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{{task|Prime Numbers}} A [[wp:Pernicious number|pernicious number]] is a positive integer whose [[population count]] is a prime.
The population count is the number of ''ones'' in the binary representation of a non-negative integer.
;Example '''22''' (which is '''10110''' in binary) has a population count of '''3''', which is prime, and therefore '''22''' is a pernicious number.
;Task
- display the first '''25''' pernicious numbers (in decimal).
- display all pernicious numbers between '''888,888,877''' and '''888,888,888''' (inclusive).
- display each list of integers on one line (which may or may not include a title).
;See also
- Sequence [[oeis:A052294|A052294 pernicious numbers]] on The On-Line Encyclopedia of Integer Sequences.
- Rosetta Code entry [[Population_count|population count, evil numbers, odious numbers]].
360 Assembly
{{trans|FORTRAN}} For maximum compatibility, this program uses only the basic instruction set (S/360) with 2 ASSIST macros (XDECO,XPRNT).
* Pernicious numbers 04/05/2016
PERNIC CSECT
USING PERNIC,R13 base register and savearea pointer
SAVEAREA B STM-SAVEAREA(R15)
DC 17F'0'
STM STM R14,R12,12(R13) save registers
ST R13,4(R15) link backward SA
ST R15,8(R13) link forward SA
LR R13,R15 establish addressability
SR R7,R7 n=0
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi
LA R6,1 i=1
LOOPI1 C R7,=F'25' do i=1 while(n<25)
BNL ELOOPI1
LR R1,R6 i
BAL R14,POPCOUNT
LR R1,R0 popcount(i)
BAL R14,ISPRIME
C R0,=F'1' if isprime(popcount(i))=1
BNE NOTPRIM1
XDECO R6,XDEC edit i
MVC 0(3,R10),XDEC+9 output i format I3
LA R10,3(R10) pgi=pgi+3
LA R7,1(R7) n=n+1
NOTPRIM1 LA R6,1(R6) i=i+1
B LOOPI1
ELOOPI1 XPRNT PG,80 print buffer
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi
L R6,=F'888888877' i=888888877
LOOPI2 C R6,=F'888888888' do i to 888888888
BH ELOOPI2
LR R1,R6 i
BAL R14,POPCOUNT
LR R1,R0 popcount(i)
BAL R14,ISPRIME
C R0,=F'1' if isprime(popcount(i))=1
BNE NOTPRIM2
XDECO R6,XDEC edit i
MVC 0(10,R10),XDEC+2 output i format I10
LA R10,10(R10) pgi=pgi+10
NOTPRIM2 LA R6,1(R6) i=i+1
B LOOPI2
ELOOPI2 XPRNT PG,80 print buffer
L R13,4(0,R13) restore savearea pointer
LM R14,R12,12(R13) restore registers
XR R15,R15 return code = 0
BR R14 -------------- end main
POPCOUNT CNOP 0,4 -------------- popcount(xx) [R8,R11]
ST R14,POPCOUSA save return address
ST R1,XX store argument
SR R11,R11 rr=0
SR R8,R8 ii=0
LOOPII C R8,=F'31' do ii=0 to 31
BH ELOOPII
L R1,XX xx
LR R2,R8 ii
BAL R14,BTEST
C R0,=F'1' if btest(xx,ii)=1
BNE NOTBTEST
LA R11,1(R11) rr=rr+1
NOTBTEST LA R8,1(R8) ii=ii+1
B LOOPII
ELOOPII LR R0,R11 return(rr)
L R14,POPCOUSA
BR R14 -------------- end popcount
ISPRIME CNOP 0,4 -------------- isprime(number) [R9]
ST R14,ISPRIMSA save return address
ST R1,NUMBER store argument
C R1,=F'2' if number=2
BNE ELSE1
MVC ISPRIMEX,=F'1' isprimex=1
B ELOOPJJ
ELSE1 L R1,NUMBER
C R1,=F'2' if number<2
BL EVEN
L R4,NUMBER
SRDA R4,32
D R4,=F'2' mod(number,2)
C R4,=F'0' if mod(number,2)=0
BNE ELSE2
EVEN MVC ISPRIMEX,=F'0' isprimex=0
B ELOOPJJ
ELSE2 MVC ISPRIMEX,=F'1' isprimex=1
LA R9,3 jj=3
LOOPJJ LR R5,R9 jj
MR R4,R9 jj*jj
C R5,NUMBER do jj=3 by 1 while jj*jj<=number
BH ELOOPJJ
L R4,NUMBER
SRDA R4,32
DR R4,R9 mod(number,jj)
LTR R4,R4 if mod(number,jj)=0
BNZ ITERJJ
MVC ISPRIMEX,=F'0' isprimex=0
L R0,ISPRIMEX return(isprimex)
B ISPRIMRT
ITERJJ LA R9,1(R9) jj=jj+1
B LOOPJJ
ELOOPJJ L R0,ISPRIMEX return(isprimex)
ISPRIMRT L R14,ISPRIMSA
BR R14 -------------- end isprime
BTEST CNOP 0,4 -------------- btest(word,n) [R0:R3]
LA R0,1 ok=1; return(1) if word(n)='1'b
LR R3,R2 i=n
LOOPB LTR R3,R3 if i=0
BZ ELOOPB
SRL R1,1 Shift Right Logical
BCTR R3,0 i=i-1
B LOOPB
ELOOPB STC R1,BTESTX x=word
TM BTESTX,B'00000001' if bit(word,n)='1'b
BO BTESTRET
LA R0,0 ok=0; return(0) if word(n)='0'b
BTESTRET BR R14 -------------- end btest
XX DS F paramter of popcount
NUMBER DS F paramter of isprime
ISPRIMEX DS F return value of isprime
BTESTX DS X byte to see in btest
POPCOUSA DS A return address of popcount
ISPRIMSA DS A return address of isprime
PG DS CL80 buffer
XDEC DS CL12 edit zone
YREGS
END PERNIC
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Ada
Uses package Population_Count from [[Population count#Ada]].
with Ada.Text_IO, Population_Count; use Population_Count;
procedure Pernicious is
Prime: array(0 .. 64) of Boolean;
-- we are using 64-bit numbers, so the population count is between 0 and 64
X: Num; use type Num;
Cnt: Positive;
begin
-- initialize array Prime; Prime(I) must be true if and only if I is a prime
Prime := (0 => False, 1 => False, others => True);
for I in 2 .. 8 loop
if Prime(I) then
Cnt := I + I;
while Cnt <= 64 loop
Prime(Cnt) := False;
Cnt := Cnt + I;
end loop;
end if;
end loop;
-- print first 25 pernicious numbers
X := 1;
for I in 1 .. 25 loop
while not Prime(Pop_Count(X)) loop
X := X + 1;
end loop;
Ada.Text_IO.Put(Num'Image(X));
X := X + 1;
end loop;
Ada.Text_IO.New_Line;
-- print pernicious numbers between 888_888_877 and 888_888_888 (inclusive)
for Y in Num(888_888_877) .. 888_888_888 loop
if Prime(Pop_Count(Y)) then
Ada.Text_IO.Put(Num'Image(Y));
end if;
end loop;
Ada.Text_IO.New_Line;
end;
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
A small modification allows to count all the pernicious numbers between 1 and 2**32 in about 32 seconds:
Counter: Natural;
begin
-- initialize array Prime; Prime(I) must be true if and only if I is a prime
...
