# Perl Weekly Challenge 168: prime umbers in many ways!

It is sad that, after more than two years of me doing Raku, I still don’t have any production code project to work on. Therefore, in order to keep my coding and Raku-ing (is that a term?) knowdledge, I try to solve every Perl Weekly Challenge tasks.

In the following, the assigned tasks for Challenge 168.

and for the sake of some Perl 5, let’s do some stuff also in PostgreSQL Pl/Perl:
Last, the solutions in PostgreSQL PL/PgSQL:

## PWC 168 - Task 1

Compute first 13 Perrin prime numbers, that are numbers in the Perrin sequence that are also primes. At glance, I tried to use the Raku sequence `...` operator with something like the following:

``````my @perrin = 3, 0, 2, -> \$left, \$right { \$left + \$right } ... *;
my @perrin-primes = @perrin.grep( *.is-prime );
``````

However, this requires too much time on my machine, so I produced something more “classical” as the following:

``````sub MAIN( Int \$limit where { \$limit > 1 } = 13 ) {
my @perrin = 3, 0, 2;
my @perrin-primes;

while ( @perrin-primes.elems < \$limit ) {
@perrin.push: @perrin[ * - 2 ] + @perrin[ * - 3 ];
@perrin-primes.push: @perrin[ * - 1 ] if @perrin[ * - 1 ].is-prime && ! @perrin-primes.grep( @perrin[ * - 1 ] );
}

@perrin-primes.sort.join( "\n" ).say;
}
``````

The idea is to populate the `@perrin` array with the sequence, and then put a new prime number inot the `@perrin-primes` only if not already inserted (Perrin numbers can repeat).

## PWC 168 - Task 2

Compute the home prime value of a given input number. A Home Prime number is the prime number obtained out of the sequence of using factors of the input numbers as a compound digit.

``````sub prime-factors( Int \$n where { \$n > 0 } )
{
my \$number = \$n;
my @factors;
return \$n if \$n.is-prime;

for 2 ..^ \$n {
next if ! \$_.is-prime;
next if \$number !%% \$_;
next if \$_ > \$number;

while ( \$number %% \$_ ) {
@factors.push: \$_;
\$number /= \$_;
}

}

return @factors;
}

sub HP( Int \$n where { \$n > 0 } )
{
my \$number = prime-factors( \$n ).join.Int;
return \$number if \$number.is-prime;
return HP( \$number );
}

sub MAIN( Int \$n where { \$n > 1 } = 10 ) {
say HP( \$n );
}

``````

As you can see, the `MAIN` is really simple and it calls only the `HP` function. The `HP` function in turn invokes the `prime-factors` on its input to get the array of prime factors. For example, `prime-factors(10)` gives the array with `2,5`. The `HP` composes the prime factors into a single digit (e.g., `2, 5` becomes `25`) and test if the number is prime, otherwise recursively calls itself.

## PWC 168 - Task 1 in PostgreSQL PL/Perl

Straightforward implementation using an anonymous function to see if a number is prime:

``````CREATE OR REPLACE FUNCTION
RETURNS SETOF bigint
AS \$CODE\$
my ( \$limit ) = @_;
\$limit //= 13;
my @perrin = (3, 0, 2);
my \$seen = {};

my \$is_prime = sub {
my ( \$number ) = @_;

for ( 2 .. \$number - 1 ) {
return undef if \$number % \$_ == 0;
}

return 1;
};

while ( \$limit > 0 ) {
my \$current = \$perrin[ -2 ] + \$perrin[ -3 ];
elog( DEBUG, "Limit \$n and current is \$current" );
push @perrin, \$current;
next if ! \$is_prime->( \$current );
next if \$seen->{ \$current };

# found!
\$seen->{ \$current }++;
return_next( \$current );
\$limit--;
}

return undef;
\$CODE\$
LANGUAGE plperl;

``````

The workflow is the same as in the Raku implementation, but this time I use an hash to catch already seen Perrin prime numbers. Every time a new number is found (and it is tested as prime), it is appended to the result set. Once the requested number of primes is reached (i.e., `\$limit` is zero), the function ends.
It is worth saying that this can take a very long time!

