Wilson primes of order n: Difference between revisions

=={{header|jq}}==

'''Works with [[jq]]''' (*)

'''Works with gojq, the Go implementation of jq'''

See e.g. [[Erd%C5%91s-primes#jq]] for a suitable implementation of `is_prime` as used here.

(*) The C implementation of jq lacks the precision for handling the case p<11,000

so the output below is based on a run of gojq.

'''Preliminaries'''

<lang jq>def emit_until(cond; stream): label $out | stream | if cond then break $out else . end;

# For 0 <= $n <= ., factorials[$n] is $n !

def factorials:

reduce range(1; .+1) as $n ([1];

.[$n] = $n * .[$n-1]);

def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;

def primes: 2, (range(3; infinite; 2) | select(is_prime));</lang>

'''Wilson primes'''

<lang jq># Input: the limit of $p

def wilson_primes:

def sgn: if . % 2 == 0 then 1 else -1 end;

. as $limit

| factorials as $facts

| " n: Wilson primes\n--------------------",

(range(1;12) as $n

| "\($n|lpad(2)) : \(

[emit_until( . >= $limit; primes)

| select(. as $p

| $p >= $n and

(($facts[$n - 1] * $facts[$p - $n] - ($n|sgn)) % ($p*$p) == 0 )) ])" );

11000 | wilson_primes</lang>

{{out}}

gojq -ncr -f rc-wilson-primes.jq

<pre>

n: Wilson primes

--------------------

1 : [5,13,563]

2 : [2,3,11,107,4931]

3 : [7]

4 : [10429]

5 : [5,7,47]

6 : [11]

7 : [17]

8 : []

9 : [541]

10 : [11,1109]

11 : [17,2713]

</pre>