# Prime words

Prime words 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.

A word is a   prime word   if all its individual letters   (expressed as an ASCII decimal code)   are primes.

```        A   ASCII decimal code is:   65
B   ASCII decimal code is:   66
C   ASCII decimal code is:   67

X   ASCII decimal code is:   88
Y   ASCII decimal code is:   89
Z   ASCII decimal code is:   90

a   ASCII decimal code is:   97
b   ASCII decimal code is:   98
c   ASCII decimal code is:   99

x   ASCII decimal code is:   120
y   ASCII decimal code is:   121
z   ASCII decimal code is:   122
```

Show here on this page every   prime word   in unixdict.txt.

## 11l

```F is_prime(Int a)
I a == 2
R 1B
I a < 2 | a % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(a))).step(2)
I a % i == 0
R 0B
R 1B

Set[Int] prime_chars
L(c) ‘a’.code .. ‘z’.code
I is_prime(c)
L(c) ‘A’.code .. ‘Z’.code
I is_prime(c)

L(c) word
I c.code !C prime_chars
L.break
L.was_no_break
print(word)```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Action!

In the following solution the input file is loaded from H6 drive. Altirra emulator automatically converts CR/LF character from ASCII into 155 character in ATASCII charset used by Atari 8-bit computer when one from H6-H10 hard drive under DOS 2.5 is used.

```INCLUDE "H6:SIEVE.ACT"

BYTE FUNC IsPrimeWord(CHAR ARRAY word BYTE ARRAY primes)
BYTE i,c

FOR i=1 TO word(0)
DO
c=word(i)
IF primes(c)=0 THEN
RETURN (0)
FI
OD
RETURN (1)

PROC FindPrimeWords(CHAR ARRAY fname BYTE ARRAY primes)
CHAR ARRAY line(256)
CHAR ARRAY tmp(256)
BYTE pos,dev=

pos=2
Close(dev)
Open(dev,fname,4)
WHILE Eof(dev)=0
DO
InputSD(dev,line)
IF IsPrimeWord(line,primes) THEN
IF pos+line(0)>=39 THEN
PutE() pos=2
FI
Print(line) Put(32)
pos==+line(0)+1
FI
OD
Close(dev)
RETURN

PROC Main()
DEFINE MAX="128"
BYTE ARRAY primes(MAX+1)
CHAR ARRAY fname="H6:UNIXDICT.TXT"

Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FindPrimeWords(fname,primes)
RETURN```
Output:
```a aaa age agee ak am ama e egg eke em emma g ga gag gage gam game gamma ge gee gem gemma gm k keg m ma mae magma make mamma me meek meg q
```

## ALGOL 68

Does not distinguish between letters and non-letter ASCII codes (as with the REXX sample).

```# find words whose character codes are primes                                     #
IF  FILE input file;
STRING file name = "unixdict.txt";
open( input file, file name, stand in channel ) /= 0
THEN
# failed to open the file #
print( ( "Unable to open """ + file name + """", newline ) )
ELSE
# file opened OK #
BOOL at eof := FALSE;
# set the EOF handler for the file #
on logical file end( input file, ( REF FILE f )BOOL:
BEGIN
# note that we reached EOF on the #
# latest read #
at eof := TRUE;
# return TRUE so processing can continue #
TRUE
END
);
# construct a sieve of primes up to the maximum character                      #
PR read "primes.incl.a68" PR
[]BOOL s = PRIMESIEVE max abs char;
# find the prime words                                                         #
INT prime count := 0;
WHILE STRING word;
get( input file, ( word, newline ) );
NOT at eof
DO
BOOL is prime := FALSE;
FOR w pos FROM LWB word TO UPB word WHILE ( is prime := s[ ABS word[ w pos ] ] ) DO SKIP OD;
IF is prime THEN
prime count +:= 1;
print( ( whole( prime count, -5 ), ": ", word, newline ) )
FI
OD;
close( input file )
FI```
Output:
```    1: a
2: aaa
3: age
4: agee
5: ak
6: am
7: ama
8: e
9: egg
10: eke
11: em
12: emma
13: g
14: ga
15: gag
16: gage
17: gam
18: game
19: gamma
20: ge
21: gee
22: gem
23: gemma
24: gm
25: k
26: keg
27: m
28: ma
29: mae
30: magma
31: make
32: mamma
33: me
34: meek
35: meg
36: q
```

## Arturo