Counter := 0;
-- count p. numbers below 2**32
for Y in Num(2) .. 2**32 loop
if Prime(Pop_Count(Y)) then
Counter := Counter + 1;
end if;
end loop;
Ada.Text_IO.Put_Line(Natural'Image(Counter));
end Count_Pernicious;
{{out}}
> time ./count_pernicious
1421120880
real 0m33.375s
user 0m33.372s
sys 0m0.000s
ALGOL 68
# calculate various pernicious numbers #
# returns the population (number of bits on) of the non-negative integer n #
PROC population = ( INT n )INT:
BEGIN
INT number := n;
INT result := 0;
WHILE number > 0 DO
IF ODD number THEN result +:= 1 FI;
number OVERAB 2
OD;
result
END # population # ;
# as we are dealing with 32 bit numbers, the maximum possible population is 32 #
# so we only need a table of whether the integers 0 : 32 are prime or not #
# we use the sieve of Eratosthenes... #
INT max number = 32;
[ 0 : max number ]BOOL is prime;
is prime[ 0 ] := FALSE;
is prime[ 1 ] := FALSE;
FOR i FROM 2 TO max number DO is prime[ i ] := TRUE OD;
FOR i FROM 2 TO ENTIER sqrt( max number ) DO
IF is prime[ i ] THEN FOR p FROM i * i BY i TO max number DO is prime[ p ] := FALSE OD FI
OD;
# returns TRUE if n is pernicious, FALSE otherwise #
PROC is pernicious = ( INT n )BOOL: is prime[ population( n ) ];
# find the first 25 pernicious numbers, 0 and 1 are not pernicious #
INT pernicious count := 0;
FOR i FROM 2 WHILE pernicious count < 25 DO
IF is pernicious( i ) THEN
# found a pernicious number #
print( ( whole( i, 0 ), " " ) );
pernicious count +:= 1
FI
OD;
print( ( newline ) );
# find the pernicious numbers between 888 888 877 and 888 888 888 #
FOR i FROM 888 888 877 TO 888 888 888 DO
IF is pernicious( i ) THEN
print( ( whole( i, 0 ), " " ) )
FI
OD;
print( ( newline ) )
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
AutoHotkey
{{works with|AutoHotkey 1.1}}
c := 0
while c < 25
if IsPern(A_Index)
Out1 .= A_Index " ", c++
Loop, 12
if IsPern(n := 888888876 + A_Index)
Out2 .= n " "
MsgBox, % Out1 "`n" Out2
IsPern(x) { ;https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
static p := {2:1, 3:1, 5:1, 7:1, 11:1, 13:1, 17:1, 19:1, 23:1, 29:1, 31:1, 37:1, 41:1, 43:1, 47:1, 53:1, 59:1, 61:1}
x -= (x >> 1) & 0x5555555555555555
, x := (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
, x := (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f
return p[(x * 0x0101010101010101) >> 56]
}
{{Out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
AWK
# syntax: GAWK -f PERNICIOUS_NUMBERS.AWK
BEGIN {
pernicious(25)
pernicious(888888877,888888888)
exit(0)
}
function pernicious(x,y, count,n) {
if (y == "") { # print first X pernicious numbers
while (count < x) {
if (is_prime(pop_count(++n)) == 1) {
printf("%d ",n)
count++
}
}
}
else { # print pernicious numbers in X-Y range
for (n=x; n<=y; n++) {
if (is_prime(pop_count(n)) == 1) {
printf("%d ",n)
}
}
}
print("")
}
function dec2bin(n, str) {
while (n) {
if (n%2 == 0) {
str = "0" str
}
else {
str = "1" str
}
n = int(n/2)
}
if (str == "") {
str = "0"
}
return(str)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
function pop_count(n) {
n = dec2bin(n)
return gsub(/1/,"&",n)
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Befunge
Based more or less on the '''[[Pernicious_numbers#C|C]]''' implementation, although we don't bother supporting ''n'' = 0, so we can use a smaller prime bit set that fits inside a signed 32 bit int (most Befunge implementations wouldn't support anything higher).
Also note that the extra spaces in the output are just to ensure it's readable on buggy interpreters that don't include a space after numeric output. They can easily be removed by replacing the comma on line 3 with a dollar.
55*00p1>:"ZOA>/"***7-*>\:2>/\v
>8**`!#^_$@\<(^v^)>/#2^#\<2 2
^+**"X^yYo":+1<_:.48*,00v|: <%
v".D}Tx"$,+55_^#!p00:-1g<v |<
> * + : * * + ^^ ! % 2 $ <^ <^
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
C
#include <stdio.h>
typedef unsigned uint;
uint is_pern(uint n)
{
uint c = 2693408940u; // int with all prime-th bits set
while (n) c >>= 1, n &= (n - 1); // take out lowerest set bit one by one
return c & 1;
}
int main(void)
{
uint i, c;
for (i = c = 0; c < 25; i++)
if (is_pern(i))
printf("%u ", i), ++c;
putchar('\n');
for (i = 888888877u; i <= 888888888u; i++)
if (is_pern(i))
printf("%u ", i);
putchar('\n');
return 0;
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
C++
#include <iostream>
#include <algorithm>
#include <bitset>
using namespace std;
class pernNumber
{
public:
void displayFirst( unsigned cnt )
{
unsigned pn = 3;
while( cnt )
{
if( isPernNumber( pn ) )
{
cout << pn << " "; cnt--;
}
pn++;
}
}
void displayFromTo( unsigned a, unsigned b )
{
for( unsigned p = a; p <= b; p++ )
if( isPernNumber( p ) )
cout << p << " ";
}
private:
bool isPernNumber( unsigned p )
{
string bin = bitset<64>( p ).to_string();
unsigned c = count( bin.begin(), bin.end(), '1' );
return isPrime( c );
}
bool isPrime( unsigned p )
{
if( p == 2 ) return true;
if( p < 2 || !( p % 2 ) ) return false;
for( unsigned x = 3; ( x * x ) <= p; x += 2 )
if( !( p % x ) ) return false;
return true;
}
};
int main( int argc, char* argv[] )
{
pernNumber p;
p.displayFirst( 25 ); cout << endl;
p.displayFromTo( 888888877, 888888888 ); cout << endl;
return 0;
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
C#
using System;
using System.Linq;
namespace PerniciousNumbers
{
class Program
{
public static int PopulationCount(long n)
{
int cnt = 0;
do
{
if ((n & 1) != 0)
{
cnt++;
}
} while ((n >>= 1) > 0);
return cnt;
}
public static bool isPrime(int x)
{
if (x <= 2 || (x & 1) == 0)
{
return x == 2;
}
var limit = Math.Sqrt(x);
for (int i = 3; i <= limit; i += 2)
{
if (x % i == 0)
{
return false;
}
}
return true;
}
private static IEnumerable<int> Pernicious(int start, int count, int take)
{
return Enumerable.Range(start, count).Where(n => isPrime(PopulationCount(n))).Take(take);
}
static void Main(string[] args)
{
foreach (var n in Pernicious(0, int.MaxValue, 25))
{
Console.Write("{0} ", n);
}
Console.WriteLine();
foreach (var n in Pernicious(888888877, 11, 11))
{
Console.Write("{0} ", n);
}
Console.ReadKey();
}
}
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Clojure
(defn counting-numbers
([] (counting-numbers 1))
([n] (lazy-seq (cons n (counting-numbers (inc n))))))
(defn divisors [n] (filter #(zero? (mod n %)) (range 1 (inc n))))
(defn prime? [n] (= (divisors n) (list 1 n)))
(defn pernicious? [n]
(prime? (count (filter #(= % \1) (Integer/toString n 2)))))
(println (take 25 (filter pernicious? (counting-numbers))))
(println (filter pernicious? (range 888888877 888888889)))
{{Output}}
(3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36)
(888888877 888888878 888888880 888888883 888888885 888888886)
Common Lisp
Using primep from [[Primality_by_trial_division#Common_Lisp|Primality by trial division]] task.
(format T "~{~a ~}~%"
(loop for n = 1 then (1+ n)
when (primep (logcount n))
collect n into numbers
when (= (length numbers) 25)
return numbers))
(format T "~{~a ~}~%"
(loop for n from 888888877 to 888888888
when (primep (logcount n))
collect n))
{{Out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
D
void main() {
import std.stdio, std.algorithm, std.range, core.bitop;
immutable pernicious = (in uint n) => (2 ^^ n.popcnt) & 0xA08A28AC;
uint.max.iota.filter!pernicious.take(25).writeln;
iota(888_888_877, 888_888_889).filter!pernicious.writeln;
}
{{out}}
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Where 0xA08A28AC == 0b_1010_0000__1000_1010__0010_1000__1010_1100, that is a bit set equivalent to the prime numbers [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] of the range (0, 31].
