Additive Primes amongst first x Primes

Question

Definition of Additive Primes:

• Numbers which have exactly 2 divisors are called Prime numbers.

• Numbers which are prime and their sum of digits is also a prime number are called Additive Primes

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Task:

Given an integer x, compute all the additive primes amongst the first x prime numbers, with 2 being considered both the first prime and additive prime number. The numbers are represented in base 10.

Rules:

• The output consists of all the additive primes amongst the first x primes
• 0 < x < 151, for this challenge, for functionality purposes
• Since the additive primes are all integers, decimals are not allowed (e.g.: you should output 2, not 2.0) and they must not be displayed as a fraction.

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Examples:

10 -> 2 3 5 7 11 23 29

Explanation:

The first 10 primes are 2 3 5 7 11 13 17 19 23 29, and only 2 3 5 7 11 23 29 have their sum of digits prime numbers, those being, respectively 2,3,5,7,2,5,11, so they are additive primes

Following the explanation from example 1, other test cases may be:

2 -> 2 3

25 -> 2 3 5 7 11 23 29 41 43 47 61 67 83 89

7 -> 2 3 5 7 11

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Leaderboard:

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NOTE: Please read the newly-edited rule 1, it brings changes to the output format slightly

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Your code should be as short as possible, since this is code-golf, so the shortest answer in bytes wins. Good luck!

Answer 1

Röda, 136 135 bytes

f n{P=[2]S=[2]seq 3,863|{|i|{P|{P+=i;s=0;((""..i)/"")|parseInteger _|s+=_;S+=i if[s in P and not(i in S)]}if{|p|[i%p>0]}_}if[#P<n]}_;S}

Try it online!

It's a function that returns the requested additive primes.

Usage: main { f(25) | print ap for ap } The code uses version 0.12, which is in branch roda-0.12.

Ungolfed:

function f(n) {
    primes := [2]
    ultraprimes := [2]
    seq(3, 863) | for i do
        break if [ #primes = n ]
        if [ i%p != 0 ] for p in primes do
            primes += i
            sum := 0
            ((""..i)/"") | parseInteger _ | sum += digit for digit
            ultraprimes += i if [ sum in primes and not (i in ultraprimes) ]
        done
    done
    ultraprimes
}

Answer 2

Pyke, 9 7 bytes

~p>#Yss

Try it online!

The single byte is_prime was only pushed 3 hours ago. Github commit.

~p      -    All the prime numbers
  >     -   first input of them
   #Yss -  filter(^)
    Y   -     digits(^)
     s  -    sum(^)
      s -   is_prime(^)

Answer 3

Python 2, 124 118 bytes

With help from Riker:

n,f,P=input(),filter,lambda n:all(n%i for i in range(2,n))
f(lambda x:P(sum(map(int,`x`)))&P(x),f(P,range(2,n*n))[:n])

Original:

n,o,c,P=input(),0,2,lambda n:all(n%i for i in range(2,n))
while o<n:
 o+=P(c)
 if P(sum(map(int,`c`)))and P(c):print c
 c+=1

Checking primality in Python ain't fun.

Answer 4

Perl 6, 53 bytes

{grep *.comb.sum.is-prime,grep(*.is-prime,0..*)[^$_]}

Try it

Expanded:

{
  grep
    *.comb.sum.is-prime, # find the ultra primes from:
    grep(
      *.is-prime,        # find the primes
      0..*               # from all integers
    )[ ^$_ ]             # grab only the first x primes
}

If this challenge were changed so that you took the first x ultraprimes this could be shortened to just

{grep({($_&.comb.sum).is-prime},0..*)[^$_]}

Answer 5

Python 2, 96 87 bytes

p=-input(),0;m=k=1
while sum(p):
 m*=k*k;k+=1;p+=m%k,
 if m%k*p[int(`k`,36)%35]:print k

Thanks to @xnor for golfing off 9 bytes!

Try it online!

Answer 6

Mathematica, 61 47 bytes

Prime@Range@#~Select~PrimeQ@*Tr@*IntegerDigits&

Answer 7

Jelly, 10 bytes

ÆNDS$€ĖÆPM

Try it online!

How?

A slightly different approach...

ÆNDS$€ĖÆPM - Main link: n (>0)           e.g. 10
ÆN         - nth prime number                 29
     €     - for each in range(1,nth prime)   [1,    2,    3,   ..., 27,    28,     29]
    $      - last two links as a monad
  D        -     decimal digit list          [[1],  [2],  [3],  ...,[2,7], [2,8],  [2,9]]
   S       -     sum                          [1,    2,    3,   ..., 9,     10,     11]
      Ė    - enumerate                       [[1,1],[2,2],[3,3],...,[9,27],[10,28],[11,29]]
       ÆP  - is prime? (vectorises)          [[0,0],[1,1],[1,1],...,[0,1], [0,0],  [1,1]]
         M - indices of maximal elements     [       2,    3,   ...,                29]

Answer 8

05AB1E, 9 bytes

ÝبvySOp—

Uses the CP-1252 encoding. Try it online!

Answer 9

Jelly, 11 bytes

ÆN€DS$ÆP$Ðf

Try it online!

Explanation:

ÆN€DS$ÆP$Ðf Main link (args: z)
ÆN€         Generate first z primes.
   DS$      Take the digital sum.
      ÆP    Check if it's prime.
        $   Join last two links and make a monad.
         Ðf Only keep elements which conform to the criterion above.

