Erdős-primes
In mathematics, Erdős-primes are prime numbers which sum of digits are also primes.
- Definitions
- Task
Write a program to determine (and show here) all Erdős-primes whose elements are less than 500.
Optionally, show the number of Erdős-primes.
Julia
<lang julia>using Primes
let
p = primesmask(500) println("Erdős primes under 500:") pcount = 0 for i in 2:499 if p[i] && p[sum(digits(i))] pcount += 1 print(lpad(i, 4), pcount % 20 == 0 ? "\n" : "") end end println("\n\n$pcount Erdős primes found.")
end
</lang>
- Output:
Erdős primes under 500: 2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487 54 Erdős primes found.
REXX
<lang rexx>/*REXX program counts and shows the number of Erdős primes under a specified number N. */ parse arg n cols . /*get optional number of primes to find*/ if n== | n=="," then n= 500 /*Not specified? Then assume default.*/ if cols== | cols=="," then cols= 10 /* " " " " " .*/ Ocols= cols; cols= abs(cols) /*Use the absolute value of cols. */ call genP n /*generate all primes under N. */ primes= 0 /*initialize the number of Erdős primes*/ $= /*a list of Erdős primes (so far). */
do j=1 until j>=n; if \!.j then iterate /*Is J not a prime? Then skip it. */ _= sumDigs(j); if \!._ then iterate /*Is sum of J's digs a prime? No, skip.*/ primes= primes + 1 /*bump the count of Erdős primes. */ if Ocols<1 then iterate /*Build the list (to be shown later)? */ $= $ right(j, w) /*add the Erdős prime to the $ list. */ if primes//cols\==0 then iterate /*have we populated a line of output? */ say substr($, 2); $= /*display what we have so far (cols). */ end /*j*/
if $\== then say substr($, 2) /*possible display some residual output*/ say say 'found ' primes " Erdős primes < " n exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sumDigs: parse arg x 1 s 2; do k=2 for length(x)-1; s= s + substr(x,k,1); end; return s /*──────────────────────────────────────────────────────────────────────────────────────*/ genP: parse arg n; @.=.; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; #= 7
w= length(n); !.=0; !.2=1; !.3=1; !.5=1; !.7=1; !.11=1; !.13=1; !.17=1 do j=@.7+2 by 2 while j<n /*continue on with the next odd prime. */ parse var j -1 _ /*obtain the last digit of the J var.*/ if _ ==5 then iterate /*is this integer a multiple of five? */ if j // 3 ==0 then iterate /* " " " " " " three? */ /* [↓] divide by the primes. ___ */ do k=4 to # while k*k<=j /*divide J by other primes ≤ √ J */ if j//@.k == 0 then iterate j /*÷ by prev. prime? ¬prime ___ */ end /*k*/ /* [↑] only divide up to √ J */ #= # + 1; @.#= j; !.j= 1 /*bump prime count; assign prime & flag*/ end /*j*/ return</lang>
- output when using the default inputs:
2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487 found 54 Erdős primes < 500
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl see "Erdős-primes are:" + nl
row = 0 limit = 500
for n = 1 to limit
num = 0 if isprime(n) strn = string(n) for m = 1 to len(strn) num = num + number(strn[m]) next if isprime(num) row = row + 1 see "" + n + " " if row%10 = 0 see nl ok ok ok
next
see nl + "found " + row + " Erdös-primes." + nl see "done..." + nl </lang>
- Output:
working... Erdős-primes are: 2 3 5 7 11 23 29 41 43 47 61 67 83 89 101 113 131 137 139 151 157 173 179 191 193 197 199 223 227 229 241 263 269 281 283 311 313 317 331 337 353 359 373 379 397 401 409 421 443 449 461 463 467 487 found 54 Erdös-primes. done...