Is it a super-prime?

Question

Background

A super-prime is a prime number whose index in the list of all primes is also prime. The sequence looks like this:

3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, ...

Challenge

Given a positive integer, determine whether it is a super-prime.

Test Cases

2: false
3: true
4: false
5: true
7: false
11: true
13: false
17: true
709: true
851: false
991: true

Scoring

This is code-golf, so the shortest answer in each language wins.

First thought after reading what a super-prime is: What would you call super-super-primes? Or super^3-primes? What is bigger, the number of atoms in the universe or the 11th super^11-prime? You, dear internet person, are stealing another few hours of my hours of my prime time! — J_F_B_M, Jul 8 '17 at 19:28
@J_F_B_M 11 is a super-prime who's index in the super-prime list is also a super-prime (3), so the 11'th super-prime is a super-super-super-prime — Skidsdev, Jul 10 '17 at 8:33

Dennis · Accepted Answer · 2017-07-07 21:51:00Z

21

Jelly, 5 bytes

ÆRÆNċ

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How it works

ÆRÆNċ  Main link. Argument: n

ÆR     Prime range; yield the array of all primes up to n.
  ÆN   N-th prime; for each p in the result, yield the p-th prime.
    ċ  Count the occurrences of n.

edited Jul 7 '17 at 21:51

answered Jul 7 '17 at 21:48

Dennis

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8

\$\begingroup\$ Gosh darn it, you win again... \$\endgroup\$ – ETHproductions Jul 7 '17 at 21:50
3

\$\begingroup\$ He always does... \$\endgroup\$ – Gryphon Jul 8 '17 at 4:20
\$\begingroup\$ @ETHproductions Well, solution is pretty obvious...it's just the ninja here. \$\endgroup\$ – Erik the Outgolfer Jul 8 '17 at 13:52

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Martin Ender · Accepted Answer · 2017-07-08 06:39:23Z

14

Mathematica, 26 23 bytes

Thanks to user202729 for saving 3 bytes.

PrimeQ/@(#&&PrimePi@#)&

This makes use of the fact that Mathematica leaves most nonsensical expressions unevaluated (in this case, the logical And of two numbers) and Map can be applied to any expression, not just lists. So we compute the And of the input and its prime index, which just remains like that, and then we Map the primality test over this expression which turns the two operands of the And into booleans, such that the And can then be evaluated.

edited Jul 8 '17 at 6:39

answered Jul 7 '17 at 21:26

Martin Ender

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1

\$\begingroup\$ 23 bytes: PrimeQ/@(#&&PrimePi@#)&. \$\endgroup\$ – user202729 Jul 8 '17 at 3:36
\$\begingroup\$ @user202729 Nice, thank you. :) \$\endgroup\$ – Martin Ender Jul 8 '17 at 6:37

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ETHproductions · Accepted Answer · 2017-07-07 21:35:10Z

Jelly, 6 bytes

ÆRi³ÆP

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Uses the same technique as my Japt answer: Generate the primes up to n, get the index of n in that list, and check that for primality. If n itself is not prime, the index is 0, which is also not prime, so 0 is returned anyway.

ETHproductions · Accepted Answer · 2017-07-07 21:46:07Z

Japt, 13 11 bytes

õ fj bU Ä j

Test it online!

Explanation

This is actually very straight-forward, unlike my original submission:

 õ fj bU Ä  j    
Uõ fj bU +1 j    Ungolfed
                 Implicit: U = input integer
Uõ               Generate the range [1..U].
   fj            Take only the items that are prime.
      bU         Take the (0-indexed) index of U in this list (-1 if it doesn't exist).
         +1 j    Add 1 and check for primality.
                 This is true iff U is at a prime index in the infinite list of primes.
                 Implicit: output result of last expression

C McAvoy · Accepted Answer · 2017-07-07 21:53:47Z

4

Python 3, 104 97 93 bytes

p=lambda m:(m>1)*all(m%x for x in range(2,m))
f=lambda n:p(n)*p(len([*filter(p,range(n+1))]))

Returns 0/1, at most 4 bytes longer if it has to be True/False.

