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Write a program which determines if a given number is prime.

The catch: No digits or arithmetical operators. This means:

  1. No digits from 0 to 9, anywhere in the program, and whatever the meaning
  2. No using any built-in operators for addition (and incrementing), subtraction (and decrementing), multiplication, division, exponentiation, or modulus, anywhere in the program
  3. This includes symbols like + and functions like num.add()
  4. All other operations are permitted
  5. You may define your own functions for the forbidden operations
  6. You may use symbols like - when they mean things other than the forbidden operations

Shortest code wins - any language permitted.

Example solution

An ungolfed solution in Java can be found here.

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marked as duplicate by Mhmd, ProgramFOX, Timtech, plannapus, user80551 Apr 9 '14 at 11:48

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Probably because this is impossible? (Without abusing built-in prime functions, that is.) – Doorknob Apr 7 '14 at 20:48
Even if not impossible, it is so exclusive of the established techniques for prime detection to be kind of silly ... Feel free to post to Sandbox first to get a feel for how things will turn out before you post. – ProgrammerDan Apr 7 '14 at 20:51
@ProgrammerDan I added a solution using a typical prime-detection method. – Ypnypn Apr 7 '14 at 21:35
Quite similar to Is it a prime? w/o math? – daniero Apr 8 '14 at 0:19
In light of algorithmshark's solution; Should point two be updated to prohibit built in primality tests? – Taemyr Apr 8 '14 at 8:26

PHP, 117 characters

This one is based on regular expressions. If a string containing $n characters can be split into chunks of equal length, then $n must be composite.

(Assumes $n is a positive integer.)

function p($n){$u=true;$s=str_repeat('x',$n);return($s!='x'&&!preg_match('/^(xx{'.$u.',})\\'.$u.'{'.$u.',}$/U',$s));}


for ($i=1; $i<=100; $i++) if (p($i)) echo "$i ";

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 
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I believe this is the epitome of "two problems." +1 – wchargin Apr 8 '14 at 4:13

Sage, 18

Looks like this is allowed.

input()in Primes()

3 gives True, 4 gives False

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PERL 53 54 52 48


Thanks to reddit:

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Interesting. However, from the question: "1. No digits from 0 to 9, anywhere in the program, and whatever the meaning." The variable can be read in a shorter way: $a=pop; – Heiko Oberdiek Apr 8 '14 at 0:48
Thanks, any character will do, i used 'a'.. but I need the \1 for the capture. :-S – ilmale Apr 8 '14 at 0:52
A named capture helps: ('a'x($_=pop))=~/^a?$|^(?<a>aa+?)\g{a}+$/||print (48 bytes) – Heiko Oberdiek Apr 8 '14 at 0:57
Thanks you, I was looking for a short way to use name reference. Also I didn't know the empty print trick. :D – ilmale Apr 8 '14 at 1:03
@SeanCheshire Rule 3 only seems to disallow using + as an arithmetic operator, not as a regex symbol. This is in contrast to rule 1, which expressly forbids any use of digits in any context. – Venge Apr 8 '14 at 22:44

J - 7 char



This verb is in the form of a hook. Applied to an argument y, it will evaluate as follows. (Feel free to check for yourself: Hook, Reflex/Passive, Equals, Primes.)

(p:~=~) y          NB. (F G) y  becomes  y F (G y)   (Hook)
y p:~ (=~ y)       NB. x F~ y   becomes  y F x       (Passive)
(=~ y) p: y        NB. F~ y     becomes  y F y       (Reflex)
(y = y) p: y       NB. anything is equal to itself, so y=y becomes 1
1 p: y             NB. 1 p: y tests for primality of y


   (p:~=~) 5
   (p:~=~) 6
   (p:~=~) 8675309
   NB. test every element of a list
   (p:~=~)every 1627 5231 7610 6311 4549 6990 4220 9028 4066 3496
1 1 0 1 1 0 0 0 0 0
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I feel that using a built in primality tester goes against the spirit of the challenge. – Taemyr Apr 8 '14 at 8:27
@Taemyr (*@{.=*./)@(+.}.@i.) for 20 char. +. is GCD, *. is LCM, * is Signum. But until the specs change, the 7 char solution is the shortest valid solution. – algorithmshark Apr 8 '14 at 19:36

Python 3, 85

(lambda i:not any(' '*i==(' '*u)*v for u in range(i)for v in range(i)))(int(input()))

Where * is not a multiplication operator but a string multiple self-concatenation operator.

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Ruby, 30


Declares a function that returns whether its argument is prime.

Alternative version (same length):

require'prime';f=proc &:prime?

Obviously bending the rules, but you never said built-in prime functions aren't allowed.

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He shouldn't have to say it: – corsiKa Apr 8 '14 at 19:40

PHP - 208

function i($n){if($n==strlen(" "))return!!"";foreach(range(strlen("  "),$n) as$_){if($_!=$n){$a=array_fill(!!"",$n,"");while(count($a)>=$_)array_splice($a,!!"",$_);if(!count($a))return!!"";}}return!"";}

Type juggling in PHP is fun!

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