This high-level code is fast enough to allow to count all the 1_421_120_880 Pernicious numbers in the unsigned 32 bit range in less than 48 seconds with this line:
uint.max.iota.filter!pernicious.walkLength.writeln;
EchoLisp
(lib 'sequences)
(define (pernicious? n) (prime? (bit-count n)))
(define pernicious (filter pernicious? [1 .. ]))
(take pernicious 25)
→ (3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36)
(take (filter pernicious? [888888877 .. 888888889]) #:all)
→ (888888877 888888878 888888880 888888883 888888885 888888886)
Eiffel
class
APPLICATION
create
make
feature
make
-- Test of is_pernicious_number.
local
test: LINKED_LIST [INTEGER]
i: INTEGER
do
create test.make
from
i := 1
until
test.count = 25
loop
if is_pernicious_number (i) then
test.extend (i)
end
i := i + 1
end
across
test as t
loop
io.put_string (t.item.out + " ")
end
io.new_line
across
888888877 |..| 888888888 as c
loop
if is_pernicious_number (c.item) then
io.put_string (c.item.out + " ")
end
end
end
is_pernicious_number (n: INTEGER): BOOLEAN
-- Is 'n' a pernicious_number?
require
positiv_input: n > 0
do
Result := is_prime (count_population (n))
end
feature{NONE}
count_population (n: INTEGER): INTEGER
-- Population count of 'n'.
require
positiv_input: n > 0
local
j: INTEGER
math: DOUBLE_MATH
do
create math
j := math.log_2 (n).ceiling + 1
across
0 |..| j as c
loop
if n.bit_test (c.item) then
Result := Result + 1
end
end
end
is_prime (n: INTEGER): BOOLEAN
--Is 'n' a prime number?
require
positiv_input: n > 0
local
i: INTEGER
max: REAL_64
math: DOUBLE_MATH
do
create math
if n = 2 then
Result := True
elseif n <= 1 or n \\ 2 = 0 then
Result := False
else
Result := True
max := math.sqrt (n)
from
i := 3
until
i > max
loop
if n \\ i = 0 then
Result := False
end
i := i + 2
end
end
end
end
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Elixir
defmodule SieveofEratosthenes do
def init(lim) do
find_primes(2,lim,(2..lim))
end
def find_primes(count,lim,nums) when (count * count) > lim do
nums
end
def find_primes(count,lim,nums) when (count * count) <= lim do
e = Enum.reject(nums,&(rem(&1,count) == 0 and &1 > count))
find_primes(count+1,lim,e)
end
end
defmodule PerniciousNumbers do
def take(n) do
primes = SieveofEratosthenes.init(100)
Stream.iterate(1,&(&1+1))
|> Stream.filter(&(pernicious?(&1,primes)))
|> Enum.take(n)
|> IO.inspect
end
def between(a..b) do
primes = SieveofEratosthenes.init(100)
a..b
|> Stream.filter(&(pernicious?(&1,primes)))
|> Enum.to_list
|> IO.inspect
end
def ones(num) do
num
|> Integer.to_string(2)
|> String.codepoints
|> Enum.count(fn n -> n == "1" end)
end
def pernicious?(n,primes), do: Enum.member?(primes,ones(n))
end
PerniciousNumbers.take(25)
PerniciousNumbers.between(888_888_877..888_888_888)
{{out}} [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
=={{header|F#|F sharp}}==
open System
//Taken from https://gist.github.com/rmunn/bc49d32a586cdfa5bcab1c3e7b45d7ac
let bitcount (n : int) =
let count2 = n - ((n >>> 1) &&& 0x55555555)
let count4 = (count2 &&& 0x33333333) + ((count2 >>> 2) &&& 0x33333333)
let count8 = (count4 + (count4 >>> 4)) &&& 0x0f0f0f0f
(count8 * 0x01010101) >>> 24
//Modified from other examples to actually state the 1 is not prime
let isPrime n =
if n < 2 then
false
else
let sqrtn n = int <| sqrt (float n)
seq { 2 .. sqrtn n } |> Seq.exists(fun i -> n % i = 0) |> not
[<EntryPoint>]
let main _ =
[1 .. 100] |> Seq.filter (bitcount >> isPrime) |> Seq.take 25 |> Seq.toList |> printfn "%A"
[888888877 .. 888888888] |> Seq.filter (bitcount >> isPrime) |> Seq.toList |> printfn "%A"
0 // return an integer exit code
{{out}}
[3; 5; 6; 7; 9; 10; 11; 12; 13; 14; 17; 18; 19; 20; 21; 22; 24; 25; 26; 28; 31; 33; 34; 35; 36]
[888888877; 888888878; 888888880; 888888883; 888888885; 888888886]
Factor
USING: lists lists.lazy math.bits math.primes math.ranges ;
: pernicious? ( n -- ? ) make-bits [ t = ] count prime? ;
0 lfrom [ pernicious? ] lfilter 25 swap ltake list>array . ! print first 25 pernicious numbers
888,888,877 888,888,888 [a,b] [ pernicious? ] filter . ! print pernicious numbers in range
{{out}}
{ 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 }
{ 888888877 888888878 888888880 888888883 888888885 888888886 }
Fortran
{{works with|Fortran|95 and later}}
program pernicious
implicit none
integer :: i, n
i = 1
n = 0
do
if(isprime(popcnt(i))) then
write(*, "(i0, 1x)", advance = "no") i
n = n + 1
if(n == 25) exit
end if
i = i + 1
end do
write(*,*)
do i = 888888877, 888888888
if(isprime(popcnt(i))) write(*, "(i0, 1x)", advance = "no") i
end do
contains
function popcnt(x)
integer :: popcnt
integer, intent(in) :: x
integer :: i
popcnt = 0
do i = 0, 31
if(btest(x, i)) popcnt = popcnt + 1
end do
end function
function isprime(number)
logical :: isprime
integer, intent(in) :: number
integer :: i
if(number == 2) then
isprime = .true.
else if(number < 2 .or. mod(number,2) == 0) then
isprime = .false.
else
isprime = .true.
do i = 3, int(sqrt(real(number))), 2
if(mod(number,i) == 0) then
isprime = .false.
