Next special primes
- Task
n is smallest prime such that the difference of successive terms is strictly increasing,
where n < 1050.
REXX
<lang rexx>/*REXX program finds next special primes: difference of successive terms is increasing.*/ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1050 /* " " " " " " */ if cols== | cols=="," then cols= 10 /* " " " " " " */ call genP /*build array of semaphores for primes.*/ w= 10 /*width of a number in any column. */
@nsp= ' next special primes < ' commas(hi) ,
" such that the different of successive terms is increasing"
if cols>0 then say ' index │'center(@nsp , 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') op= @.1 /*assign oldPrime to the first prime.*/ nsp= 0; idx= 1 /*initialize number of nsp and index.*/ $= /*a list of nice primes (so far). */
do j=1; np= op + j /*assign newPrime to oldPrime + j */
if np>=hi then leave /*Is newPrime ≥ hi? Then leave loop. */
if \!.np then iterate /*Is np a prime? Then skip this J.*/
nsp= nsp + 1 /*bump the number of nsp's. */
op= np /*set oldPrime to the value of newPrime*/
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(np) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add a nice prime ──► list, allow big#*/
if nsp//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ say say 'Found ' commas(nsp) @nsp exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: !.= 0 /*placeholders for primes (semaphores).*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; s.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 to hi /*find odd primes from here on. */
parse var j -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
/* [↑] the above five lines saves time*/
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return</lang>
- output when using the default inputs:
index │ next special primes < 1,050 such that the different of successive terms is increasing ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 3 5 11 19 29 41 59 79 101 127 11 │ 157 191 227 269 313 359 409 461 521 587 21 │ 659 733 809 887 967 1,049 Found 26 next special primes < 1,050 such that the different of successive terms is increasing
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl
row = 0 num = null limit1 = 100 nextPrime = 2 oldPrime = 2
for n = 1 to limit1
nextPrime = oldPrime + n
if isprime(nextPrime)
row = row + 1
see "" + nextPrime + " "
if (row%5) = 0
see nl
ok
oldPrime = nextPrime
ok
next
see nl + "done..." + nl
</lang>
- Output:
working... 3 5 11 19 29 41 59 79 101 127 157 191 227 269 313 359 409 461 521 587 659 733 809 887 967 1049 done...