```words: read.lines relative "unixdict.txt"

loop words 'word [
if every? split word 'ch -> prime? to :integer to :char ch ->
print word
]
```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q```

## AWK

```# syntax: GAWK -f PRIME_WORDS.AWK unixdict.txt
BEGIN {
for (i=0; i<=255; i++) {
if (is_prime(i)) {
prime_chars = sprintf("%s%c",prime_chars,i)
}
}
pattern = sprintf("^[%s]+\$",prime_chars)
}
{   if (\$0 ~ pattern) {
printf("%s ",\$0)
}
}
END {
printf("\n")
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:
```a aaa age agee ak am ama e egg eke em emma g ga gag gage gam game gamma ge gee gem gemma gm k keg m ma mae magma make mamma me meek meg q
```

## C++

```#include <algorithm>
#include <cstdlib>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <string>
#include "prime_sieve.hpp"

int main(int argc, char** argv) {
const char* filename(argc < 2 ? "unixdict.txt" : argv);
std::ifstream in(filename);
if (!in) {
std::cerr << "Cannot open file '" << filename << "'.\n";
return EXIT_FAILURE;
}
std::string line;
prime_sieve sieve(UCHAR_MAX);
auto is_prime = [&sieve](unsigned char c){ return sieve.is_prime(c); };
int n = 0;
while (getline(in, line)) {
if (std::all_of(line.begin(), line.end(), is_prime)) {
++n;
std::cout << std::right << std::setw(2) << n << ": "
<< std::left << std::setw(10) << line;
if (n % 4 == 0)
std::cout << '\n';
}
}
return EXIT_SUCCESS;
}
```

Contents of prime_sieve.hpp:

```#ifndef PRIME_SIEVE_HPP
#define PRIME_SIEVE_HPP

#include <algorithm>
#include <vector>

/**
* A simple implementation of the Sieve of Eratosthenes.
* See https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes.
*/
class prime_sieve {
public:
explicit prime_sieve(size_t);
bool is_prime(size_t) const;
private:
std::vector<bool> is_prime_;
};

/**
* Constructs a sieve with the given limit.
*
* @param limit the maximum integer that can be tested for primality
*/
inline prime_sieve::prime_sieve(size_t limit) {
limit = std::max(size_t(3), limit);
is_prime_.resize(limit/2, true);
for (size_t p = 3; p * p <= limit; p += 2) {
if (is_prime_[p/2 - 1]) {
size_t inc = 2 * p;
for (size_t q = p * p; q <= limit; q += inc)
is_prime_[q/2 - 1] = false;
}
}
}

/**
* Returns true if the given integer is a prime number. The integer
* must be less than or equal to the limit passed to the constructor.
*
* @param n an integer less than or equal to the limit passed to the
* constructor
* @return true if the integer is prime
*/
inline bool prime_sieve::is_prime(size_t n) const {
if (n == 2)
return true;
if (n < 2 || n % 2 == 0)
return false;
return is_prime_.at(n/2 - 1);
}

#endif
```
Output:
``` 1: a          2: aaa        3: age        4: agee
5: ak         6: am         7: ama        8: e
9: egg       10: eke       11: em        12: emma
13: g         14: ga        15: gag       16: gage
17: gam       18: game      19: gamma     20: ge
21: gee       22: gem       23: gemma     24: gm
25: k         26: keg       27: m         28: ma
29: mae       30: magma     31: make      32: mamma
33: me        34: meek      35: meg       36: q
```

## Factor

Works with: Factor version 0.99 2020-08-14
```USING: io.encodings.ascii io.files math.primes prettyprint sequences ;

"unixdict.txt" ascii file-lines [ [ prime? ] all? ] filter .
```
Output:
```{
"a"
"aaa"
"age"
"agee"
"ak"
"am"
"ama"
"e"
"egg"
"eke"
"em"
"emma"
"g"
"ga"
"gag"
"gage"
"gam"
"game"
"gamma"
"ge"
"gee"
"gem"
"gemma"
"gm"
"k"
"keg"
"m"
"ma"
"mae"
"magma"
"make"
"mamma"
"me"
"meek"
"meg"
"q"
}
```