exit
end if
end do
end if
end function
end program
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
FreeBASIC
{{trans|PureBasic}}
' FreeBASIC v1.05.0 win64
Function SumBinaryDigits(number As Integer) As Integer
If number < 0 Then number = -number ' convert negative numbers to positive
Var sum = 0
While number > 0
sum += number Mod 2
number \= 2
Wend
Return sum
End Function
Function IsPrime(number As Integer) As Boolean
If number <= 1 Then
Return false
ElseIf number <= 3 Then
Return true
ElseIf number Mod 2 = 0 OrElse number Mod 3 = 0 Then
Return false
End If
Var i = 5
While i * i <= number
If number Mod i = 0 OrElse number Mod (i + 2) = 0 Then
Return false
End If
i += 6
Wend
Return True
End Function
Function IsPernicious(number As Integer) As Boolean
Dim popCount As Integer = SumBinaryDigits(number)
Return IsPrime(popCount)
End Function
Dim As Integer n = 1, count = 0
Print "The following are the first 25 pernicious numbers :"
Print
Do
If IsPernicious(n) Then
Print Using "###"; n;
count += 1
End If
n += 1
Loop Until count = 25
Print : Print
Print "The pernicious numbers between 888,888,877 and 888,888,888 inclusive are :"
Print
For n = 888888877 To 888888888
If IsPernicious(n) Then Print Using "##########"; n;
Next
Print : Print
Print "Press any key to exit the program"
Sleep
End
{{out}}
The following are the first 25 pernicious numbers :
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
The pernicious numbers between 888,888,877 and 888,888,888 inclusive are :
888888877 888888878 888888880 888888883 888888885 888888886
Go
package main
import "fmt"
func pernicious(w uint32) bool {
const (
ff = 1<<32 - 1
mask1 = ff / 3
mask3 = ff / 5
maskf = ff / 17
maskp = ff / 255
)
w -= w >> 1 & mask1
w = w&mask3 + w>>2&mask3
w = (w + w>>4) & maskf
return 0xa08a28ac>>(w*maskp>>24)&1 != 0
}
func main() {
for i, n := 0, uint32(1); i < 25; n++ {
if pernicious(n) {
fmt.Printf("%d ", n)
i++
}
}
fmt.Println()
for n := uint32(888888877); n <= 888888888; n++ {
if pernicious(n) {
fmt.Printf("%d ", n)
}
}
fmt.Println()
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Groovy
class example{
static void main(String[] args){
def n=0;
def counter=0;
while(counter<25){
if(print(n)){
counter++;}
n=n+1;
}
println();
def x=888888877;
while(x<888888889){
print(x);
x++;}
}
static def print(def a){
def primes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47];
def c=Integer.toBinaryString(a);
String d=c;
def e=0;
for(i in d){if(i=='1'){e++;}}
if(e in primes){printf(a+" ");return 1;}
}
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Haskell
module Pernicious
where
isPernicious :: Integer -> Bool
isPernicious num = isPrime $ toInteger $ length $ filter ( == 1 ) $ toBinary num
isPrime :: Integer -> Bool
isPrime number = divisors number == [1, number]
where
divisors :: Integer -> [Integer]
divisors number = [ m | m <- [1 .. number] , number `mod` m == 0 ]
toBinary :: Integer -> [Integer]
toBinary num = reverse $ map ( `mod` 2 ) ( takeWhile ( /= 0 ) $ iterate ( `div` 2 ) num )
solution1 = take 25 $ filter isPernicious [1 ..]
solution2 = filter isPernicious [888888877 .. 888888888]
{{output}}
[3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36]
[888888877,888888878,888888880,888888883,888888885,888888886]
Or, in a point-free and applicative style, using unfoldr for the population count:
import Data.Numbers.Primes (isPrime)
import Data.List (unfoldr)
import Data.Tuple (swap)
import Data.Bool (bool)
isPernicious :: Int -> Bool
isPernicious = isPrime . popCount
popCount :: Int -> Int
popCount =
sum . unfoldr ((flip bool Nothing . Just . swap . flip quotRem 2) <*> (0 ==))
main :: IO ()
main =
mapM_
print
[ take 25 $ filter isPernicious [1 ..]
, filter isPernicious [888888877 .. 888888888]
]
{{Out}}
[3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36]
[888888877,888888878,888888880,888888883,888888885,888888886]
=={{header|Icon}} and {{header|Unicon}}==
Works in both languages:
link "factors"
procedure main(A)
every writes((pernicious(seq())\25||" ") | "\n")
every writes((pernicious(888888877 to 888888888)||" ") | "\n")
end
procedure pernicious(n)
return (isprime(c1bits(n)),n)
end
procedure c1bits(n)
c := 0
while n > 0 do c +:= 1(n%2, n/:=2)
return c
end
{{Out}}
->pn
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
->
J
Implementation:
ispernicious=: 1 p: +/"1@#:
Task (thru taken from the [[Loops/Downward_for#J|Loops/Downward for]] task).:
25{.I.ispernicious i.100
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
thru=: <. + i.@(+*)@-~
888888877 + I. ispernicious 888888877 thru 888888888
888888877 888888878 888888880 888888883 888888885 888888886
Java
public class Pernicious{
//very simple isPrime since x will be <= Long.SIZE
public static boolean isPrime(int x){
if(x < 2) return false;
for(int i = 2; i < x; i++){
if(x % i == 0) return false;
}
return true;
}
public static int popCount(long x){
return Long.bitCount(x);
}
public static void main(String[] args){
for(long i = 1, n = 0; n < 25; i++){
if(isPrime(popCount(i))){
System.out.print(i + " ");
n++;
}
}
System.out.println();
for(long i = 888888877; i <= 888888888; i++){
if(isPrime(popCount(i))) System.out.print(i + " ");
}
}
}
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
jq
{{works with|jq|1.4}} The most interesting detail in the following is perhaps the use of ''recurse/1'' to define the helper function ''bin'', which generates the binary bits.
# is_prime is designed to work with jq 1.4
def is_prime:
if . == 2 then true
else 2 < . and . % 2 == 1 and
. as $in
| (($in + 1) | sqrt) as $m
| (((($m - 1) / 2) | floor) + 1) as $max
| reduce range(1; $max) as $i
(true; if . then ($in % ((2 * $i) + 1)) > 0 else false end)
end;
def popcount:
def bin: recurse( if . == 0 then empty else ./2 | floor end ) % 2;
[bin] | add;
def is_pernicious: popcount | is_prime;
# Emit a stream of "count" pernicious numbers greater than
# or equal to m:
def pernicious(m; count):
if count > 0 then
if m | is_pernicious then m, pernicious(m+1; count -1)
else pernicious(m+1; count)
end
else empty
end;
def task:
# display the first 25 pernicious numbers:
[ pernicious(1;25) ],
# display all pernicious numbers between
# 888,888,877 and 888,888,888 (inclusive).
[ range(888888877; 888888889) | select( is_pernicious ) ]
;
task
{{Out}} [3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36] [888888877,888888878,888888880,888888883,888888885,888888886]
Julia
{{works with|Julia|0.6}}
using Primes
ispernicious(n::Integer) = isprime(count_ones(n))
nextpernicious(n::Integer) = begin n += 1; while !ispernicious(n) n += 1 end; return n end
function perniciouses(n::Int)
rst = Vector{Int}(n)
rst[1] = 3
for i in 2:n
rst[i] = nextpernicious(rst[i-1])
end
return rst
end
perniciouses(a::Integer, b::Integer) = filter(ispernicious, a:b)
println("First 25 pernicious numbers: ", join(perniciouses(25), ", "))
println("Perniciouses in [888888877, 888888888]: ", join(perniciouses(888888877, 888888888), ", "))
{{out}}
First 25 pernicious numbers: 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36
Perniciouses in [888888877, 888888888]: 888888877, 888888878, 888888880, 888888883, 888888885, 888888886
Kotlin
// version 1.0.5-2
fun isPrime(n: Int): Boolean {
if (n < 2) return false
if (n % 2 == 0) return n == 2
if (n % 3 == 0) return n == 3
var d : Int = 5
while (d * d <= n) {
if (n % d == 0) return false
d += 2
if (n % d == 0) return false
d += 4
}
return true
}
fun getPopulationCount(n: Int): Int {
if (n <= 0) return 0
var nn = n
var sum = 0
while (nn > 0) {
sum += nn % 2
nn /= 2
}
return sum
}
fun isPernicious(n: Int): Boolean = isPrime(getPopulationCount(n))
fun main(args: Array<String>) {
var n = 1
var count = 0
println("The first 25 pernicious numbers are:\n")
do {
if (isPernicious(n)) {
print("$n ")
count++
}
n++
}
while (count < 25)
println("\n")
println("The pernicious numbers between 888,888,877 and 888,888,888 inclusive are:\n")
for (i in 888888877..888888888) {
if (isPernicious(i)) print("$i ")
}
}
{{out}}
The first 25 pernicious numbers are:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
The pernicious numbers between 888,888,877 and 888,888,888 inclusive are:
888888877 888888878 888888880 888888883 888888885 888888886
Lua
-- Test primality by trial division
function isPrime (x)
if x < 2 then return false end
if x < 4 then return true end
if x % 2 == 0 then return false end
for d = 3, math.sqrt(x), 2 do
if x % d == 0 then return false end
end
return true
end
-- Take decimal number, return binary string
function dec2bin (n)
local bin, bit = ""
while n > 0 do
bit = n % 2
n = math.floor(n / 2)
bin = bit .. bin
end
return bin
end
-- Take decimal number, return population count as number
function popCount (n)
local bin, count = dec2bin(n), 0
for pos = 1, bin:len() do
if bin:sub(pos, pos) == "1" then count = count + 1 end
end
return count
end
-- Print pernicious numbers in range if two arguments provided, or
function pernicious (x, y) -- the first 'x' if only one argument.
