How to resolve the algorithm Goldbach's comet step by step in the jq programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Goldbach's comet step by step in the jq programming language
Table of Contents
Problem Statement
Goldbach's comet is the name given to a plot of the function g(E), the so-called Goldbach function. The Goldbach function is studied in relation to Goldbach's conjecture. The function g(E) is defined for all even integers E>2 to be the number of different ways in which E can be expressed as the sum of two primes.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Goldbach's comet step by step in the jq programming language
Source code in the jq programming language
def count(s): reduce s as $_ (0; .+1);
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else
($n | sqrt) as $rt
| 23
| until( . > $rt or ($n % . == 0); .+2)
| . > $rt
end;
# emit nothing if . is odd
def G:
select(. % 2 == 0)
| count( range(2; (./2)+1) as $i
| select(($i|is_prime) and ((.-$i)|is_prime)) );
def task1:
"The first 100 G numbers:",
([range(4; 203; 2) | G] | nwise(10) | map(lpad(4)) | join(" "));
def task($n):
$n, 4, 22
|"G(\(.)): \(G)";
task1, "", task(1000000)
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