even_digits.variations_with_repetition(k, {|*a|
            next if (a.last == 0)
            var v = a.digits2num(base)
            odd_digits.each {|d|
                var n = (v*base + d)
                list << n if (n.is_prime && (n <= upto))
            }
        })
    }

    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

Library: Wren-math
Library: Wren-fmt
import "./math" for Int
import "./fmt" for Fmt

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 $,d which contain only one odd digit:", limit + 1)
Fmt.tprint("$,%(maxDigits)d", results, 9)
System.print("\nFound %(results.count) such primes.\n")

limit = 1e9 - 1
primes = Int.primeSieve(limit)
var count = 0
var pow = 10
for (prime in primes.skip(1)) {
    if (Int.digits(prime)[0...-1].all { |d| d & 1 == 0 }) count = count + 1
    if (prime > pow) {
        Fmt.print("There are $,7d such primes under $,d", count, pow)
        pow = pow * 10
    }
}
Fmt.print("There are $,7d such primes under $,d", count, pow)
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       3 such primes under 10
There are      12 such primes under 100
There are      45 such primes under 1,000
There are     171 such primes under 10,000
There are     619 such primes under 100,000
There are   2,560 such primes under 1,000,000
There are  10,774 such primes under 10,000,000
There are  46,708 such primes under 100,000,000
There are 202,635 such primes under 1,000,000,000

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;
];

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.