Prime numbers in large number

Question

Given a large number (in base 10), such as 1234567891011121314151617, find prime "subnumbers" in it.
A prime "subnumber" is a consecutive sequence of digits (taken from the input), which represents a prime number (in base 10).

• Input: A number (either a string, a file, or whatever you like).
• Output: All prime subnumbers separated somehow (either in a list, a file, comma-separated strings...) If the result is empty, you can take any convention you like (hardcoded string, empty string, gibberish, but program should not crash.
• Example
  1234 -> 2, 3, 23
  6542 -> 5, 2
  14 -> [.. empty output]

This is code-golf. The shortest program wins!
[edit] : additional rule, program must be explained! Not everybody is fluent in Jelly :)

Answer 1

05AB1E (legacy), 3 bytes

Œʒp

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Substrings of the input that are prime.

Answer 2

Perl 6, 28 bytes

{grep &is-prime,+«m:ex/.+/}

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The :ex ("exhaustive") flag to the match operator m makes it return every possible match of .+ (ie, every substring of one or more characters), even overlapping ones. The hyperoperator +« turns that list of Match objects into numbers, which are then filtered for primeness by grep &is-prime.

Answer 3

Brachylog, 4 bytes

-1 byte thanks to Kroppeb.

sᶠṗˢ

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ᶠind all substrings, ˢelect the ṗrimes

Answer 4

Python 2, 66 65 bytes

P=k=1
n=input()
while~n+k:
 if`k`in`n`>0<P%k:print k
 P*=k*k;k+=1

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Answer 5

Japt, 13 10 bytes

Thanks @Shaggy -3 bytes

ò fj f@søX

---

ò fj f@søX              Full program
                        implicity input
ò                       inclusive range [this - 1]
  fj                    filter primes and
     f@søX              values contained in input

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Answer 6

Jelly,  5  4 bytes

-1 thanks to Kevin Cruijssen (Ẓ is an alias for ÆP)

ẆḌẒƇ

A monadic Link accepting a list of digits* which yields a list of prime integers.

^{* going by "either a string, a file, or whatever you like" - to take an integer, prefix the code with a D}

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How?

ẆḌẒƇ - Link: list of integers (digits)   e.g. [1,2,3,4]
Ẇ    - non-empty contiguous substrings        [[1],[2],[3],[4],[1,2],[2,3],[3,4],[1,2,3],[2,3,4],[1,2,3,4]]
 Ḍ   - convert to decimal (vectorises)        [1,2,3,4,12,23,34,123,234,1234]
   Ƈ - filter keep if:
  Ẓ  -   is prime?                            [2,3,23]

Answer 7

Java 8, 148 147 bytes

n->{for(int l=n.length(),i=l,j;i-->0;)for(j=l;j>i;){long k=2,x=new Long(n.substring(i,j--));for(;k<x;x=x%k++<1?0:x);if(x>1)System.out.println(x);}}

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Explanation:

n->{                     // Method with String parameter and no return-type
  for(int l=n.length(),  //  Length of the input-String
          i=l,j;         //  Temp-integers
      i-->0;)            //  Loop `i` in the range [length, 0)
    for(j=l;j>i;){       //   Inner loop `j` in the range [length, 0)
      for(long k=2,      //    Set `k` to 2
               x=new Long(n.substring(i,j--)
                         //    Take the substring [`i`, `j`) from the input,
            );           //    convert it to a long, and set it as `x`
          k<x;           //    Inner loop as long as `k` is still smaller than `x`
        x=x%k++<1?       //     If `x` is divisible by `k`:
           0             //      Set `x` to 0
          :              //     Else:
           x);           //      Leave `x` unchanged
      if(x>1)            //    If `x` is now larger than 1 (a.k.a. If `x` is a prime):
        System.out.println(x);}}
                         //     Print `x` with a trailing newline to STDOUT

Answer 8

MATL, 9 bytes

&XfXUtZp)

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Explanation

&Xf   % Implicit input: string. Push cell array of non-empty substrings
XU    % Convert to number. Vectorizes
t     % Duplicate
Zp    % Isprime. Vectorizes.
)     % Index. Keeps substrings indicated by the previous result. Implicit display

Answer 9

Bash + GNU Core Utils: 80 77 Bytes

for i in $(seq `tee a|wc -c`)
{
grep -oE .{$i}<a|factor|grep -oP ': \K\d+$'
}

This cannot be the shortest, but I am having trouble coming up with anything better. Help wanted!

By sticking to only POSIX, I got 82:

for i in $(seq `tee a|wc -c`)
{
grep -oE .{$i}<a|factor|awk -F\  'NF<3{print$2}'
}

Answer 10

R, 60 bytes

function(v)Filter(function(i)grepl(i,v)&sum(!i%%1:i)==2,1:v)

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Not really efficient, inspired by @ovs python 2 answer

Answer 11

Curry (KiCS2), 61 58 bytes

-3 bytes thanks to Wheat Wizard!

Takes input as a string, returns integers. f is function which can return any of the results.

p n|n>1&&all((>0).mod n)[2..n-1]=n
f(_++a:b++_)=p$read$a:b

You can try this on Smap (select KiCS2 2.2.0 /all-values) by adding:

main = f "1234"

p is a primality test function which returns it's input if it is a prime, and doesn't return anything otherwise.

f(_++a:b++_) matches non-empty substrings of the input in a:b and f returns the value of p applied to a:b converted to integer.

Local output:

> f "1234"
[...]
Evaluating expression: f "1234"
2
23
3

Answer 12

Vyxal Ṡ, 4 bytes

ǎE~æ

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ǎE~æ # 'Ṡ' flag makes Vyxal take all input as strings
ǎ    # All substrings
 E   # Convert to numbers
  ~æ # Remove non-primes

Answer 13

Python 2, 115 114 bytes

f=lambda s:s and[n for n in[int(s[j:])for j in range(len(s))]if n>1and all(n%i for i in range(2,n))]+f(s[:-1])or[]

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Answer 14

Wolfram Language (Mathematica), 40 bytes

Select[PrimeQ@*FromDigits]@*Subsequences

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Input and output are lists of digits. In the case of no prime subnumbers the empty list {} is returned.

Uses @* for Composition of functions. Subsequences gives a list of all subsequences of the input, and Select[PrimeQ@*FromDigits] is an operator form of Select which returns a list of all elements for which PrimeQ@*FromDigits returns True.

Answer 15

Husk, 5 bytes

foṗiQ

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Answer 16

Clean, 108 bytes

import StdEnv,Data.List
$s=nub[n\\u<-inits s,n<-map(toInt o toString)(tails u)|n>1&&all(\m=n/m*m<n)[2..n-1]]

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Answer 17

Pyth, 8 bytes

fP_TsM.:

Test suite

Takes the input as a string, outputs a list of integers. Can also take input as an int by adding ` at the end for an extra byte.

Explanation:

fP_TsM.:  | Full code
fP_TsM.:Q |  with implicit variables added
          | Print (implicit)
      .:Q |  list of all substrings of the input
    sM    |   converted to integers
fP_T      |    filtered for prime numbers

And ` just converts int to str.

Answer 18

Matlab, 89 bytes

function[m]=f(x),m=1;for i=1:length(x),m=[m;str2num(combnk(x,i))];end,m=m(isprime(m));end

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