Extra primes: Difference between revisions

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991st through 1000th: 25337353 25353227 25353373 25353577 25355227 25355333 25355377 25357333 25357357 25357757
991st through 1000th: 25337353 25353227 25353373 25353577 25355227 25355333 25355377 25357333 25357357 25357757
Crossing 10th order of magnitude: 777777227 777777577 777777773 2222222377 2222222573 2222225273</pre>
Crossing 10th order of magnitude: 777777227 777777577 777777773 2222222377 2222222573 2222225273</pre>

=={{header|REXX}}==
<lang rexx></lang>
ooooooooooooooooooooooooooo
<pre>

</pre>


=={{header|Ring}}==
=={{header|Ring}}==

Revision as of 03:49, 2 December 2020

Extra primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Definition

n is an extra prime if n is prime and its digits and sum of digits are also primes.

Task

Show the extra primes under 10000

Reference

OEIS:A062088 - Primes with every digit a prime and the sum of the digits a prime.

Related tasks


Factor

Translation of: Wren
Works with: Factor version 0.99 2020-08-14

<lang factor>USING: formatting io kernel math math.functions math.primes sequences sequences.extras ;

digit ( seq seq -- seq ) [ suffix ] cartesian-map concat ;
front ( -- seq ) { { 2 } { 3 } { 5 } { 7 } } ;
middle ( seq -- newseq ) { 2 3 5 7 } digit ;
end ( seq -- newseq ) { 3 7 } digit ;
candidates ( -- seq )
   front
   front end
   front middle end
   front middle middle end
   append append append ;
digits>number ( seq -- n )
   <reversed> 0 [ 10^ * + ] reduce-index ;

"The extra primes with up to 4 digits are:" print candidates [ sum prime? ] filter [ digits>number ] [ prime? ] map-filter [ 1 + swap "%2d: %4d\n" printf ] each-index</lang>

Output:
The extra primes with up to 4 digits are:
 1:    2
 2:    3
 3:    5
 4:    7
 5:   23
 6:  223
 7:  227
 8:  337
 9:  353
10:  373
11:  557
12:  577
13:  733
14:  757
15:  773
16: 2333
17: 2357
18: 2377
19: 2557
20: 2753
21: 2777
22: 3253
23: 3257
24: 3323
25: 3527
26: 3727
27: 5233
28: 5237
29: 5273
30: 5323
31: 5527
32: 7237
33: 7253
34: 7523
35: 7723
36: 7727

Phix

Minor reworking of Numbers_with_prime_digits_whose_sum_is_13#Phix#iterative <lang Phix>constant lim = 99999999, -- (erm, the real limit is actually (lim+1)*10) 

        dgts = {2,3,5,7}

function extra_primes() 

   sequence res = {}, q = Template:0,0
   integer s, -- partial digit sum
           v  -- corresponding value
   while length(q) do
       {s,v} = q[1]
       q = q[2..$]
       for i=1 to length(dgts) do
           integer d = dgts[i], {ns,nv} = {s+d,v*10+d}
           if is_prime(ns) and is_prime(nv) then res &= nv end if
           if nv<lim then q &= Template:Ns,nv end if
       end for
   end while
   return res

end function

printf(1,"Extra primes < %,d:\n",{(lim+1)*10}) sequence res = extra_primes() printf(1,"[1..37]: %s\n",ppf(res[1..37],{pp_Indent,9,pp_Maxlen,94})) printf(1,"[991..1000]: %v\n",{res[991..1000]}) integer l = length(res) printf(1,"[%d..%d]: %v\n",{l-8,l,res[l-8..l]})</lang>

Output:
Extra primes < 1,000,000,000:
[1..37]: {2,3,5,7,23,223,227,337,353,373,557,577,733,757,773,2333,2357,2377,2557,2753,2777,
          3253,3257,3323,3527,3727,5233,5237,5273,5323,5527,7237,7253,7523,7723,7727,22573}
[991..1000]: {25337353,25353227,25353373,25353577,25355227,25355333,25355377,25357333,25357357,25357757}
[9050..9058]: {777755753,777773333,777773753,777775373,777775553,777775577,777777227,777777577,777777773}

Raku

For the time being, (Doctor?), I'm going to assume that the task is really "Sequence of primes with every digit a prime and the sum of the digits a prime". Outputting my own take on a reasonable display of results, compact and easily doable but exercising it a bit.