## FreeBASIC

```dim shared as boolean prime(0 to 29) =_
{false, true, false, true, true, false, false, true, false, true, false, false, true, false,_
false, false, true, false, true, true, false, true, true, false, true, false, false, false, false}

function isprimeletter( s as string ) as boolean
dim as ubyte n = asc(s)
if n mod 2 = 0 then return false
return prime( (n-65)/2 )
end function

function isprimeword( s as string ) as boolean
for i as uinteger = 1 to len(s)
if not isprimeletter( mid(s,i,1) ) then return false
next i
return true
end function

dim as string word

open "unixdict.txt" for input as #1
while true
line input #1, word
if word = "" then exit while
if isprimeword( word ) then print word
wend
close #1
end
```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q```

## Go

```package main

import (
"bytes"
"fmt"
"io/ioutil"
"log"
"strings"
)

func isPrime(n int) bool {
if n < 2 {
return false
}
if n%2 == 0 {
return n == 2
}
if n%3 == 0 {
return n == 3
}
d := 5
for d*d <= n {
if n%d == 0 {
return false
}
d += 2
if n%d == 0 {
return false
}
d += 4
}
return true
}

func main() {
// cache prime runes with codepoints between 33 and 255 say
var primeRunes []rune
for i := 33; i < 256; i += 2 {
if isPrime(i) {
primeRunes = append(primeRunes, rune(i))
}
}
primeString := string(primeRunes)
wordList := "unixdict.txt"
b, err := ioutil.ReadFile(wordList)
if err != nil {
}
bwords := bytes.Fields(b)
fmt.Println("Prime words in", wordList, "are:")
for _, bword := range bwords {
word := string(bword)
ok := true
for _, c := range word {
if !strings.ContainsRune(primeString, c) {
ok = false
break
}
}
if ok {
fmt.Println(word)
}
}
}
```
Output:
```Prime words in unixdict.txt are:
a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## J

```   (\$~ _2 */\ q:@#)(#~ (1 */@p: 3 u: ])@>) cutLF fread'unixdict.txt'
┌─────┬───┬─────┬────┬─────┬───┬────┬───┬────┐
│a    │aaa│age  │agee│ak   │am │ama │e  │egg │
├─────┼───┼─────┼────┼─────┼───┼────┼───┼────┤
│eke  │em │emma │g   │ga   │gag│gage│gam│game│
├─────┼───┼─────┼────┼─────┼───┼────┼───┼────┤
│gamma│ge │gee  │gem │gemma│gm │k   │keg│m   │
├─────┼───┼─────┼────┼─────┼───┼────┼───┼────┤
│ma   │mae│magma│make│mamma│me │meek│meg│q   │
└─────┴───┴─────┴────┴─────┴───┴────┴───┴────┘
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

A suitable implementation of `is_prime` is given at Erdős-primes#jq and is therefore not repeated here.

The task description suggests that perhaps the appropriate definition of `is_prime_word` should focus on the alphabetic characters, perhaps along the lines of:

`def is_prime_word: all(gsub("[^A-Za-z]";"") | explode[]; is_prime);`

All such variations are as easy to accommodate as to envision, but for unixdict.txt the following suffices:

`def is_prime_word: all(explode[]; is_prime);`
`inputs | select(is_prime_word)`
Output:

Invocation (example): jq -Rrn -f prime-words.jq unixdict.txt

```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Julia

See Alternade_words#Julia for the foreachword function.

```const primelettervalues = [67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]
isprimeword(w, _) = all(c -> Int(c) in primelettervalues, collect(w)) ? w : ""
foreachword("unixdict.txt", isprimeword, colwidth=10, numcols=9)
```
Output:
```Word source: unixdict.txt

a         aaa       age       agee      ak        am        ama       e         egg
eke       em        emma      g         ga        gag       gage      gam       game
gamma     ge        gee       gem       gemma     gm        k         keg       m
ma        mae       magma     make      mamma     me        meek      meg       q
```

## Mathematica/Wolfram Language

```dict=Import["https://web.archive.org/web/20180611003215/http://www.puzzlers.org/pub/wordlists/unixdict.txt","String"];
dict//=StringSplit[#,"\n"]&;
chars=CharacterRange["A","Z"]~Join~CharacterRange["a","z"];
chars//=Select[ToCharacterCode/*First/*PrimeQ];
Select[dict,StringMatchQ[Repeated[Alternatives@@chars]]]//Column
```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q```

## Nim