if y then
for n = x, y do
if isPrime(popCount(n)) then io.write(n .. " ") end
end
else
local n, count = 0, 0
while count < x do
if isPrime(popCount(n)) then
io.write(n .. " ")
count = count + 1
end
n = n + 1
end
end
print()
end
-- Main procedure
pernicious(25)
pernicious(888888877, 888888888)
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Maple
ispernicious := proc(n::posint)
return evalb(isprime(rhs(Statistics:-Tally(StringTools:-Explode(convert(convert(n, binary), string)))[-1])));
end proc;
print_pernicious := proc(n::posint)
local k, count, list_num;
count := 0;
list_num := [];
for k while count < n do
if ispernicious(k) then
count := count + 1;
list_num := [op(list_num), k];
end if;
end do;
return list_num;
end proc:
range_pernicious := proc(n::posint, m::posint)
local k, list_num;
list_num := [];
for k from n to m do
if ispernicious(k) then
list_num := [op(list_num), k];
end if;
end do;
return list_num;
end proc:
{{out}}
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Mathematica
popcount[n_Integer] := IntegerDigits[n, 2] // Total
perniciousQ[n_Integer] := popcount[n] // PrimeQ
perniciouscount = 0;
perniciouslist = {};
i = 0;
While[perniciouscount < 25,
If[perniciousQ[i], AppendTo[perniciouslist, i]; perniciouscount++];
i++]
Print["first 25 pernicious numbers"]
perniciouslist
(*******)
perniciouslist2 = {};
Do[
If[perniciousQ[i], AppendTo[perniciouslist2, i]]
, {i, 888888877, 888888888}]
Print["Pernicious numbers between 888,888,877 and 888,888,888 (inclusive)"]
perniciouslist2
{{out}}
first 25 pernicious numbers
{3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36}
Pernicious numbers between 888,888,877 and 888,888,888 (inclusive)
{888888877, 888888878, 888888880, 888888883, 888888885, 888888886}
Alternate Code
test function
perniciousQ[n_Integer] := PrimeQ@Total@IntegerDigits[n, 2]
First 25 pernicious numbers
n = 0; NestWhile[Flatten@{#, If[perniciousQ[++n], n, {}]} &, {}, Length@# < 25 &]
Pernicious numbers betweeen 888888877 and 888888888 inclusive
Cases[Range[888888877, 888888888], _?(perniciousQ@# &)]
=={{header|Modula-2}}==
MODULE Pernicious;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE IsPrime(x : LONGINT) : BOOLEAN;
VAR i : LONGINT;
BEGIN
IF x<2 THEN RETURN FALSE END;
FOR i:=2 TO x-1 DO
IF x MOD i = 0 THEN RETURN FALSE END
END;
RETURN TRUE
END IsPrime;
PROCEDURE BitCount(x : LONGINT) : LONGINT;
VAR count : LONGINT;
BEGIN
count := 0;
WHILE x>0 DO
x := x BAND (x-1);
INC(count)
END;
RETURN count
END BitCount;
VAR
buf : ARRAY[0..63] OF CHAR;
i,n : LONGINT;
BEGIN
i := 1;
n := 0;
WHILE n<25 DO
IF IsPrime(BitCount(i)) THEN
FormatString("%l ", buf, i);
WriteString(buf);
INC(n)
END;
INC(i)
END;
WriteLn;
FOR i:=888888877 TO 888888888 DO
IF IsPrime(BitCount(i)) THEN
FormatString("%l ", buf, i);
WriteString(buf)
END;
END;
ReadChar
END Pernicious.
Nim
{{trans|Python}}
import strutils
proc count(s: string, sub: char): int =
var i = 0
while true:
i = s.find(sub, i)
if i < 0:
break
inc i
inc result
proc popcount(n): int = n.toBin(64).count('1')
const primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
var p = newSeq[int]()
var i = 0
while p.len < 25:
if popcount(i) in primes: p.add i
inc i
echo p
p = @[]
i = 888_888_877
while i <= 888_888_888:
if popcount(i) in primes: p.add i
inc i
echo p
{{Out}}
@[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
@[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
PARI/GP
pern(n)=isprime(hammingweight(n))
select(pern, [1..36])
select(pern,[888888877..888888888])
{{out}}
%1 = [3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
%2 = [888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
Panda
fun prime(a) type integer->integer
a where count{{a.factor}}==2
fun pernisc(a) type integer->integer
a where sum{{a.radix:2 .char.integer}}.integer.prime
1..36.pernisc
888888877..888888888.pernisc
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Pascal
{{works with|Free Pascal}} Inspired by [[Pernicious numbers#Ada|Ada]], using array of primes to simply add.An if-then takes to long.
Added easy counting of pernicious numbers for full Bit ranges like 32-Bit
program pernicious;
{$IFDEF FPC}
{$OPTIMIZATION ON,Regvar,ASMCSE,CSE,PEEPHOLE}// 3x speed up
{$ENDIF}
uses
sysutils;//only used for time
type
tbArr = array[0..64] of byte;
{
PrimeTil64 : array[0..64] of byte =
(0,0,2,3,0,5,0, 7,0,0,0,11,0,13,0,0,0,17,0,19,0,0,0,23,0,0,0,0,0,29,0,
31,0,0,0,0,0,37,0,0,0,41,0,43,0,0,0,47,0, 0,0,0,0,53,0,0,0,0,0,59,0,
61,0,0,0);
}
const
PrimeTil64 : tbArr =
(0,0,1,1,0,1,0, 1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,
1,0,0,0,0,0, 1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,
1,0,0,0);
function n_beyond_k(n,k: NativeInt):Uint64;
var
i : NativeInt;
Begin
result := 1;
IF 2*k>= n then
k := n-k;
For i := 1 to k do
Begin
result := result *n DIV i;
dec(n);
end;
end;
function popcnt32(n:Uint32):NativeUint;
//https://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
const
K1 = $0101010101010101;
K33 = $3333333333333333;
K55 = $5555555555555555;
KF1 = $0F0F0F0F0F0F0F0F;
begin
n := n- (n shr 1) AND NativeUint(K55);
n := (n AND NativeUint(K33))+ ((n shr 2) AND NativeUint(K33));
n := (n + (n shr 4)) AND NativeUint(KF1);
n := (n*NativeUint(K1)) SHR 24;
popcnt32 := n;
end;
var
bit1cnt,
k : LongWord;
PernCnt : Uint64;
Begin
writeln('the 25 first pernicious numbers');
k:=1;
PernCnt:=0;
repeat
IF PrimeTil64[popCnt32(k)] <> 0 then Begin
inc(PernCnt); write(k,' ');end;
inc(k);
until PernCnt >= 25;
writeln;
writeln('pernicious numbers in [888888877..888888888]');
For k := 888888877 to 888888888 do
IF PrimeTil64[popCnt32(k)] <> 0 then
write(k,' ');
writeln(#13#10);
k := 8;
repeat
PernCnt := 0;
For bit1cnt := 0 to k do
Begin
//i == number of Bits set,n_beyond_k(k,i) == number of arrangements
IF PrimeTil64[bit1cnt] <> 0 then
inc(PernCnt,n_beyond_k(k,bit1cnt));
end;
writeln(PernCnt,' pernicious numbers in [0..2^',k,'-1]');
inc(k,k);
until k>64;
end.
