Examples collection
/ P40 - Goldbach's conjecture.
P40 - Goldbach's conjecture.
Specification
P40 (**) Goldbach's conjecture.
Goldbach's conjecture says that every positive even number greater
than 2 is the sum of two prime numbers. Example: 28 = 5 + 23. It is
one of the most famous facts in number theory that has not been proved
to be correct in the general case. It has been numerically confirmed
up to very large numbers (much larger than we can go with our Prolog
system). Write a predicate to find the two prime numbers that sum up
to a given even integer.
Example
> say ~goldbach 28
5 23
use v6;
subset Even of Int where * %% 2;
sub goldbach (Even $n where * > 2 ) {
for 2..$n/2 -> $k {
if $k.is-prime && ($n-$k).is-prime {
return ($k, $n-$k);
}
}
return; # fail
}
say ~ goldbach $_ for 28, 36, 52, 110, 62710560;
# vim: expandtab shiftwidth=4 ft=perl6
See Also P04-topo.pl
P04 - Find the number of elements in a list.
P06-ajs.pl
P06 - Find out whether a list is a palindrome.
P06-topo.pl
P06 - Find out whether a list is a palindrome.
P08-eric256.pl
P08 - Eliminate consecutive duplicates of list elements.
P08-topo.pl
P08 - Eliminate consecutive duplicates of list elements.
P08-viklund.pl
P08 - Eliminate consecutive duplicates of list elements.
P09-rje.pl
P09 - Pack consecutive duplicates of list elements into sublists.
P09-scottp.pl
P09 - Pack consecutive duplicates of list elements into sublists.
P09-topo.pl
P09 - Pack consecutive duplicate elements of a list into sublists.
P09-unobe.pl
P09 - Pack consecutive duplicates of list elements into sublists.
P13-rhebus.pl
P13 - Run-length encoding of a list (direct solution).
P15-rhebus.pl
P15 - Replicate the elements of a list a given number of times.
P15-topo.pl
P15 - Replicate the elements of a list a given number of times.
P15-unobe.pl
P15 - Replicate the elements of a list a given number of times.
P17-topo.pl
P17 - Split a list into two parts; the length of the first part is given.
P17-unobe.pl
P17 - Split a list into two parts; the length of the first part is given.
P18-topo.pl
P18 - Extract a slice from a list. Indices start at 1.
P21-scottp.pl
P21 - Insert an element at a given position into an array.
P21-topo.pl
P21 - Insert an element at a given position into a list.
P22-scottp.pl
P22 - Create a list containing all integers within a given range.
P22-topo.pl
P22 - Create a list containing all integers within a given range.
P23-topo.pl
P23 - Extract a given number of randomly selected elements from a list.
P24-topo.pl
P24 - Draw N different random numbers from the set 1..M.
P25-topo.pl
P25 - Generate a random permutation of the elements of a list.
P26-topo.pl
P26 - Generate the combinations of k distinct objects chosen from the n elements of a list.
P31-rhebus.pl
P31 - Determine whether a given integer number is prime.
P32-rhebus.pl
P32 - Determine the greatest common divisor of two positive integer
P33-rhebus.pl
P33 - Determine whether two positive integer numbers are coprime.
P35-rhebus.pl
P35 - Determine the prime factors of a given positive integer.
P36-ovid.pl
P36 - Determine the prime factors of a given positive integer (2).
P36-rhebus.pl
P36 - Determine the prime factors of a given positive integer (2).
P37-rhebus.pl
P37 - Calculate Euler's totient function phi(m) (improved).
š¦ / Examples collection
/ P40 - Goldbach's conjecture.
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