```import strformat, strutils

func isPrime(n: Natural): bool =
if n < 2: return false
if n mod 2 == 0: return n == 2
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

# Build set of prime characters.
const PrimeChars = static:
var pchars: set[char]
for c in Letters:
if ord(c).isPrime: pchars.incl c
pchars

var count = 0
for word in "unixdict.txt".lines:
if word.allCharsInSet(PrimeChars):
inc count
echo &"{count:2}: {word}"
```
Output:
``` 1: a
2: aaa
3: age
4: agee
5: ak
6: am
7: ama
8: e
9: egg
10: eke
11: em
12: emma
13: g
14: ga
15: gag
16: gage
17: gam
18: game
19: gamma
20: ge
21: gee
22: gem
23: gemma
24: gm
25: k
26: keg
27: m
28: ma
29: mae
30: magma
31: make
32: mamma
33: me
34: meek
35: meg
36: q```

## Perl

```#!/usr/bin/perl

use strict;
use warnings;

my \$pat = join '', grep +(1 x ord) !~ /^(11+)\1+\$/, 'a'..'z', 'A'..'Z';
@ARGV = 'unixdict.txt';
print join('', grep /^[\$pat]+\$/, <>) =~ tr/\n/ /r =~ s/.{1,71}\K /\n/gr;
```
Output:
```a aaa age agee ak am ama e egg eke em emma g ga gag gage gam game gamma
ge gee gem gemma gm k keg m ma mae magma make mamma me meek meg q
```

## Phix

```with javascript_semantics
function sap(string word) return sum(apply(word,is_prime))==length(word) end function
sequence words = filter(unix_dict(),sap)
printf(1,"%d prime words found: %s\n",{length(words),join(shorten(words,"",3),", ")})
```
Output:
```36 prime words found: a, aaa, age, ..., meek, meg, q
```

## Plain English

```To run:
Start up.
Put "c:\unixdict.txt" into a path.
Read the path into a buffer.
Slap a rider on the buffer.
Loop.
Move the rider (text file rules).
Subtract 1 from the rider's token's last. \newline
Put the rider's token into a word string.
If the word is blank, break.
If the word is composed of prime letters, write the word on the console.
Repeat.
Wait for the escape key.
Shut down.

To decide if a byte is prime:
If the byte is in "aegkmq", say yes.
Say no.

To decide if a string is composed of prime letters:
Slap a substring on the string.
Loop.
If the substring is blank, say yes.
If the substring's first's target is not prime, say no.
Add 1 to the substring's first.
Repeat.```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Python

Given that the set is known and quite small, 52 in length, a bit of pre-processing to determine all prime positioned characters before hand will speed up the task significantly rather than determining it every time for every word in the list.

Here is the brute force pre-processor, again this can be done easily manually, but if you are feeling lazy, like me :)

```for i in range(65,123):
check = 1
for j in range(2,i):
if i%j == 0:
check = 0
if check==1:
print(chr(i),end='')
```

This produces the following string :

```CGIOSYaegkmq
```

It's possible to speed it up even more by dropping capitals since the file only contains lower case characters, but we will give that a pass.....

And here's the main program which hardcodes the output of the pre-processor above. As always :

Tested on Python 3+, the file download will work only if the link is still active. It is possible that you may be able to fetch the file in your browser but download via code may still fail. Check whether you are connected to a VPN, it works on open networks.

```#Aamrun, 6th November 2021

import urllib.request
from collections import Counter

urllib.request.urlretrieve("http://wiki.puzzlers.org/pub/wordlists/unixdict.txt", "unixdict.txt")

dictionary = open("unixdict.txt","r")

dictionary.close()

primeSet = set("CGIOSYaegkmq")

[print(word) for word in wordList if len(set(word).difference(primeSet))==0]
```

And here's the final output :

Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q

```

## Raku

Another in a continuing series of tasks that are a minimal variation of previous ones. This is essentially Smarandache prime-digital sequence using ords instead of numerical digits. Sigh.