{{out}}
the 25 first pernicious numbers
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
pernicious numbers in [888888877..888888888]
888888877 888888878 888888880 888888883 888888885 888888886
148 pernicious numbers in [0..2^8-1]
21416 pernicious numbers in [0..2^16-1]
1421120880 pernicious numbers in [0..2^32-1]
1214766910143514374 pernicious numbers in [0..2^64-1]
Perl
{{trans|C}}
sub is_pernicious {
my $n = shift;
my $c = 2693408940; # primes < 32 as set bits
while ($n) { $c >>= 1; $n &= ($n - 1); }
$c & 1;
}
my ($i, @p) = 0;
while (@p < 25) {
push @p, $i if is_pernicious($i);
$i++;
}
print join ' ', @p;
print "\n";
($i, @p) = (888888877,);
while ($i < 888888888) {
push @p, $i if is_pernicious($i);
$i++;
}
print join ' ', @p;
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Alternately, generating the same output using a method similar to Pari/GP: {{libheader|ntheory}}
use ntheory qw/is_prime hammingweight/;
my $i = 1;
my @pern = map { $i++ while !is_prime(hammingweight($i)); $i++; } 1..25;
print "@pern\n";
print join(" ", grep { is_prime(hammingweight($_)) } 888888877 .. 888888888), "\n";
Perl 6
Straightforward implementation using Perl 6's ''is-prime'' built-in subroutine.
sub is-pernicious(Int $n --> Bool) {
is-prime [+] $n.base(2).comb;
}
say (grep &is-pernicious, 0 .. *)[^25];
say grep &is-pernicious, 888_888_877 .. 888_888_888;
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Phix
function is_prime(atom n)
if n<2 then return false end if
for i=2 to floor(sqrt(n)) do
if mod(n,i)=0 then return false end if
end for
return true
end function
function pernicious(integer n)
return is_prime(sum(int_to_bits(n,32)))
end function
sequence s = {}
integer n = 1
while length(s)<25 do
if pernicious(n) then
s &= n
end if
n += 1
end while
?s
s = {}
for i=888_888_877 to 888_888_888 do
if pernicious(i) then
s &= i
end if
end for
?s
{{out}}
{3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36}
{888888877,888888878,888888880,888888883,888888885,888888886}
PicoLisp
Using 'prime?' from [[Primality by trial division#PicoLisp]].
(de pernicious? (N)
(prime? (cnt = (chop (bin N)) '("1" .))) )
Test:
: (let N 0
(do 25
(until (pernicious? (inc 'N)))
(printsp N) ) )
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 -> 36
: (filter pernicious? (range 888888877 888888888))
-> (888888877 888888878 888888880 888888883 888888885 888888886)
PL/I
pern: procedure options (main);
declare (i, n) fixed binary (31);
n = 3;
do i = 1 to 25, 888888877 to 888888888;
if i = 888888877 then do; n = i ; put skip; end;
do while ( ^is_prime ( tally(bit(n), '1'b) ) );
n = n + 1;
end;
put edit( trim(n), ' ') (a);
n = n + 1;
end;
is_prime: procedure (n) returns (bit(1));
declare n fixed (15);
declare i fixed (10);
if n < 2 then return ('0'b);
if n = 2 then return ('1'b);
if mod(n, 2) = 0 then return ('0'b);
do i = 3 to sqrt(n) by 2;
if mod(n, i) = 0 then return ('0'b);
end;
return ('1'b);
end is_prime;
end pern;
Results:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886 888888889 888888890 888888892 888888897 888888898 888888900
PowerShell
function pop-count($n) {
(([Convert]::ToString($n, 2)).toCharArray() | where {$_ -eq '1'}).count
}
function isPrime ($n) {
if ($n -eq 1) {$false}
elseif ($n -eq 2) {$true}
elseif ($n -eq 3) {$true}
else{
$m = [Math]::Floor([Math]::Sqrt($n))
(@(2..$m | where {($_ -lt $n) -and ($n % $_ -eq 0) }).Count -eq 0)
}
}
$i = 0
$num = 1
$arr = while($i -lt 25) {
if((isPrime (pop-count $num))) {
$i++
$num
}
$num++
}
"first 25 pernicious numbers"
"$arr"
""
"pernicious numbers between 888,888,877 and 888,888,888"
"$(888888877..888888888 | where{isprime(pop-count $_)})"
Output:
First 25 pernicious numbers
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
Pernicious numbers between 888,888,877 and 888,888,888
888888877 888888878 888888880 888888883 888888885 888888886
As An Advanced Function
Just an exercise in how to make the input more "PowerShelly".
The '''PopCount''' property is available in each of the returned integers.
function Select-PerniciousNumber
{
[CmdletBinding()]
[OutputType([int])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true,
Position=0)]
$InputObject
)
Begin
{
function Test-Prime ([int]$n)
{
$n = [Math]::Abs($n)
if ($n -eq 0 -or $n -eq 1) {return $false}
for ($m = 2; $m -le [Math]::Sqrt($n); $m++)
{
if (($n % $m) -eq 0) {return $false}
}
return $true
}
[scriptblock]$popCount = {(([Convert]::ToString($this, 2)).ToCharArray() | Where-Object {$_ -eq '1'}).Count}
}
Process
{
foreach ($object in $InputObject)
{
$object | Add-Member -MemberType ScriptProperty -Name PopCount -Value $popCount -Force -PassThru | ForEach-Object {
if (Test-Prime $_.PopCount)
{
$_
}
}
}
}
}
$start, $end = 0, 999999
$range1 = $start..$end | Select-PerniciousNumber | Select-Object -First 25
"First {0} pernicious numbers:`n{1}`n" -f $range1.Count, ($range1 -join ", ")
$start, $end = 888888877, 888888888
$range2 = $start..$end | Select-PerniciousNumber
"Pernicious numbers between {0} and {1}:`n{2}`n" -f $start, $end, ($range2 -join ", ")
{{Out}}
First 25 pernicious numbers:
3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36
Pernicious numbers between 888888877 and 888888888:
888888877, 888888878, 888888880, 888888883, 888888885, 888888886
PureBasic
EnableExplicit
Procedure.i SumBinaryDigits(Number)
If Number < 0 : number = -number : EndIf; convert negative numbers to positive
Protected sum = 0
While Number > 0
sum + Number % 2
Number / 2
Wend
ProcedureReturn sum
EndProcedure
Procedure.i IsPrime(Number)
If Number <= 1
ProcedureReturn #False
ElseIf Number <= 3
ProcedureReturn #True
ElseIf Number % 2 = 0 Or Number % 3 = 0
ProcedureReturn #False
EndIf
Protected i = 5
While i * i <= Number
If Number % i = 0 Or Number % (i + 2) = 0
ProcedureReturn #False
EndIf
i + 6
Wend
ProcedureReturn #True
EndProcedure
Procedure.i IsPernicious(Number)
Protected popCount = SumBinaryDigits(Number)
ProcedureReturn Bool(IsPrime(popCount))
EndProcedure
Define n = 1, count = 0
If OpenConsole()
PrintN("The following are the first 25 pernicious numbers :")
PrintN("")
Repeat
If IsPernicious(n)
Print(RSet(Str(n), 3))
count + 1
EndIf
n + 1
Until count = 25
PrintN("")
PrintN("")
PrintN("The pernicious numbers between 888,888,877 and 888,888,888 inclusive are : ")
PrintN("")
For n = 888888877 To 888888888
If IsPernicious(n)
Print(RSet(Str(n), 10))
EndIf
Next
PrintN("")
PrintN("")
PrintN("Press any key to close the console")
Repeat: Delay(10) : Until Inkey() <> ""
CloseConsole()
EndIf
{{out}}
The following are the first 25 pernicious numbers :
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
The pernicious numbers between 888,888,877 and 888,888,888 inclusive are :
888888877 888888878 888888880 888888883 888888885 888888886
Python
def popcount(n): return bin(n).count("1")
>>> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
>>> p, i = [], 0
>>> while len(p) < 25:
if popcount(i) in primes: p.append(i)
i += 1
>>> p
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
>>> p, i = [], 888888877
>>> while i <= 888888888:
if popcount(i) in primes: p.append(i)
i += 1
>>> p
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
>>>
Racket
#lang racket
(require math/number-theory rnrs/arithmetic/bitwise-6)
(define pernicious? (compose prime? bitwise-bit-count))
(define (dnl . strs)
(for-each displayln strs))
(define (show-sequence seq)
(string-join (for/list ((v (in-values*-sequence seq))) (~a ((if (list? v) car values) v))) ", "))
(dnl
"Task requirements:"
"display the first 25 pernicious numbers."
