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Semiprime: Difference between revisions
→version 2: added a count of semprimes found, changed comments, source, whitespace, indented the output.
(→version 2: added a count of semprimes found, changed comments, source, whitespace, indented the output.) |
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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)) + 5 /*obtain the maximum width of numbers. */
numeric digits max(9, w) /*ensure there're enough decimal digits*/
#=0
?=isSemiPrime(n); #=#+? /*Is N a semiprime?; Maybe
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. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
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end /*k*/ /* [↑] see if 2nd factor is prime or ¬*/
end /*j*/ /* [↑] J is never a multiple of three.*/</lang>
<br>(Shown at three-quarter size.)
<pre style="font-size:75%;height:
-1 isn't semiprime.▼
106 is semiprime.
found 35 semiprimes.
</pre>
<br>(Shown at three-quarter size.)
<pre style="font-size:75%;height:
found 7 semiprimes.
</pre>
===version 3, with memoization===
This REXX version is overt 20% faster than version 2   (when in the ''millions'' range).
If the 2<sup>nd</sup> argument ('''top''') is negative (it's absolute value is used), individual numbers in the range aren't shown, but the count of semiprimes found is shown.
It gets its speed increase by the use of memoization of the prime numbers found, and other speed improvements.
<lang rexx>/*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</lang>
{{out|output|text= is identical to the previous REXX version.}} <br><br>
=={{header|Ring}}==
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