# ETOOBUSY đźš€ minimal blogging for the impatient

# PWC158 - Additive Primes

**TL;DR**

Here we are with TASK #1 from The Weekly Challenge #158. Enjoy!

# The challenge

Write a script to find out all

`Additive Primes <= 100`

.Additive primes are prime numbers for which the sum of their decimal digits are also primes.

Output`2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89`

# The questions

This time I have a little nit-pick on the language used, in that â€śthe
sumâ€ť (singular) â€śare also primesâ€ť (plural). Does this mean that this
should go all the way up reaching one digit only? Iâ€™ll assume not,
because the `89`

in the example has decimal digits sum `17`

, which is
prime but not additive prime by itself (the sum of its digits being
`8`

).

# The solution

The test for an additive prime will be very very straightforward:

- check that the number is prime
- check that the number resulting from the sum of its digits is prime.

Letâ€™s start with Raku:

```
#!/usr/bin/env raku
use v6;
sub MAIN (Int:D $M = 100) {
(2 .. $M).grep({$_.is-prime && $_.comb.sum.is-prime}).join(', ').put;
}
```

Short and sweet. The check for primality is a built-in `is-prime`

;
summing the digits leverages on the fact that the default representation
of `Int`

s as strings is in base 10, so it suffices to isolate the
individual digits with `comb`

and `sum`

them.

The Perl version is more or less on par, with a few more inclusions
for extra batteries (`is_prime`

and `sum`

):

```
#!/usr/bin/env perl
use v5.24;
use FindBin '$Bin';
use lib "$Bin/local/lib/perl5";
use ntheory 'is_prime';
use List::Util 'sum';
my $M = shift // 100;
say join ', ', grep { is_prime($_) && is_prime sum split m{}mxs } 2 .. $M;
```

The primality test is courtesy of ntheory, although in this specific case itâ€™s overkill because getting primes up to 100 might be done with a simple lookup table. Whatever.

Stay safe folks!

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