## PWC 168 - Task 2 in PostgreSQL PL/Perl

A straightforward translation of the Raku implementation, where I use two inner subroutines to handle the test for prime-ness and gte the factors:

``````CREATE OR REPLACE FUNCTION
RETURNS int
AS \$CODE\$

my ( \$value ) = @_;

my \$is_prime = sub {
my ( \$number ) = @_;

for ( 2 .. \$number - 1 ) {
return 0 if ( \$number % \$_ == 0 );
}

return 1;
};

my \$prime_factors = sub {
my ( \$number ) = @_;
my @factors;

return if \$is_prime->( \$number );

for ( 2 .. \$number - 1 ) {
next if ! \$is_prime->( \$_ );
next if \$number % \$_ != 0;
next if \$_ > \$number;

while ( ( \$number % \$_ ) == 0 ) {
push @factors, \$_;
\$number /= \$_;
}
}

return @factors;
};

my \$value = join( '', \$prime_factors->( \$value ) );
while ( ! \$is_prime->( \$value ) ) {
\$value = join( '', \$prime_factors->( \$value ) );
}

return \$value;

\$CODE\$
LANGUAGE plperl;
``````

The workhorse of the function is the last four lines: `\$value` is set to the join of its prime factors. Then, I do loop until a new prime number is found using the prime factors and re-join technique.

## PWC 168 - Task 1 in PostgreSQL PL/PgSQL

I implemented a function to test if a number is prime, then the workhorse function to generate the Perrin sequence, last a query to combine the two properties:

``````CREATE OR REPLACE FUNCTION
pwc168.is_prime( n bigint )
RETURNS bool
AS \$CODE\$
DECLARE
i bigint;
BEGIN
FOR i IN 2 .. n - 1 LOOP
IF n % i = 0 THEN
RETURN FALSE;
END IF;
END LOOP;

RETURN TRUE;
END
\$CODE\$
LANGUAGE plpgsql;

CREATE OR REPLACE FUNCTION
pwc168.task1_plpgsql( l bigint default 5000 )
RETURNS SETOF BIGINT
AS \$CODE\$
DECLARE
a bigint;
b bigint;
c bigint;
d bigint;
BEGIN
-- bootstrap
a := 3;
b := 0;
c := 2;

RETURN NEXT a;
RETURN NEXT b;
RETURN NEXT c;

WHILE l > 0 LOOP
d := a + b;
a := b;
b := c;
c := d;

RAISE INFO 'Level % value %', l, c;
RETURN NEXT c;
l := l - 1;
END LOOP;

RETURN;
END
\$CODE\$
LANGUAGE plpgsql;

-- use more than 50 to get all the numbers
-- BUT THIS CAN BE VERY SLOW from 70 and beyond!
SELECT DISTINCT n
WHERE pwc168.is_prime( n )
ORDER BY 1
LIMIT 13;

``````

The last query does all the work: limits the output result set, provides non-repeated numbers (via `DISTINCT` and extract only prime numbers via `is_prime`.

## PWC 168 - Task 2 in PostgreSQL PL/PgSQL

Exploits the same `is_prime()` function of the previous task, then add a `prime_factors()` function to get a result set with the prime factors of the given number.
The task is implemented in the last function, that iterates over the result set of prime factors concatenating them together to a single string `v`, that is then converted into an integer and tested for primeness. If not prime, the same set of oeprations is repeated.

``````CREATE OR REPLACE FUNCTION
RETURNS SETOF int
AS \$CODE\$
DECLARE
i int;
p bool;
BEGIN

FOR i IN 2 .. n - 1 LOOP
p := pwc168.is_prime( i );

IF p AND n % i = 0  THEN
WHILE n % i = 0 LOOP
n := n / i;
RETURN NEXT i;
END LOOP;
END IF;
END LOOP;

RETURN;
END
\$CODE\$
LANGUAGE plpgsql;

/*
testdb=> select * from pwc168.task2_plpgsql( 10 );
---------------
773

*/

CREATE OR REPLACE FUNCTION
pwc168.task2_plpgsql( n int DEFAULT 10 )
RETURNS int
AS \$CODE\$
DECLARE
i int;
v text;
p bool;
BEGIN
v = '0';
FOR i IN SELECT * FROM pwc168.task2_prime_factors( n ) LOOP
v := v || i;
END LOOP;

p := pwc168.is_prime( v::int );

WHILE NOT p LOOP
i := v::int;
v = '0';
FOR i IN SELECT * FROM pwc168.task2_prime_factors( i ) LOOP
v := v || i;
END LOOP;
p := pwc168.is_prime( v::int );
END LOOP;

RETURN v::int;
END
\$CODE\$
LANGUAGE plpgsql;

``````

The article Perl Weekly Challenge 168: prime numbers in many ways! has been posted by Luca Ferrari on June 6, 2022