Just another update
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41
Task/Truncatable-primes/Common-Lisp/truncatable-primes.lisp
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41
Task/Truncatable-primes/Common-Lisp/truncatable-primes.lisp
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@ -0,0 +1,41 @@
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(defun start ()
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(format t "Largest right-truncatable ~a~%" (max-right-truncatable))
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(format t "Largest left-truncatable ~a~%" (max-left-truncatable)))
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(defun max-right-truncatable ()
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(loop for el in (6-digits-R-truncatables)
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maximizing el into max
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finally (return max)))
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(defun 6-digits-R-truncatables (&optional (lst '(2 3 5 7)) (n 5))
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(if (zerop n)
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lst
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(6-digits-R-truncatables (R-trunc lst) (- n 1))))
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(defun R-trunc (lst)
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(remove-if (lambda (x) (not (primep x)))
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(loop for el in lst
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append (mapcar (lambda (x) (+ (* 10 el) x)) '(1 3 7 9)))))
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(defun max-left-truncatable ()
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(loop for el in (6-digits-L-truncatables)
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maximizing el into max
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finally (return max)))
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(defun 6-digits-L-truncatables (&optional (lst '(3 7)) (n 5))
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(if (zerop n)
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lst
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(6-digits-L-truncatables (L-trunc lst (- 6 n)) (- n 1))))
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(defun L-trunc (lst n)
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(remove-if (lambda (x) (not (primep x)))
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(loop for el in lst
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append (mapcar (lambda (x) (+ (* (expt 10 n) x) el)) '(1 2 3 4 5 6 7 8 9)))))
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(defun primep (n)
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(primep-aux n 2))
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(defun primep-aux (n d)
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(cond ((> d (sqrt n)) t)
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((zerop (rem n d)) nil)
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(t (primep-aux n (+ d 1)))))
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@ -38,7 +38,7 @@ public class Main {
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if(rightTrunc == -1)
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{
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int right = prime;
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while(right > 0 && primeList.get(right >> 1)) right /= 10;
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while(right > 0 && right % 2 != 0 && primeList.get(right >> 1)) right /= 10;
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if(right == 0) rightTrunc = prime;
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}
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@ -1,41 +1,10 @@
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my @primes := 2, 3, 5, -> $p { ($p+2, $p+4 ... &prime)[*-1] } ... *;
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my @isprime = False,False; # 0 and 1 are not primes by definition
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sub prime($i) { @isprime[$i] //= ($i %% none @primes ...^ * > $_ given $i.sqrt.floor) }
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constant ltp = [2, 3, 5, 7], -> @ltp {
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[ grep &is-prime, ((1..9) X~ @ltp) ]
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} ... *;
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sub ltp {
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for 9...1 -> $a {
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for 9...1 -> $b {
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for 9...1 -> $c {
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for 9...1 -> $d {
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for 9...1 -> $e {
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for 9,7,3 -> $f {
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my @x := [\+] $f, $e, $d, $c, $b, $a Z* (1,10,100 ... *);
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return @x[*-1] if not grep {not prime $^n}, @x;
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}
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}
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}
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}
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}
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}
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}
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constant rtp = [2, 3, 5, 7], -> @rtp {
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[ grep &is-prime, (@rtp X~ (1..9)) ]
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} ... *;
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sub infix:<*+> ($a,$b) { $a * 10 + $b }
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sub rtp {
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for 7,5,3 {
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for grep &prime, ($_ X*+ 9,7,3,1) {
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for grep &prime, ($_ X*+ 9,7,3,1) {
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for grep &prime, ($_ X*+ 9,7,3,1) {
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for grep &prime, ($_ X*+ 9,7,3,1) {
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for grep &prime, ($_ X*+ 9,7,3,1) {
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return $_;
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}
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}
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}