<lang perl6>my @ppp = lazy flat 2, 3, 5, 7, 23, grep { .is-prime && .comb.sum.is-prime }, 

              flat (2..*).map: { flat ([X~] (2, 3, 5, 7) xx $_) X~ (3, 7) };

put 'First 20 terms: '.fmt('%34s'), @ppp[^20]; put '991st through 1000th: '.fmt('%34s'), @ppp[990 .. 999]; put 'Crossing 10th order of magnitude: ', @ppp[9055..9060];</lang>

Output:
                  First 20 terms: 2 3 5 7 23 223 227 337 353 373 557 577 733 757 773 2333 2357 2377 2557 2753
            991st through 1000th: 25337353 25353227 25353373 25353577 25355227 25355333 25355377 25357333 25357357 25357757
Crossing 10th order of magnitude: 777777227 777777577 777777773 2222222377 2222222573 2222225273

REXX

<lang rexx></lang> ooooooooooooooooooooooooooo

Ring

<lang ring> load "stdlib.ring"

limit = 10000 num = 0 for n = 1 to limit 

   x1 = prime1(n)
   x2 = prime2(n)
   x3 = isprime(n)
   if x1 = 1 and x2 = 1 and x3
      num = num + 1
      see "The " + num + "th Extra Prime is: " + n + nl
   ok

next

func prime1(x) 

    pstr = string(x)
    len = len(pstr)
    count = 0
    for n = 1 to len 
        if isprime(number(pstr[n]))
           count = count + 1
        ok
    next
    if count = len 
       return 1
    else
       return 0
    ok

func prime2(x) 

    pstr = string(x)
    len = len(pstr)
    sum = 0
    for n = 1 to len
        sum = sum + number(pstr[n])
    next
    if isprime(sum)
       return 1
    else
       return 0
    ok

</lang> Output: 

The 1th Extra Prime is: 2
The 2th Extra Prime is: 3
The 3th Extra Prime is: 5
The 4th Extra Prime is: 7
The 5th Extra Prime is: 23
The 6th Extra Prime is: 223
The 7th Extra Prime is: 227
The 8th Extra Prime is: 337
The 9th Extra Prime is: 353
The 10th Extra Prime is: 373
The 11th Extra Prime is: 557
The 12th Extra Prime is: 577
The 13th Extra Prime is: 733
The 14th Extra Prime is: 757
The 15th Extra Prime is: 773
The 16th Extra Prime is: 2333
The 17th Extra Prime is: 2357
The 18th Extra Prime is: 2377
The 19th Extra Prime is: 2557
The 20th Extra Prime is: 2753
The 21th Extra Prime is: 2777
The 22th Extra Prime is: 3253
The 23th Extra Prime is: 3257
The 24th Extra Prime is: 3323
The 25th Extra Prime is: 3527
The 26th Extra Prime is: 3727
The 27th Extra Prime is: 5233
The 28th Extra Prime is: 5237
The 29th Extra Prime is: 5273
The 30th Extra Prime is: 5323
The 31th Extra Prime is: 5527
The 32th Extra Prime is: 7237
The 33th Extra Prime is: 7253
The 34th Extra Prime is: 7523
The 35th Extra Prime is: 7723
The 36th Extra Prime is: 7727

Wren

Library: Wren-math
Library: Wren-fmt

Unsure of the task - see talk page. <lang ecmascript>import "/math" for Int import "/fmt" for Fmt

var digits = [2, 3, 5, 7] // the only digits which are primes var digits2 = [3, 7] // a prime > 5 can't end in 2 or 5 var candidates = [[2, 2], [3, 3], [5, 5], [7, 7]] // [number, sum of its digits]

for (a in digits) { 

   for (b in digits2) candidates.add([10*a + b, a + b])

}

for (a in digits) { 

   for (b in digits) {
      for (c in digits2) candidates.add([100*a + 10*b + c, a + b + c])
   }

}

for (a in digits) { 

   for (b in digits) {
       for (c in digits) {
           for (d in digits2) candidates.add([1000*a + 100*b + 10*c + d, a + b + c + d])
       }
   }

}

System.print("The extra primes with up to 4 digits are:") var count = 0 for (cand in candidates) { 

  if (Int.isPrime(cand[0]) && Int.isPrime(cand[1])) {
     count = count + 1
     Fmt.print("$2d: $4d", count, cand[0])
  }

}</lang>

Output:
The extra primes with up to 4 digits are:
 1:    2
 2:    3
 3:    5
 4:    7
 5:   23
 6:  223
 7:  227
 8:  337
 9:  353
10:  373
11:  557
12:  577
13:  733
14:  757
15:  773
16: 2333
17: 2357
18: 2377
19: 2557
20: 2753
21: 2777
22: 3253
23: 3257
24: 3323
25: 3527
26: 3727
27: 5233
28: 5237
29: 5273
30: 5323
31: 5527
32: 7237
33: 7253
34: 7523
35: 7723
36: 7727
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