In an effort to anticipate / head-off a rash of tiny variant tasks, a series of one-liners:

```my @words = 'unixdict.txt'.IO.words».fc;

sub display (\$n, @n, \$s = "First 20: ") {"\$n;\n{\$s}{@n.join: ', '}"}

say 'Number of words whose ords are all prime: ',
@words.hyper.grep({ .ords.all.is-prime }).&{display +\$_, \$_, ''};

# Twelve other minor variants
say "\nNumber of words whose ordinal sum is prime: ",
@words.grep({ .ords.sum.is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words whose ords are all prime, and whose ordinal sum is prime: ",
@words.hyper.grep({ .ords.all.is-prime && .ords.sum.is-prime }).&{display +\$_, \$_, ''};

say "\n\nInterpreting the words as if they were base 36 numbers:";

say "\nNumber of words whose 'digits' are all prime in base 36: ",
@words.hyper.grep({ !.contains(/\W/) && all(.comb».parse-base(36)).is-prime }).&{display +\$_, \$_, ''};

say "\nNumber of words that are prime in base 36: ",
@words.grep({ !.contains(/\W/) && :36(\$_).is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words whose base 36 digital sum is prime: ",
@words.grep({ !.contains(/\W/) && .comb».parse-base(36).sum.is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words that are prime in base 36, and whose digital sum is prime: ",
@words.grep({ !.contains(/\W/) && :36(\$_).is-prime && .comb».parse-base(36).sum.is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words that are prime in base 36, whose digits are all prime, and whose digital sum is prime: ",
@words.hyper.grep({ !.contains(/\W/) && all(.comb».parse-base(36)).is-prime && :36(\$_).is-prime && .comb».parse-base(36).sum.is-prime }).&{display +\$_, \$_, ''};

use Base::Any:ver<0.1.2+>;
set-digits('a'..'z');

say "\n\nTests using a custom base 26 where 'a' through 'z' is 0 through 25 and words are case folded:";

say "\nNumber of words whose 'digits' are all prime using a custom base 26: ",
@words.hyper.grep({ !.contains(/<-alpha>/) && all(.comb».&from-base(26)).is-prime }).&{display +\$_, \$_, ''};

say "\nNumber of words that are prime using a custom base 26: ",
@words.grep({ !.contains(/<-alpha>/) && .&from-base(26).is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words whose digital sum is prime using a custom base 26: ",
@words.grep({ !.contains(/<-alpha>/) && .comb».&from-base(26).sum.is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words that are prime in a custom base 26 and whose digital sum is prime in that base: ",
@words.grep({ !.contains(/<-alpha>/) && .&from-base(26).is-prime && .comb».&from-base(26).sum.is-prime }).&{display +\$_, .head(20)};

say "\nNumber of words that are prime in custom base 26, whose digits are all prime, and whose digital sum is prime: ",
@words.hyper.grep({ !.contains(/<-alpha>/) && all(.comb».&from-base(26)).is-prime && .&from-base(26).is-prime && .comb».&from-base(26).sum.is-prime }).&{display +\$_, \$_, ''};
```
Output:
```Number of words whose ords are all prime: 36;
a, aaa, age, agee, ak, am, ama, e, egg, eke, em, emma, g, ga, gag, gage, gam, game, gamma, ge, gee, gem, gemma, gm, k, keg, m, ma, mae, magma, make, mamma, me, meek, meg, q

Number of words whose ordinal sum is prime: 3778;
First 20: 10th, 9th, a, a's, aau, ababa, abate, abhorred, abject, ablate, aboard, abrade, abroad, absentee, absentia, absolute, absorptive, absurd, abusive, accelerate

Number of words whose ords are all prime, and whose ordinal sum is prime: 12;
a, e, egg, g, gem, k, keg, m, mae, mamma, meg, q

Interpreting the words as if they were base 36 numbers:

Number of words whose 'digits' are all prime in base 36: 18;
2nd, 5th, 7th, b, d, h, j, n, nd, nh, nj, nv, t, tn, tnt, tv, v, vt

Number of words that are prime in base 36: 1106;
First 20: 10th, 1st, 2nd, 5th, 6th, 7th, abandon, abbott, abdomen, ablution, abolish, abort, abrupt, absorb, abstention, abstract, abutted, accept, accident, acid

Number of words whose base 36 digital sum is prime: 4740;
First 20: 10th, 3rd, 7th, aba, abacus, abalone, abase, abater, abelian, abelson, aberrant, abeyant, ablaze, abort, aboveground, abraham, abrasion, abrasive, abreact, abridge

Number of words that are prime in base 36, and whose digital sum is prime: 300;
First 20: 10th, 7th, abort, accident, acid, ad, adorn, adulthood, afterthought, albeit, alvin, armload, around, arragon, arraign, assassin, asteroid, astound, augean, avocation

Number of words that are prime in base 36, whose digits are all prime, and whose digital sum is prime: 8;
7th, b, d, h, j, n, t, v

Tests using a custom base 26 where 'a' through 'z' is 0 through 25 and words are case folded:

Number of words whose 'digits' are all prime using a custom base 26: 30;
c, cdc, cf, crt, ct, d, dc, dr, f, fcc, fl, ft, ftc, h, l, ltd, n, nc, ncr, nd, nh, nrc, r, rd, t, tn, tnt, ttl, tx, x

Number of words that are prime using a custom base 26: 987;
First 20: abhorrent, abolish, abreact, absurd, ac, act, actual, actuarial, ad, adjutant, adult, advisor, aerosol, aft, agent, agricultural, ah, aid, ajar, al

Number of words whose digital sum is prime using a custom base 26: 5473;
First 20: ababa, aback, abacus, abalone, abase, abater, abc, abdicate, abdomen, abe, abelian, abelson, aberrant, abeyant, ablaze, abolish, abominate, aborigine, aboveground, abraham

Number of words that are prime in a custom base 26 and whose digital sum is prime in that base: 292;
First 20: abolish, abreact, absurd, ac, ad, adjutant, adult, agricultural, ah, aid, al, allah, allied, altar, an, annal, ar, arclength, argonaut, asocial

Number of words that are prime in custom base 26, whose digits are all prime, and whose digital sum is prime: 9;
c, d, f, h, l, n, r, t, x```

## REXX

No attempt was made to exclude any "word" if it contained any non-letter (Latin alphabet) characters.

