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September 2017 Update

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Ingy döt Net 2017-09-23 10:01:46 +02:00
parent bba7bfd280
commit ba8067c3b7
14570 changed files with 153136 additions and 63871 deletions
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15
Task/Semiprime/00DESCRIPTION
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@ -1,6 +1,15 @@
Semiprime numbers are natural numbers that are products of exactly two (possibly equal) [[prime_number|prime numbers]].
'''Semiprimes'''   are also known as:
:::*   '''semi-primes'''
:::*   '''biprimes'''
:::*   '''bi-primes'''
:::*   ''' ''2-almost'' '''   primes
:::* &nbsp; or simply: &nbsp; ''' ''P<sub>2</sub> '' '''
;Example:
<big> 1679 = 23 &times; 73 </big>
@ -9,4 +18,10 @@ Semiprime numbers are natural numbers that are products of exactly two (possibly
;Task;
Write a function determining whether a given number is semiprime.
;See also:
* The Wikipedia article: &nbsp; [http://mathworld.wolfram.com/Semiprime.html semiprime].
* The Wikipedia article: &nbsp; [http://mathworld.wolfram.com/AlmostPrime.html almost prime].
* The OEIS article: &nbsp; [http://oeis.org/A001358 semiprimes] &nbsp; which has a shorter definition: ''the product of two primes''.
<br><br>

71
Task/Semiprime/360-Assembly/semiprime.360 Normal file
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@ -0,0 +1,71 @@
* Semiprime 14/03/2017
SEMIPRIM CSECT
USING SEMIPRIM,R13 base register
B 72(R15) skip savearea
DC 17F'0' savearea
STM R14,R12,12(R13) save previous context
ST R13,4(R15) link backward
ST R15,8(R13) link forward
LR R13,R15 set addressability
LA R10,PG pgi=0
LA R8,0 m=0
L R6,=F'2' i=2
DO WHILE=(C,R6,LE,=F'100') do i=2 to 100
ST R6,N n=i
LA R9,0 f=0
LA R7,2 j=2
LOOPJ EQU * do j=2 while f<2 and j*j<=n
C R9,=F'2' if f<2
BNL EXITJ then exit do j
LR R5,R7 j
MR R4,R7 *j
C R5,N if j*j<=n
BH EXITJ then exit do j
LOOPK EQU * do while n mod j=0
L R4,N n
SRDA R4,32 ~
DR R4,R7 /j
LTR R4,R4 if n mod <>0
BNZ EXITK then exit do j
ST R5,N n=n/j
LA R9,1(R9) f=f+1
B LOOPK enddo k
EXITK LA R7,1(R7) j++
B LOOPJ enddo j
EXITJ L R4,N n
IF C,R4,GT,=F'1' THEN if n>1 then
LA R2,1 g=1
ELSE , else
LA R2,0 g=0
ENDIF , endif
AR R2,R9 +f
IF C,R2,EQ,=F'2' THEN if f+(n>1)=2 then
XDECO R6,XDEC edit i
MVC 0(5,R10),XDEC+7 output i
LA R10,5(R10) pgi=pgi+10
LA R8,1(R8) m=m+1
LR R4,R8 m
SRDA R4,32 ~
D R4,=F'16' m/16
IF LTR,R4,Z,R4 THEN if m mod 16=0 then
XPRNT PG,L'PG print buffer
MVC PG,=CL80' ' clear buffer
LA R10,PG pgi=0
ENDIF , endif
ENDIF , endif
LA R6,1(R6) i++
ENDDO , enddo i
XPRNT PG,L'PG print buffer
MVC PG,=CL80'..... semiprimes' init buffer
XDECO R8,XDEC edit m
MVC PG(5),XDEC+7 output m
XPRNT PG,L'PG print buffer
L R13,4(0,R13) restore previous savearea pointer
LM R14,R12,12(R13) restore previous context
XR R15,R15 rc=0
BR R14 exit
N DS F n
PG DC CL80' ' buffer
XDEC DS CL12 temp
YREGS
END SEMIPRIM

14
Task/Semiprime/Clojure/semiprime.clj Normal file
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@ -0,0 +1,14 @@
(ns example
(:gen-class))
(defn semi-prime? [n]
(loop [a 2
b 0
c n]
(cond
(> b 2) false
(<= c 1) (= b 2)
(= 0 (rem c a)) (recur a (inc b) (int (/ c a)))
:else (recur (inc a) b c))))
(println (filter semi-prime? (range 1 100)))

