# Partition an integer X into N primes

``````func prime_partition(num, parts) {

if (parts == 1) {
return (num.is_prime ? [num] : [])
}

num.primes.combinations(parts, {|*c|
return c if (c.sum == num)
})

return []
}

var tests = [
[   18, 2], [   19, 3], [   20,  4],
[99807, 1], [99809, 1], [ 2017, 24],
[22699, 1], [22699, 2], [22699,  3],
[22699, 4], [40355, 3],
]

for num,parts (tests) {
say ("Partition %5d into %2d prime piece" % (num, parts),
parts == 1 ? ':  ' : 's: ', prime_partition(num, parts).join('+') || 'not possible')
}
``````

#### Output:

``````Partition    18 into  2 prime pieces: 5+13
Partition    19 into  3 prime pieces: 3+5+11
Partition    20 into  4 prime pieces: not possible
Partition 99807 into  1 prime piece:  not possible
Partition 99809 into  1 prime piece:  99809
Partition  2017 into 24 prime pieces: 2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+97+1129
Partition 22699 into  1 prime piece:  22699
Partition 22699 into  2 prime pieces: 2+22697
Partition 22699 into  3 prime pieces: 3+5+22691
Partition 22699 into  4 prime pieces: 2+3+43+22651
Partition 40355 into  3 prime pieces: 3+139+40213
``````