```/*REXX program finds words whose ASCII code for its letters are prime (in a dictionary).*/
parse arg iFID .                                 /*obtain optional arguments from the CL*/
if iFID=='' | iFID=="," then iFID='unixdict.txt' /*Not specified?  Then use the default.*/
call genPrimes                                   /*generate all primes less than 256.   */
say 'reading the dictionary file: '   iFID       /*show which dictionary is being read. */
say
#= 0                                             /*count of prime words found  (so far).*/
do recs=0  while lines(iFID)\==0         /*read each word in the file  (word=X).*/
x= strip( linein( iFID) )                /*pick off a word from the input line. */

do j=1  for length(x)           /*examine each letter (char) in word.  */
_= c2d( substr(x, j, 1) )       /*convert each letter to a decimal num.*/
if \@._  then iterate recs      /*is this ASCII code letter a prime ?  */
end   /*j*/
say x                                    /*display a prime word to the terminal.*/
#= # + 1                                 /*bump the count of  prime words.      */
end      /*recs*/                        /* [↑]   semaphore name is uppercased. */
say
say copies("─", 30)     recs     " words in the dictionary file: "       iFID
say
say 'found '    #    " prime words in the dictionary."
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genPrimes: p=   2   3  5    7  11  13  17  19  23  29  31  37  41  43  47  53  59  61  ,
67  71  73  79  83  89  97 101 103 107 109 113 127 131 137 139 149 151  ,
157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251
@.= 0;    do j=1  for words(p);  _= word(p, j);  @._= 1;  end  /*j*/;    return
```
output   when using the default input:
```reading the dictionary file:  unixdict.txt

a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q

────────────────────────────── 25104  words in the dictionary file:  unixdict.txt

found  36  prime words in the dictionary.
```

## Ring

```load "stdlib.ring"

wordList = str2list(cStr)
Words = []

for n = 1 to len(wordList)
num = 0
len = len(wordList[n])
for m = 1 to len
asc = ascii(wordList[n][m])
if isprime(asc)
num = num + 1
else
exit
ok
next
if num = len
ok
next

see "Prime words are:" + nl
see Words```

Output:

```Prime words are:
a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Ruby

```require 'prime'

puts File.open("unixdict.txt").select{|line| line.chomp.chars.all?{|c| c.ord.prime?} }
```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Rust