(show-sequence (in-parallel (sequence-filter pernicious? (in-naturals 1)) (in-range 25)))
"display all pernicious numbers between 888,888,877 and 888,888,888 (inclusive)."
(show-sequence (sequence-filter pernicious? (in-range 888888877 (add1 888888888)))))
(module+ test
(require rackunit)
(check-true (pernicious? 22)))
{{out}}
Task requirements:
display the first 25 pernicious numbers.
3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36
display all pernicious numbers between 888,888,877 and 888,888,888 (inclusive).
888888877, 888888878, 888888880, 888888883, 888888885, 888888886
REXX
Programming note: to increase the size of the numbers being tested (to greater than 100 decimal digits),
all that is needed is to extend the list of low primes in the 2nd line in the '''pernicious''' procedure (below);
the highest prime (Hprime) should exceed the number of decimal digits in 2Hprime.
The program could be easily extended by programmatically generating enough primes to handle much larger numbers.
╔════════════════════════════════════════════════════════════════════════════════════════╗
╠═════ How the ─── popCount ─── function works (working from the inner─most level): ═════╣
║ ║
║ arg(1) obtains the value of the 1st argument passed to the (popCount) function. ║
║ d2x converts a decimal string ──► heXadecimal (it may have a leading zeroes).║
║ +0 adds zero to the (above) string, removing any superfluous leading zeroes. ║
║ translate converts all zeroes to blanks (the 2nd argument defaults to a blank). ║
║ space removes all blanks from the character string (now only containing '1's). ║
║ length counts the number of characters in the string. ║
║ return returns the above value to the invoker. ║
║ ║
║ Note that all values in REXX are stored as (eight─bit) characters. ║
╚════════════════════════════════════════════════════════════════════════════════════════╝
/*REXX program computes and displays a number (and also a range) of pernicious numbers.*/
numeric digits 100 /*be able to handle large numbers. */
parse arg N L H . /*obtain optional arguments from the CL*/
if N=='' | N==',' then N=25 /*N not given? Then use the default. */
if L=='' | L==',' then L=888888877 /*L " " " " " " */
if H=='' | H==',' then H=888888888 /*H " " " " " " */
say 'The 1st ' N " pernicious numbers are:" /*display a nice title for the numbers.*/
say pernicious(1,,N) /*get all pernicious # from 1 ─~─► N. */
say /*display a blank line for a separator.*/
say 'Pernicious numbers between ' L " and " H ' (inclusive) are:'
say pernicious(L,H) /*get all pernicious # from L ───► H. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
pernicious: procedure; parse arg bot,top,lim /*obtain the bot and top numbers, limit*/
p='2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101'
@.=0
do k=1 until _=='' /*examine the list of some low primes.*/
_=word(p, k); @._=1 /*generate an array " " " " */
end /*k*/
$= /*list of pernicious numbers (so far). */
if m=='' then m=999999999 /*Not given? Then use a gihugic limit.*/
if top=='' then top=999999999 /* " " " " " " " */
#=0 /*number of pernicious numbers (so far)*/
do j=bot to top until #==lim /*generate pernicious #s 'til satisfied*/
pc=popCount(j) /*obtain the population count for J. */
if \@.pc then iterate /*if popCount not in @.prime, skip it.*/
$=$ j /*append a pernicious number to list. */
#=#+1 /*bump the pernicious number count. */
end /*j*/
return substr($, 2) /*return the results, sans 1st blank. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
popCount: return length( space( translate( x2b( d2x(arg(1))) +0,, 0), 0)) /*count 1's.*/
'''output''' when the default inputs are used:
The 1st 25 pernicious numbers are:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
Pernicious numbers between 888888877 and 888888888 (inclusive) are:
888888877 888888878 888888880 888888883 888888885 888888886
Ring
Programming note: as written, this program can't handle the large numbers required for the 2nd task requirement (it receives a '''Numeric Overflow''').
# Project : Pernicious numbers
see "The first 25 pernicious numbers:" + nl
nr = 0
for n=1 to 50
sum = 0
str = decimaltobase(n, 2)
for m=1 to len(str)
if str[m] = "1"
sum = sum + 1
ok
next
if isprime(sum)
nr = nr + 1
see "" + n + " "
ok
if nr = 25
exit
ok
next
func decimaltobase(nr, base)
binary = 0
i = 1
while(nr != 0)
remainder = nr % base
nr = floor(nr/base)
binary= binary + (remainder*i)
i = i*10
end
return string(binary)
func isprime num
if (num <= 1) return 0 ok
if (num % 2 = 0 and num != 2) return 0 ok
for i = 3 to floor(num / 2) -1 step 2
if (num % i = 0) return 0 ok
next
return 1
Output:
The first 25 pernicious numbers:
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
Ruby
require "prime"
class Integer
def popcount
to_s(2).count("1") #Ruby 2.4: digits(2).count(1)
end
def pernicious?
popcount.prime?
end
end
p 1.step.lazy.select(&:pernicious?).take(25).to_a
p ( 888888877..888888888).select(&:pernicious?)
{{out}}
[3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36]
[888888877, 888888878, 888888880, 888888883, 888888885, 888888886]
=={{header|S-lang}}==
variable mx = int(sqrt(n)), i;
_for i (3, mx, 1) { if ((n mod i) == 0) return(0); } return(1); }
define population(n) { variable pc = 0; do { if (n & 1) pc++; n /= 2; } while (n); return(pc); }
define is_pernicious(n) { return(is_prime(population(n))); }
variable plist = {}, n = 0; while (length(plist) < 25) { n++; if (is_pernicious(n)) list_append(plist, string(n)); } print(strjoin(list_to_array(plist), " "));
plist = {}; _for n (888888877, 888888888, 1) { if (is_pernicious(n)) list_append(plist, string(n)); } print(strjoin(list_to_array(plist), " "));
{{out}}
"3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36"
{{out}}
"888888877 888888878 888888880 888888883 888888885 888888886"
## Scala
```scala
def isPernicious( v:Long ) : Boolean = BigInt(v.toBinaryString.toList.filter( _ == '1' ).length).isProbablePrime(16)
// Generate the output
{
val (a,b1,b2) = (25,888888877L,888888888L)
println( Stream.from(2).filter( isPernicious(_) ).take(a).toList.mkString(",") )
println( {for( i <- b1 to b2 if( isPernicious(i) ) ) yield i}.mkString(",") )
}
{{out}}
3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36
888888877,888888878,888888880,888888883,888888885,888888886
Seed7
The function popcount below [http://seed7.sourceforge.net/libraries/bitset.htm#bitset(in_integer) converts]
the integer into a [http://seed7.sourceforge.net/libraries/bitset.htm bitset].
The function [http://seed7.sourceforge.net/libraries/bitset.htm#card(in_bitset) card]
is used to compute the population count of the bitset.