18
Task/Semiprime/Kotlin/semiprime.kotlin Normal file
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@ -0,0 +1,18 @@
// version 1.1.2
fun isSemiPrime(n: Int): Boolean {
var nf = 0
var nn = n
for (i in 2..nn)
while (nn % i == 0) {
if (nf == 2) return false
nf++
nn /= i
}
return nf == 2
}
fun main(args: Array<String>) {
for (v in 1675..1680)
println("$v ${if (isSemiPrime(v)) "is" else "isn't"} semi-prime")
}

18
Task/Semiprime/Nim/semiprime.nim Normal file
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@ -0,0 +1,18 @@
proc isSemiPrime(k: int): string =
var
i: int = 2
compte: int = 0
x: int = k
while i<=x and compte<3:
if (x mod i)==0:
x = x div i
compte += 1
else:
i += 1
if compte==2:
result = "is semi-prime"
else:
result = "isn't semi-prime"
for k in 1675..1680:
echo k," ",isSemiPrime(k)

0
Task/Semiprime/Perl-6/semiprime.pl6 → Task/Semiprime/Perl-6/semiprime-1.pl6
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38
Task/Semiprime/Perl-6/semiprime-2.pl6 Normal file
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sub is-semiprime ( Int $n where * > 0 ) {
return False if $n.is-prime;
my $factor = find-factor( $n );
return True if $factor.is-prime && ( $n div $factor ).is-prime;
False;
}
sub find-factor ( Int $n, $constant = 1 ) {
my $x = 2;
my $rho = 1;
my $factor = 1;
while $factor == 1 {
$rho *= 2;
my $fixed = $x;
for ^$rho {
$x = ( $x * $x + $constant ) % $n;
$factor = ( $x - $fixed ) gcd $n;
last if 1 < $factor;
}
}
$factor = find-factor( $n, $constant + 1 ) if $n == $factor;
$factor;
}
INIT my $start = now;
# Infinite list of semiprimes
constant @semiprimes = 4, 6, 9, -> $p { ($p + 1 ... &is-semiprime).tail } ... *;
# Show the semiprimes < 100
say 'Semiprimes less than 100:';
say @semiprimes[^ @semiprimes.first: * > 100, :k ], "\n";
# Check individual integers, or in this case, a range
my $s = 2⁹⁷ - 1;
say "Is $_ semiprime?: ", is-semiprime( $_ ) for $s .. $s + 30;
say 'elapsed seconds: ', now - $start;

8
Task/Semiprime/Perl/semiprime-1.pl
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@ -1,4 +1,4 @@
use ntheory "factor";
print join(" ", grep { scalar factor($_) == 2 } 1..100),"\n";
print join(" ", grep { scalar factor($_) == 2 } 1675..1681),"\n";
print join(" ", grep { scalar factor($_) == 2 } (2,4,99,100,1679,5040,32768,1234567,9876543,900660121)),"\n";
use ntheory "is_semiprime";
for ([1..100], [1675..1681], [2,4,99,100,1679,5030,32768,1234567,9876543,900660121]) {
print join(" ",grep { is_semiprime($_) } @$_),"\n";
}

11
Task/Semiprime/Perl/semiprime-2.pl
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@ -1,9 +1,2 @@
use ntheory qw/factor is_prime trial_factor/;
sub issemi {
my $n = shift;
if ((my @p = trial_factor($n,500)) > 1) {
return 0 if @p > 2;
return !!is_prime($p[1]) if @p == 2;
}
2 == factor($n);
}
use ntheory "factor";
print join(" ", grep { scalar factor($_) == 2 } 1..100),"\n";

9
Task/Semiprime/Perl/semiprime-3.pl Normal file
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@ -0,0 +1,9 @@
use ntheory qw/factor is_prime trial_factor/;
sub issemi {
my $n = shift;
if ((my @p = trial_factor($n,500)) > 1) {
return 0 if @p > 2;
return !!is_prime($p[1]) if @p == 2;
}
2 == factor($n);
}