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}
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}
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}
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}
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say "Highest ltp: ", ltp;
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say "Highest rtp: ", rtp;
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say "Highest ltp = ", ltp[5][*-1];
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say "Highest rtp = ", rtp[5][*-1];
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@ -1,11 +1,11 @@
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/*REXX pgm finds largest left- and right-truncatable primes < 1 million.*/
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parse arg high .; if high=='' then high=1000000 /*assume 1 million.*/
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/*REXX pgm finds largest left- & right-truncatable primes ≤1m (or arg1).*/
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parse arg high .; if high=='' then high=1000000 /*assume 1 million.*/
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!.=0; Lp=0; Rp=0; w=length(high) /*placeholders for primes, Lp, Rp*/
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p.1=2; p.2=3; p.3=5; p.4=7; p.5=11; p.6=13; p.7=17 /*some low primes.*/
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!.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1 /*low prime flags.*/
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n=7; s.n=p.n**2 /*number of primes so far. */
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@.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17 /*some low primes. */
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!.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1 /*low prime flags. */
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#=7; s.#=@.#**2 /*number of primes so far, prime²*/
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/*───────────────────────────────────────generate more primes ≤ high. */
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do j=p.n+2 by 2 to high /*only find odd primes from here.*/
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do j=@.#+2 by 2 to high /*only find odd primes from here.*/
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if j//3 ==0 then iterate /*is J divisible by three? */
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if right(j,1)==5 then iterate /*is the right-most digit a "5" ?*/
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if j//7 ==0 then iterate /*is J divisible by seven? */
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@ -13,29 +13,29 @@ n=7; s.n=p.n**2 /*number of primes so far. */
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if j//13 ==0 then iterate /*is J divisible by thirteen? */
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/*[↑] above five lines saves time*/
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do k=7 while s.k<=j /*divide by known odd primes. */
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if j//p.k==0 then iterate j /*Is J divisible by X? ¬ prime.*/
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if j//@.k==0 then iterate j /*Is J divisible by X? ¬ prime.*/
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end /*k*/
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n=n+1 /*bump number of primes found. */
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p.n=j; s.n=j*j /*assign to sparse array; prime².*/
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#=#+1 /*bump number of primes found. */
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@.#=j; s.#=j*j /*assign to sparse array; prime².*/
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!.j=1 /*indicate that J is a prime.*/
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end /*j*/
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/*─────────────────────────────────────find largest left truncatable P. */
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do L=n by -1 for n; if pos(0,p.L)\==0 then iterate
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do k=1 for length(p.L)-1; _=right(p.L,k) /*L truncate #.*/
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do L=# by -1 for #; if pos(0,@.L)\==0 then iterate
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do k=1 for length(@.L)-1; _=right(@.L,k) /*L truncate #.*/
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if \!._ then iterate L /*Truncated # ¬prime? Skip it.*/
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end /*k*/
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leave /*leave the DO loop, we found one*/
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end /*L*/
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/*─────────────────────────────────────find largest right truncatable P.*/
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do R=n by -1 for n; if pos(0,p.R)\==0 then iterate
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do k=1 for length(p.R)-1; _=left(p.R,k) /*R truncate #.*/
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do R=# by -1 for #; if pos(0,@.R)\==0 then iterate
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do k=1 for length(@.R)-1; _=left(@.R,k) /*R truncate #.*/
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if \!._ then iterate R /*Truncated # ¬prime? Skip it.*/
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end /*k*/
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leave /*leave the DO loop, we found one*/
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end /*R*/
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/*───────────────────────────────────────show largest left/right trunc P*/
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say 'The last prime found is ' p.n " (there are" n 'primes ≤' high")."
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say 'The last prime found is ' @.# " (there are" # 'primes ≤' high")."
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say copies('─',70) /*show a separator line. */
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say 'The largest left-truncatable prime ≤' high " is " right(p.L,w)
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say 'The largest right-truncatable prime ≤' high " is " right(p.R,w)
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say 'The largest left-truncatable prime ≤' high " is " right(@.L,w)
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say 'The largest right-truncatable prime ≤' high " is " right(@.R,w)
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/*stick a fork in it, we're done.*/
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