$ include "seed7_05.s7i";
const set of integer: primes is {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61};
const func integer: popcount (in integer: number) is
return card(bitset(number));
const proc: main is func
local
var integer: num is 0;
var integer: count is 0;
begin
for num range 0 to integer.last until count >= 25 do
if popcount(num) in primes then
write(num <& " ");
incr(count);
end if;
end for;
writeln;
for num range 888888877 to 888888888 do
if popcount(num) in primes then
write(num <& " ");
end if;
end for;
writeln;
end func;
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Sidef
{{trans|Perl}}
func is_pernicious(n) {
var c = 2693408940; # primes < 32 as set bits
while (n > 0) { c >>= 1; n &= (n - 1) }
c & 1;
}
var (i, *p) = 0;
while (p.len < 25) {
p << i if is_pernicious(i);
++i;
}
say p.join(' ');
var (i, *p) = 888888877;
while (i < 888888888) {
p << i if is_pernicious(i);
++i;
}
say p.join(' ');
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Symsyn
primes : 0b0010100000100000100010100010000010100000100010100010100010101100
| the first 25 pernicious numbers
$T | clear string
num_pn | set to zero
2 n | start at 2
5 hi_bit
if num_pn LT 25
call popcount | count ones
if primes bit pop_cnt | if pop_cnt bit of bit vector primes is one
+ num_pn | inc number of pernicious numbers
~ n $S | convert to decimal string
+ ' ' $S | pad a space
+ $S $T | add to string $T
endif
+ pop_cnt | next number (odd) has one more bit than previous (even)
+ n | next number
if primes bit pop_cnt
+ num_pn
~ n $S
+ ' ' $S
+ $S $T
endif
+ n
goif | go back to if
endif
$T [] | display numbers
| pernicious numbers in range 888888877 .. 888888888
$T | clear string
num_pn | set to zero
888888876 n | start at 888888876
29 hi_bit
if n LE 888888888
call popcount | count ones
if primes bit pop_cnt | if pop_cnt bit of bit vector primes is one
+ num_pn | inc number of pernicious numbers
~ n $S | convert to decimal string
+ ' ' $S | pad a space
+ $S $T | add to string $T
endif
+ pop_cnt | next number (odd) has one more bit than previous (even)
+ n | next number
if primes bit pop_cnt
+ num_pn
~ n $S
+ ' ' $S
+ $S $T
endif
+ n
goif | go back to if
endif
$T [] | display numbers
stop
popcount | count ones in bit field
pop_cnt | pop_cnt to zero
1 bit_num | only count even numbers so skip bit 0
if bit_num LE hi_bit
if n bit bit_num
+ pop_cnt
endif
+ bit_num
goif
endif
return
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36 37
888888877 888888878 888888880 888888883 888888885 888888886 888888889
Tcl
{{tcllib|math::numtheory}}
package require math::numtheory
proc pernicious {n} {
::math::numtheory::isprime [tcl::mathop::+ {*}[split [format %b $n] ""]]
}
for {set n 0;set p {}} {[llength $p] < 25} {incr n} {
if {[pernicious $n]} {lappend p $n}
}
puts [join $p ","]
for {set n 888888877; set p {}} {$n <= 888888888} {incr n} {
if {[pernicious $n]} {lappend p $n}
}
puts [join $p ","]
{{out}}
3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36
888888877,888888878,888888880,888888883,888888885,888888886
VBA
{{trans|Phix}}
Private Function population_count(ByVal number As Long) As Integer
Dim result As Integer
Dim digit As Integer
Do While number > 0
If number Mod 2 = 1 Then
result = result + 1
End If
number = number \ 2
Loop
population_count = result
End Function
Function is_prime(n As Integer) As Boolean
If n < 2 Then
is_prime = False
Exit Function
End If
For i = 2 To Sqr(n)
If n Mod i = 0 Then
is_prime = False
Exit Function
End If
Next i
is_prime = True
End Function
Function pernicious(n As Long)
Dim tmp As Integer
tmp = population_count(n)
pernicious = is_prime(tmp)
End Function
Public Sub main()
Dim count As Integer
Dim n As Long: n = 1
Do While count < 25
If pernicious(n) Then
Debug.Print n;
count = count + 1
End If
n = n + 1
Loop
Debug.Print
For n = 888888877 To 888888888
If pernicious(n) Then
Debug.Print n;
End If
Next n
End Sub
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
VBScript
'check if the number is pernicious
Function IsPernicious(n)
IsPernicious = False
bin_num = Dec2Bin(n)
sum = 0
For h = 1 To Len(bin_num)
sum = sum + CInt(Mid(bin_num,h,1))
Next
If IsPrime(sum) Then
IsPernicious = True
End If
End Function
'prime number validation
Function IsPrime(n)
If n = 2 Then
IsPrime = True
ElseIf n <= 1 Or n Mod 2 = 0 Then
IsPrime = False
Else
IsPrime = True
For i = 3 To Int(Sqr(n)) Step 2
If n Mod i = 0 Then
IsPrime = False
Exit For
End If
Next
End If
End Function
'decimal to binary converter
Function Dec2Bin(n)
q = n
Dec2Bin = ""
Do Until q = 0
Dec2Bin = CStr(q Mod 2) & Dec2Bin
q = Int(q / 2)
Loop
End Function
'display the first 25 pernicious numbers
c = 0
WScript.StdOut.Write "First 25 Pernicious Numbers:"
WScript.StdOut.WriteLine
For k = 1 To 100
If IsPernicious(k) Then
WScript.StdOut.Write k & ", "
c = c + 1
End If
If c = 25 Then
Exit For
End If
Next
WScript.StdOut.WriteBlankLines(2)
'display the pernicious numbers between 888,888,877 to 888,888,888 (inclusive)
WScript.StdOut.Write "Pernicious Numbers between 888,888,877 to 888,888,888 (inclusive):"
WScript.StdOut.WriteLine
For l = 888888877 To 888888888
If IsPernicious(l) Then
WScript.StdOut.Write l & ", "
End If
Next
WScript.StdOut.WriteLine
{{out}}
First 25 Pernicious Numbers:
3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36,
Pernicious Numbers between 888,888,877 to 888,888,888 (inclusive):
888888877, 888888878, 888888880, 888888883, 888888885, 888888886,
Visual Basic .NET
{{trans|C#}}
Module Module1
Function PopulationCount(n As Long) As Integer
Dim cnt = 0
Do
If (n Mod 2) <> 0 Then
cnt += 1
End If
n >>= 1
Loop While n > 0
Return cnt
End Function
Function IsPrime(x As Integer) As Boolean
If x <= 2 OrElse (x Mod 2) = 0 Then
Return x = 2
End If
Dim limit = Math.Sqrt(x)
For i = 3 To limit Step 2
If x Mod i = 0 Then
Return False
End If
Next
Return True
End Function
Function Pernicious(start As Integer, count As Integer, take As Integer) As IEnumerable(Of Integer)
Return Enumerable.Range(start, count).Where(Function(n) IsPrime(PopulationCount(n))).Take(take)
End Function
Sub Main()
For Each n In Pernicious(0, Integer.MaxValue, 25)
Console.Write("{0} ", n)
Next
Console.WriteLine()
For Each n In Pernicious(888888877, 11, 11)
Console.Write("{0} ", n)
Next
Console.WriteLine()
End Sub
End Module
{{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888888877 888888878 888888880 888888883 888888885 888888886
Wortel
The following function returns true if it's argument is a pernicious number:
:ispernum ^(@isPrime \@count \=1 @arr &\`![.toString 2])
Task:
!-ispernum 1..36 ; returns [3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36]
!-ispernum 888888877..888888888 ; returns [888888877 888888878 888888880 888888883 888888885 888888886]
zkl
The largest number of bits is 30.
primes:=T(2,3,5,7,11,13,17,19,23,29,31,37,41);
N:=0; foreach n in ([2..]){
if(n.num1s : primes.holds(_)){
print(n," ");
if((N+=1)==25) break;
}
}
foreach n in ([0d888888877..888888888]){
if (n.num1s : primes.holds(_)) "%,d; ".fmt(n).print();
}
Int.num1s returns the number of 1 bits. eg (3).num1s-->2 {{out}}
3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
888,888,877; 888,888,878; 888,888,880; 888,888,883; 888,888,885; 888,888,886;
Or in a more functional style:
primes:=T(2,3,5,7,11,13,17,19,23,29,31,37,41);
p:='wrap(n){ primes.holds(n.num1s) };
[1..].filter(25,p).toString(*).println();
[0d888888877..888888888].filter(p).println();
'wrap is syntactic sugar for a closure - it creates a function that wraps local data (variable primes in this case). We assign that function to p. {{out}}
L(3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,24,25,26,28,31,33,34,35,36)
L(888888877,888888878,888888880,888888883,888888885,888888886)