```// [dependencies]
// primal = "0.3"

use std::fs::File;

fn print_prime_words(filename: &str) -> std::io::Result<()> {
let sieve = primal::Sieve::new(std::char::MAX as usize);
let file = File::open(filename)?;
let mut n = 0;
for line in io::BufReader::new(file).lines() {
let word = line?;
if word.chars().all(|c| sieve.is_prime(c as usize)) {
n += 1;
print!("{:2}: {:<10}", n, word);
if n % 4 == 0 {
println!();
}
}
}
Ok(())
}

fn main() {
match print_prime_words("unixdict.txt") {
Ok(()) => {}
Err(error) => eprintln!("{}", error),
}
}
```
Output:
``` 1: a          2: aaa        3: age        4: agee
5: ak         6: am         7: ama        8: e
9: egg       10: eke       11: em        12: emma
13: g         14: ga        15: gag       16: gage
17: gam       18: game      19: gamma     20: ge
21: gee       22: gem       23: gemma     24: gm
25: k         26: keg       27: m         28: ma
29: mae       30: magma     31: make      32: mamma
33: me        34: meek      35: meg       36: q
```

## Swift

```import Foundation

class BitArray {
var array: [UInt32]

init(size: Int) {
array = Array(repeating: 0, count: (size + 31)/32)
}

func get(index: Int) -> Bool {
let bit = UInt32(1) << (index & 31)
return (array[index >> 5] & bit) != 0
}

func set(index: Int, value: Bool) {
let bit = UInt32(1) << (index & 31)
if value {
array[index >> 5] |= bit
} else {
array[index >> 5] &= ~bit
}
}
}

class PrimeSieve {
let composite: BitArray

init(size: Int) {
composite = BitArray(size: size/2)
var p = 3
while p * p <= size {
if !composite.get(index: p/2 - 1) {
let inc = p * 2
var q = p * p
while q <= size {
composite.set(index: q/2 - 1, value: true)
q += inc
}
}
p += 2
}
}

func isPrime(number: Int) -> Bool {
if number < 2 {
return false
}
if (number & 1) == 0 {
return number == 2
}
return !composite.get(index: number/2 - 1)
}
}

func loadDictionary(_ path: String) throws -> [String] {
let contents = try String(contentsOfFile: path, encoding: String.Encoding.ascii)
return contents.components(separatedBy: "\n").filter{!\$0.isEmpty}
}

do {
let dictionary = try loadDictionary("unixdict.txt")
let sieve = PrimeSieve(size: 255)
for word in dictionary {
if word.allSatisfy({\$0.isASCII && sieve.isPrime(number: Int(\$0.asciiValue!))}) {
print(word)
}
}
} catch {
print(error.localizedDescription)
}
```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## Wren

Library: Wren-math
Library: Wren-trait
```import "io" for File
import "/math" for Int
import "/trait" for Stepped

// cache prime characters with codepoints between 33 and 255 say
var primeChars = []
for (i in Stepped.new(33..255, 2)) {
}
var wordList = "unixdict.txt" // local copy
var words = File.read(wordList).trimEnd().split("\n")
System.print("Prime words in %(wordList) are:")
for (word in words) {
if (word.all { |c| primeChars.contains(c) }) System.print(word)
}
```
Output:
```Prime words in unixdict.txt are:
a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```

## XPL0

```func IsPrime(N);        \Return 'true' if N is prime
int  N, I;
[if N <= 2 then return N = 2;
if (N&1) = 0 then \even >2\ return false;
for I:= 3 to sqrt(N) do
[if rem(N/I) = 0 then return false;
I:= I+1;
];
return true;
];

string  0;              \use zero-terminated strings
int     I, Ch;
char    Word(25);
def     LF=\$0A, CR=\$0D, EOF=\$1A;
[FSet(FOpen("unixdict.txt", 0), ^I);
OpenI(3);
repeat  I:= 0;
loop    [repeat Ch:= ChIn(3) until Ch # CR;     \remove possible CR
if Ch = EOF then quit;
if Ch = LF then
[Word(I):= 0;  Text(0, Word);  CrLf(0);
quit;
];
if not IsPrime(Ch) then
[repeat Ch:= ChIn(3) until Ch=LF or Ch=EOF;
quit;
];
Word(I):= Ch;
I:= I+1;
];
until   Ch = EOF;
]```
Output:
```a
aaa
age
agee
ak
am
ama
e
egg
eke
em
emma
g
ga
gag
gage
gam
game
gamma
ge
gee
gem
gemma
gm
k
keg
m
ma
mae
magma
make
mamma
me
meek
meg
q
```