Data update
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Ingy döt Net
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2347 changed files with 62432 additions and 16731 deletions
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@ -1,13 +1,8 @@
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fastfunc prime n .
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if n mod 2 = 0 and n > 2
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return 0
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.
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if n mod 2 = 0 and n > 2 : return 0
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i = 3
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sq = sqrt n
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while i <= sq
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if n mod i = 0
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return 0
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.
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while i <= sqrt n
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if n mod i = 0 : return 0
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i += 2
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.
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return 1
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@ -22,14 +17,10 @@ func cycle n .
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return m + n mod p * 10
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.
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func circprime p .
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if prime p = 0
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return 0
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.
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if prime p = 0 : return 0
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p2 = cycle p
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while p2 <> p
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if p2 < p or prime p2 = 0
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return 0
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.
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if p2 < p or prime p2 = 0 : return 0
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p2 = cycle p2
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.
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return 1
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@ -37,7 +28,7 @@ func circprime p .
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p = 2
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while count < 19
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if circprime p = 1
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print p
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write p & " "
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count += 1
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.
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p += 1
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@ -1,37 +0,0 @@
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/*REXX program finds & displays circular primes (with a title & in a horizontal format).*/
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parse arg N hp . /*obtain optional arguments from the CL*/
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if N=='' | N=="," then N= 19 /* " " " " " " */
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if hp=='' | hp=="," then hip= 1000000 /* " " " " " " */
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call genP /*gen primes up to hp (200,000). */
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q= 024568 /*digs that most circular P can't have.*/
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found= 0; $= /*found: circular P count; $: a list.*/
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do j=1 until found==N; p= @.j /* [↓] traipse through all the primes.*/
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if p>9 & verify(p, q, 'M')>0 then iterate /*Does J contain forbidden digs? Skip.*/
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if \circP(p) then iterate /*Not circular? Then skip this number.*/
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found= found + 1 /*bump the count of circular primes. */
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$= $ p /*add this prime number ──► $ list. */
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end /*j*/ /*at this point, $ has a leading blank.*/
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say center(' first ' found " circular primes ", 79, '─')
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say strip($)
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exit 0 /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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circP: procedure expose @. !.; parse arg x 1 ox /*obtain a prime number to be examined.*/
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do length(x)-1; parse var x f 2 y /*parse X number, rotating the digits*/
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x= y || f /*construct a new possible circular P. */
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if x<ox then return 0 /*is number < the original? ¬ circular*/
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if \!.x then return 0 /* " " not prime? ¬ circular*/
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end /*length(x)···*/
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return 1 /*passed all tests, X is a circular P.*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; @.8=19 /*assign Ps; #Ps*/
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!.= 0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1; !.19=1 /* " primality*/
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#= 8; sq.#= @.# **2 /*number of primes so far; prime square*/
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do j=@.#+4 by 2 to hip; parse var j '' -1 _ /*get last decimal digit of J. */
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if _==5 then iterate; if j// 3==0 then iterate; if j// 7==0 then iterate
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if j//11==0 then iterate; if j//13==0 then iterate; if j//17==0 then iterate
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do k=8 while sq.k<=j /*divide by some generated odd primes. */
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if j // @.k==0 then iterate j /*Is J divisible by P? Then not prime*/
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end /*k*/ /* [↓] a prime (J) has been found. */
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#= #+1; !.j= 1; sq.#= j*j; @.#= j /*bump P cnt; assign P to @. and !. */
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end /*j*/; return
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@ -1,6 +1,9 @@
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-- 8 May 2025
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include Settings
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say version; say 'Circular primes'; say
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say 'CIRCULAR PRIMES'
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say version
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say
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call First19
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call Next3
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call HigherReps
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@ -13,7 +16,7 @@ numeric digits 10
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say 'First 19 circular primes:'
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p = Primes(200000)
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do i = 1 to p
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a = prim.prime.i
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a = prim.i
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if Verify(a,'024568','m') > 0 then
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iterate i
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b = a; l = Length(b)
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@ -21,7 +24,7 @@ do i = 1 to p
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b = Right(b,l-1)||Left(b,1)
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if b < a then
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iterate i
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if \ prime(b) then
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if \ Prime(b) then
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iterate i
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end
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call Charout ,a' '
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@ -38,8 +41,8 @@ numeric digits 320
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say 'Next 3 circular primes:'
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do i = 7 to 320
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r = Repunit(i)
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if prime(r) then
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call charout ,'R('i') '
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if Prime(r) then
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call Charout ,'R('i') '
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end
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say
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say Format(Time('e'),,3) 'seconds'
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@ -51,7 +54,7 @@ procedure expose glob.
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call Time('r')
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numeric digits 1040
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say 'Primality of R(1031):'
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if prime(Repunit(1031)) then
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if Prime(Repunit(1031)) then
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say 'R(1031) is probable prime'
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else
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say 'R(1031) is composite'
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@ -59,14 +62,8 @@ say Format(Time('e'),,3) 'seconds'
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say
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return
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Repunit:
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/* Repeat 1's function */
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procedure expose glob.
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arg x
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/* Formula */
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return Copies('1',x)
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include Functions
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include Special
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include Numbers
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include Sequences
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include Abend
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82
Task/Circular-primes/Scheme/circular-primes.scm
Normal file
82
Task/Circular-primes/Scheme/circular-primes.scm
Normal file
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@ -0,0 +1,82 @@
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(import srfi-1)
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; rotate list by n
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(define (rotate lst n)
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(if (> n 0)
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(append (drop lst n) (take lst n))
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(append (take-right lst (abs n)) (drop-right lst (abs n)))))
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; prime check
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(define (prime? n)
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(if (< n 4) (> n 1)
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(and (odd? n)
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(let loop ((k 3))
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(or (> (* k k) n)
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(and (positive? (remainder n k))
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(loop (+ k 2))))))))
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; returns number rotated in lists
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(define (circ_lists lst)
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(let
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(
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(len (length lst))
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)
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(do (
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(remaining 1 (+ 1 remaining))
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(circs '() (cons (rotate lst remaining) circs ))
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)
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((< len remaining) circs)
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)
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)
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)
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; helper function to make number a list to rotate it
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(define (number->list x)
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(string->list (number->string x))
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)
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; returns list to number
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(define (list->number x)
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(string->number (list->string x))
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)
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; checks if number is prime when the number is turned into lists
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(define (check x)
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(not (member #f (map prime? (map list->number (circ_lists (number->list x))))))
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)
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; all permutations of a number
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(define (perms x)
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(map list->number (circ_lists (number->list x)))
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)
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(define limit 19)
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; checks if all permutations of x are not in lst
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(define (not_perm x lst)
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(equal? '() (filter-map (lambda (x) (not (equal? #f x)))
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(map (lambda (x) (member x lst)) (perms x))))
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)
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(define (circular_primes x lst)
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(cond
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(
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(< (length lst) limit)
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; if is true if all permutations are prime and if all permutations are not already in the lst, which is returned
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(if (and (equal? #t (check x)) (equal? #t (not_perm x lst)))
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(circular_primes (+ x 1) (cons x lst))
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(circular_primes (+ x 1) lst)
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)
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)
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(
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lst
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)
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)
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)
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(display (reverse (circular_primes 2 '())))
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(newline)
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