18
Task/Semiprime/Phix/semiprime.phix Normal file
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function semiprime(integer n)
sequence f = prime_factors(n)
integer l = length(f)
return (l=2 and n=f[1]*f[2]) or (l=1 and n=power(f[1],2))
end function
procedure test(integer start, integer stop)
sequence s = {}
for i=start to stop do
if semiprime(i) then
s &= i
end if
end for
?s
?length(s)
end procedure
test(1,100)
test(1675,1680)

12
Task/Semiprime/REXX/semiprime-2.rexx
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@ -2,12 +2,16 @@
parse arg bot top . /*obtain optional arguments from the CL*/
if bot=='' | bot=="," then bot=random() /*None given? User wants us to guess.*/
if top=='' | top=="," then top=bot /*maybe define a range of numbers. */
w=max(length(bot), length(top)) /*obtain the maximum width of numbers. */
tell= top=>0 | top==bot /*should results be shown to the term? */
w=max(length(bot), length(top)) + 5 /*obtain the maximum width of numbers. */
numeric digits max(9, w) /*ensure there're enough decimal digits*/
do n=bot to top /*show results for a range of numbers. */
if isSemiPrime(n) then say right(n, w) " is semiprime."
else say right(n, w) " isn't semiprime."
#=0 /*initialize number of semiprimes found*/
do n=bot to abs(top) /*show results for a range of numbers. */
?=isSemiPrime(n); #=#+? /*Is N a semiprime?; Maybe bump counter*/
if tell then say right(n,w) right(word("isn't" 'is', ?+1), 6) 'semiprime.'
end /*n*/
say
if bot\==top then say 'found ' # " semiprimes."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: procedure; parse arg x; if x<2 then return 0 /*number too low?*/

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Task/Semiprime/REXX/semiprime-3.rexx Normal file
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@ -0,0 +1,41 @@
/*REXX program determines if any integer (or a range of integers) is/are semiprime. */
parse arg bot top . /*obtain optional arguments from the CL*/
if bot=='' | bot=="," then bot=random() /*None given? User wants us to guess.*/
if top=='' | top=="," then top=bot /*maybe define a range of numbers. */
tell= bot=>0 & top=>0 /*should results be shown to the term? */
w=max(length(bot), length(top)) /*obtain the maximum width of numbers. */
!.=; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1; !.19=1; !.23=1; !.29=1; !.31=1
numeric digits max(9, w) /*ensure there're enough decimal digits*/
#=0 /*initialize number of semiprimes found*/
do n=abs(bot) to abs(top) /*show results for a range of numbers. */
?=isSemiPrime(n); #=#+? /*Is N a semiprime?; Maybe bump counter*/
if tell then say right(n,w) right(word("isn't" 'is', ?+1), 6) 'semiprime.'
end /*n*/
say
if bot\==top then say 'found ' # " semiprimes."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isPrime: procedure expose !.; parse arg x; if x<2 then return 0 /*number too low?*/
if !.x==1 then return 1 /*a known prime. */
if x// 2==0 then return 0; if x//3==0 then return 0 /*÷ by 2;÷by 3?*/
parse var x '' -1 _; if _==5 then return 0 /*last digit a 5?*/
if x// 7==0 then return 0; if x//11==0 then return 0 /*÷ by 7;÷by 11?*/
if x//13==0 then return 0; if x//17==0 then return 0 /*÷ by 13;÷by 17?*/
if x//19==0 then return 0; if x//23==0 then return 0 /*÷ by 19;÷by 23?*/
do j=29 by 6 until j*j>x; if x//j==0 then return 0 /*not a prime. */
if x//(j+2)==0 then return 0 /* " " " */
end /*j*/
!.x=1; return 1 /*indicate that X is a prime number. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isSemiPrime: procedure expose !.; parse arg x; if x<4 then return 0
do i=2 for 2; if x//i==0 then if isPrime(x%i) then return 1
else return 0
end /*i*/
/* ___ */
do j=5 by 6 until j*j>x /* > √ x ?*/
do k=j by 2 for 2; if x//k==0 then if isPrime(x%k) then return 1
else return 0
end /*k*/ /* [↑] see if 2nd factor is prime or ¬*/
end /*j*/ /* [↑] J is never a multiple of three.*/
return 0

8
Task/Semiprime/Zkl/semiprime.zkl Normal file
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fcn semiprime(n){
reg f = 0;
p:=2; while(f < 2 and p*p <= n){
while(0 == n % p){ n /= p; f+=1; }
p+=1;
}
return(f + (n > 1) == 2);
}