Perfect numbers: Difference between revisions

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=={{header|Picat}}==

~~First is the slow perfect1/1 that use the simple~~ divisors/1 function:

===Simple divisors/1 function===

First is the slow <code>perfect1/1</code> that use the simple divisors/1 function:

println(perfect1=[I : I in 1..10_000, perfect1(I)]),

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<pre>perfect1 = [1,6,28,496,8128]</pre>

===Using formula for perfect number candidates===

⚫

The formula for perfect number candidates is: 2^(p-1)*(2^p-1) for prime p. This is used to find some more perfect numbers in reasonable time. <code>perfect2/1</code> is a faster version of checking if a number is perfect.

⚫

The formula for perfect number candidates is: 2^(p-1)*(2^p-1) for prime p. This is used to find some more perfect numbers in reasonable time. perfect2/1 is a faster version of checking if a number is perfect.

println("Using the formula: 2^(p-1)*(2^p-1) for prime p"),

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CPU time 118.039 seconds. Backtracks: 0</pre>

===Using list of the prime generating the perfect numbers===

Now let's cheat a little. At ~~[[Media:~~https://en.wikipedia.org/wiki/Perfect_number]] there is a list of the first 48 primes that generates perfect numbers according to the formula 2^(p-1)*(2^p-1) for prime p.

Now let's cheat a little. At https://en.wikipedia.org/wiki/Perfect_number there is a list of the first 48 primes that generates perfect numbers according to the formula 2^(p-1)*(2^p-1) for prime p.

The perfect numbers are printed only if they has < 80 digits, otherwise the number of digits are shown. The program stops when reaching a number with more than 100 000 digits. (Note: The major time running this program is getting the number of digits.)

ValidP = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607,

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prime 132049: len = 79502

prime 216091: len = 130100</pre>

=={{header|PicoLisp}}==