Penta-power prime seeds: Difference between revisions
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{{
Generate the sequence of penta-power prime seeds: positive integers '''n''' such that:
Line 495:
9 million is the 71st: 9,100,671
10 million is the 72nd: 10,347,035
</pre>
=={{header|J}}==
<syntaxhighlight lang=j> ps=. ] #~ 1 p: 1 + ^~ + ]
_10 ]\ 4x ps 3x ps 2 ps 1 ps 0 ps i. 1520000
1 5 69 1665 2129 25739 29631 62321 77685 80535
82655 126489 207285 211091 234359 256719 366675 407945 414099 628859
644399 770531 781109 782781 923405 1121189 1158975 1483691 1490475 1512321</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.math.BigInteger;
public final class PentaPowerPrimeSeeds {
public static void main(String[] args) {
System.out.println("The first 30 penta-power prime seeds:");
int index = 0;
int number = 1;
boolean searching = true;
while ( searching ) {
if ( isPentaPowerPrimeSeed(number) ) {
index += 1;
if ( index <= 30 ) {
System.out.print(String.format("%7d%s", number, ( index % 6 == 0 ? "\n" : " " )));
} else if ( number > 10_000_000 ) {
System.out.println();
System.out.println("The first penta-power prime seed greater than 10,000,000 is "
+ number + " at index " + index);
searching = false;
}
}
number += 2;
}
}
private static boolean isPentaPowerPrimeSeed(long number) {
BigInteger p = BigInteger.ONE;
BigInteger nPlus1 = BigInteger.valueOf(number + 1);
for ( int i = 0; i <= 4; i++ ) {
if ( ! p.add(nPlus1).isProbablePrime(15) ) {
return false;
}
p = p.multiply(BigInteger.valueOf(number));
}
return true;
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first 30 penta-power prime seeds:
1 5 69 1665 2129 25739
29631 62321 77685 80535 82655 126489
207285 211091 234359 256719 366675 407945
414099 628859 644399 770531 781109 782781
923405 1121189 1158975 1483691 1490475 1512321
The first penta-power prime seed greater than 10,000,000 is 10347035 at index 72
</pre>
=={{header|Julia}}==
This solution uses Primes to determine primality.
<syntaxhighlight lang=julia>
using Primes, Printf
function ispenta(n)
all(0:4) do i
isprime(n^i + n + 1)
end
end
function firstpenta(m, T=BigInt)
nums = Iterators.countfrom(T(1))
pentas = Iterators.filter(ispenta, nums)
firstn = Iterators.take(pentas, m)
return collect(firstn)
end
function table_display(nums, num_columns)
num_elements = length(nums)
num_rows = div(num_elements, num_columns)
remaining_elements = num_elements % num_columns
for i in 1:num_rows
for j in 1:num_columns
index = (i - 1) * num_columns + j
print(nums[index], "\t")
end
println()
end
for i in 1:remaining_elements
index = num_rows * num_columns + i
print(nums[index], "\t")
end
println()
end
function stretch_penta(goal, T=BigInt)
nums = Iterators.countfrom(T(1))
pentas = Iterators.filter(ispenta, nums)
firstn = Iterators.takewhile(<=(goal), pentas)
return collect(firstn)
end
function run_rosetta()
fp = firstpenta(30)
println("First 30 Penta power prime seeds:")
table_display(fp, 10)
sp = stretch_penta(20000000)
milestones = 1000000 .* (1:10)
for milestone in milestones
index = findfirst(>(milestone), sp)
@printf "First element over %9i: %9i, index:%4i\n" milestone sp[index] index
end
end
if abspath(PROGRAM_FILE) == @__FILE__
run_rosetta()
end
</syntaxhighlight>
<pre>
First 30 Penta power prime seeds:
1 5 69 1665 2129 25739 29631 62321 77685 80535
82655 126489 207285 211091 234359 256719 366675 407945 414099 628859
644399 770531 781109 782781 923405 1121189 1158975 1483691 1490475 1512321
First element over 1000000: 1121189, index: 26
First element over 2000000: 2066079, index: 39
First element over 3000000: 3127011, index: 47
First element over 4000000: 4059525, index: 51
First element over 5000000: 5279175, index: 59
First element over 6000000: 6320601, index: 63
First element over 7000000: 7291361, index: 68
First element over 8000000: 8334915, index: 69
First element over 9000000: 9100671, index: 71
First element over 10000000: 10347035, index: 72
</pre>
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=={{header|Nim}}==
{{libheader|Nim-Integers}}
<syntaxhighlight lang=Nim>import std/[strformat, strutils]
import integers
Line 797 ⟶ 942:
nine million is the 71st: 9,100,671
ten million is the 72nd: 10,347,035</pre>
=={{header|RPL}}==
Directly adapted from [[Quad-power prime seeds#RPL|Quad-power prime seeds]], but faster since seeds must be odd to get <code>n<sup>0</sup> + n + 1</code> primality. However, needs to be run on an emulator to get the result in around half an hour.
{{works with|HP|49}}
« { } 1
'''WHILE''' OVER SIZE 30 < '''REPEAT'''
1 SF
0 4 '''FOR''' j
DUP j ^ OVER + 1 +
'''IF''' ISPRIME? NOT '''THEN''' 1 CF 4 'j' STO '''END'''
'''NEXT'''
'''IF''' 1 FS? '''THEN''' SWAP OVER + SWAP '''END '''
2 +
'''END'''
» '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1:{1 5 69 1665 2129 25739 29631 62321 77685 80535 82655 126489 207285 211091 234359 256719 366675 407945 414099 628859 644399 770531 781109 782781 923405 1121189 1158975 1483691 1490475 1512321}
</pre>
=={{header|Ruby}}==
Line 812 ⟶ 976:
644399 770531 781109 782781 923405 1121189 1158975 1483691 1490475 1512321
</pre>
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
import scala.annotation.tailrec
import java.math.BigInteger
object PentaPowerPrimeSeeds extends App {
println("The first 30 penta-power prime seeds:")
val first30 = Stream.from(1, 2).filter(isPentaPowerPrimeSeed).take(30)
first30.zipWithIndex.foreach { case (seed, index) =>
print(f"$seed%7d${if ((index + 1) % 6 == 0) "\n" else " "}")
}
val firstAbove10M = Stream.from(1, 2).filter(isPentaPowerPrimeSeed).find(_ > 10000000)
firstAbove10M match {
case Some(seed) => println(s"\nThe first penta-power prime seed greater than 10,000,000 is $seed")
case None => println("No penta-power prime seed greater than 10,000,000 was found.")
}
def isPentaPowerPrimeSeed(number: Int): Boolean = {
val bigIntNumber = BigInteger.valueOf(number)
val bigIntNumberPlusOne = bigIntNumber.add(BigInteger.ONE)
(0 to 4).forall { i =>
bigIntNumber.pow(i).add(bigIntNumberPlusOne).isProbablePrime(15)
}
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 30 penta-power prime seeds:
1 5 69 1665 2129 25739
29631 62321 77685 80535 82655 126489
207285 211091 234359 256719 366675 407945
414099 628859 644399 770531 781109 782781
923405 1121189 1158975 1483691 1490475 1512321
The first penta-power prime seed greater than 10,000,000 is 10347035
</pre>
=={{header|Wren}}==
{{libheader|Wren-gmp}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
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