Ultra useful primes: Difference between revisions

Uses Algol 68G's LONG LONG INT which has programmer-specifiable precision. Uses Miller Rabin primality testing.

{{libheader|ALGOL 68-primes}}

PR precision 650 PR # set number of digits for LONG LOMG INT #

# 2^(2^10) has 308 digits but we need more for #

DO SKIP OD

OD

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<pre>

=={{header|Arturo}}==

 

k: 1

p: (2^2^n) - k

print repeat "-" 10

loop 1..10 'x ->

 

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=={{header|Factor}}==

{{works with|Factor|0.99 2021-06-02}}

 

: useful ( -- list )

[ 2^ 2^ 1 lfrom [ - prime? ] with lfilter car ] lmap-lazy ;

 

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<pre>

=={{header|Go}}==

{{libheader|GMP(Go wrapper)}}

 

import (

fmt.Printf("%2d %d\n", n, a(n))

}

 

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Implementation:

 

ref=. 2x^2^y+1

k=. 1

while. -. 1 p: ref-k do. k=. k+2 end.

 

I don't have the patience to get this little laptop to compute the first 10 such elements, so here I only show the first five:

 

 

=={{header|Julia}}==

 

nearpow2pow2prime(n) = findfirst(k -> isprime(2^(big"2"^n) - k), 1:10000)

 

@time println([nearpow2pow2prime(n) for n in 1:12])

<pre>

[1, 3, 5, 15, 5, 59, 159, 189, 569, 105, 1557, 2549]

 

=={{header|Mathematica}}/{{header|Wolfram Language}}==

FindUltraUsefulPrimeK[n_] := Module[{num, tmp},

num = 2^(2^n);

]

res = FindUltraUsefulPrimeK /@ Range[13];

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<pre>1 1

=={{header|Perl}}==

{{libheader|ntheory}}

use warnings;

use feature 'say';

}

 

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<pre>1 3 5 15 5 59 159 189 569 105 1557 2549 2439</pre>

 

=={{header|Phix}}==

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>

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<pre>

The first 10 take less than a quarter second. 11 through 13, a little under 30 seconds. Drops off a cliff after that.

 

(|$n).map: {

my $p = 1 +< ( 1 +< $_ );

put useful 1..10;

 

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<pre>1 3 5 15 5 59 159 189 569 105

 

=={{header|Sidef}}==

say("----------")

 

var t = 2**(2**n)

printf("%2d %d\n", n, {|k| t - k -> is_prob_prime }.first)

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<pre>

{{libheader|Wren-fmt}}

Manages to find the first ten but takes 84 seconds to do so.

import "./fmt" for Fmt

 

System.print(" n k")

System.print("----------")

 

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{{libheader|Wren-gmp}}

The following takes about 17 seconds to get to n = 13 but 7 minutes 10 seconds to reach n = 14. I didn't bother after that.

import "./fmt" for Fmt

 

System.print(" n k")

System.print("----------")

 

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