I got outgolfed.

Answer 10

MATL, 15 13 bytes

2 bytes saved thanks to @Luis

:Yq"@V!UsZp?@

Try it at MATL Online

Explanation

        % Implicitly grab input as a number (N)
:       % Create an array [1...N]
Yq      % Get the k-th prime for each element k in that array
"       % For each element in this list
  @     % Get the current element
  V!U   % Break it into digits
  s     % Sum up the digits
  Zp    % Determine if this is a prime number
  ?@    % If it is, push the value to the stack
        % Implicit end of for loop and implicit display of the stack

Answer 11

Fig, \$12\log_{256}(96)\approx\$ 9.877 bytes

FtxFmC@p'pSf

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Explanation:

 t            # take the first
  x           # x items from
    mC        # all positive integers
   F          # filtered by
      @p      # is prime,
F       '     # then filter those by
          S   # the sum of
           f  # the digits
         p    # is prime

Answer 12

Bash + coreutils, 97 bytes

p()(factor $1|wc -w)
for((;++n,c<$1;)){((`p $n`-2||(c++,`p $[n%10+n/10%10+n/100]`-2)))||echo $n;}

Try it online!

Answer 13

Ohm, 10 bytes (CP437)

@▓_π;░_}Σp

This would be much shorter if I had vectorization or a component for the first N primes, but alas, I did not before this challenge (but I do now!).

Explanation:

@▓_π;░_}Σp    Main wire, arguments: a

@▓  ;         Map...over the range (1..n)
  _π            nth prime
     ░        Select from ToS where...
      _}Σ       The sum of all digits
         p      is prime

Answer 14

PowerShell, 120 bytes

for($n=$args[0];$n){for(;'1'*++$i-notmatch($s='^(?!(..+)\1+$)..')){}if('1'*([char[]]"$i"-join'+'|iex)-match$s){$i};$n--}

Try it online!

Prime checking in PowerShell sucks.

The outer for loop goes from input $n down to 0. In the inner loop, we use a prime generator on $i, then check if the digit-sum (-join'+'|iex) is also a prime. If so, we put $i on the pipeline. In either case, we decrement $n-- and the outer for loop continues. The resulting $is are gathered from the pipeline and an implicit Write-Output happens at program completion.

Answer 15

Bash + GNU utilities + bsd-games package, 69

primes 2|sed -rn 'h;s/./ + &/g;s/.*/expr &|factor/e;/\w\s/!{x;p};'$1q

Try it online.

Answer 16

Pari/GP, 59 bytes

f(x)=[p|p<-vector(x,i,prime(i)),isprime(vecsum(digits(p)))]

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Answer 17

Vyxal, 5 bytes

ʁǎ'∑æ

Try it online, or verify more test cases.

Explanation:

ʁ      # Range from 0 to n-1
 ǎ     # Nth prime (vectorising)
  '    # Filtered by:
   ∑   #   The digit sum
    æ  #   Is prime

Answer 18

MathGolf, 9 bytes

♪╒g¶<gÅΣ¶

Try it online.

Explanation:

Since the input is guaranteed to be within the range \$[1,150]\$, where the \$150^{th}\$ prime is \$877\$, we'll use this to our advantage. (Although using ó (\$2^n\$ builtin using the implicit input) instead of ♪ would have worked as well, but would be way too slow for larger inputs.)

♪╒         # Push a list in the range [1,1000]
  g        # Filter it by:
   ¶       #  Check if the number is a prime
    <      # Then only keep the first (implicit) input amount of prime numbers
     g     # Filter it again,
      Å    # using 2 characters as inner code-block:
       Σ   #  Get the digit-sum of the current integer
        ¶  #  Check if it's also a prime
           # (after which the entire stack is output implicitly as result)

Answer 19

Husk, 8 bytes

fȯṗΣd↑İp

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Answer 20

Japt, 12 bytes

Èj}jU fÈìx j

Try it

Answer 21

Factor + math.primes math.unicode math.text.utils, 47 bytes

[ nprimes [ 1 digit-groups Σ prime? ] filter ]

Try it online!

Explanation:

It's a quotation (anonymous function) that takes an integer from the data stack as input and leaves a sequence of integers on the data stack as output.

• nprimes Obtain a list of the first n primes.
• [ ... ] filter Take elements from the list that match a predicate.
• 1 digit-groups Obtain a list of digits from an integer.
• Σ Sum a sequence.
• prime? Is it prime?

Answer 22

05AB1E, 6 bytes

ÅpʒSOp

Try it online or verify all test cases.

Explanation:

Åp      # Get a list of the first (implicit) input amount of primes
  ʒ     # Filter this list by:
   S    #  Convert the prime to a list of digits
    O   #  Sum them together
     p  #  Check if this sum is a prime
        # (after which the filtered list is output implicitly as result)

Answer 23

MATL, 13 bytes

:YqtFYA!XsZp)

Try it at MATL Online!

Explanation

:      % Range [1 2 ... n], where n is implicit input
Yq     % Array of first n prime numbers
t      % Duplicate
FYA    % Convert to decimal digits. Gives a matrix, where each original 
       % number corresponds to a row. Left-pads with zeros if needed
!Xs    % Sum of rows
Zp     % Is prime? (element-wise)
)      % Use as logical index into the array of the first n prime numbers
       % Implicitly display