Try it online!

edited Jul 7 '17 at 21:53

answered Jul 7 '17 at 21:45

C McAvoy

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1

\$\begingroup\$ 0/1 is fine. Nice answer! Since you don't ever use the value of f, you can reformat your code like this and exclude it from the byte count. \$\endgroup\$ – musicman523 Jul 7 '17 at 21:57
\$\begingroup\$ @musicman523 Thanks for the tip! \$\endgroup\$ – C McAvoy Jul 9 '17 at 22:22

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Doorknob · Accepted Answer · 2017-07-07 21:28:56Z

Jelly, 7 bytes

ÆCÆPaÆP

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ÆC counts the number of primes less than or equal to the input (so, if the input is the nth prime, it returns n). Then ÆP tests this index for primality. Finally, a does a logical AND between this result and ÆP (primality test) of the original input.

Laikoni · Accepted Answer · 2017-07-07 23:48:39Z

3

Haskell, 62 bytes

p x=2==sum[1|0<-mod x<$>[1..x]]
f x=p$sum[1|y<-[1..x],p y,p x]

Try it online! Usage: f 991 yields True.

answered Jul 7 '17 at 23:48

Laikoni

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Datboi · Accepted Answer · 2017-07-07 21:39:56Z

05AB1E, 6 bytes

ÝØ<Øså

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Explanation

ÝØ<Øså
Ý      # Push range from 0 to input
 Ø     # Push nth prime number (vectorized over the array)
  <    # Decrement each element by one (vectorized)
   Ø   # Push nth prime number again
    s  # swap top items of stack (gets input)
     å # Is the input in the list?

notjagan · Accepted Answer · 2017-07-07 21:48:19Z

2

Pyth, 12 bytes

&P_QP_smP_dS

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Explanation

&P_QP_smP_dS
                Implicit input
       mP_dS    Primality of all numbers from 1 to N
      s         Sum of terms (equal to number of primes ≤ N)
    P_          Are both that number
&P_Q            and N prime?

edited Jul 7 '17 at 21:48

answered Jul 7 '17 at 21:36

notjagan

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Blue · Accepted Answer · 2017-07-07 22:54:22Z

2

Pyke, 8 bytes

sI~p>@hs

Try it here!

s        -  is_prime(input)
 I~p>@hs - if ^:
  ~p>    -    first_n_primes(input)
     @   -    ^.index(input)
      h  -   ^+1
       s -  is_prime(^)

answered Jul 7 '17 at 22:54

Blue

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Sean · Accepted Answer · 2017-07-08 06:26:15Z

2

Perl 6, 46 bytes

{$/=&is-prime;all($_∈*,$/)([grep $/,1..$_])}

Try it online!

edited Jul 8 '17 at 6:26

answered Jul 8 '17 at 4:43

Sean

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steenbergh · Accepted Answer · 2017-07-07 22:02:22Z

QBIC, 33 bytes

~µ:||\_x0]{p=p-µq|~q=a|_xµp]q=q+1

Explanation

~   |   IF   ....  THEN (do nothing)
  :         the number 'a' (read from cmd line) 
 µ |        is Prime
\_x0        ELSE (non-primes) quit, printing 0
]           END IF
{           DO
            In this next bit, q is raised by 1 every loop, and tested for primality. 
            p keeps track of how may primes we've seen (but does so negatively)
    µq|     test q for primality (-1 if so, 0 if not)
p=p-        and subtract that result from p (at the start of QBIC: q = 1, p = 0)
~q=a|       IF q == a
_xµp        QUIT, and print the prime-test over p (note that -3 is as prime as 3 is)
]           END IF
q=q+1       Reaise q and run again.

J42161217 · Accepted Answer · 2017-07-07 22:08:23Z

1

Mathematica, 35 29 bytes

P=Prime;!P@P@Range@#~FreeQ~#&

-6 bytes from @MartinEnder

edited Jul 7 '17 at 22:08

answered Jul 7 '17 at 21:39

J42161217

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\$\begingroup\$ P@P@Range@# should save a bunch. \$\endgroup\$ – Martin Ender Jul 7 '17 at 21:55

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Sergii Martynenko Jr · Accepted Answer · 2017-07-07 22:32:00Z

1

Haskell, 121 bytes

f=filter
p x=2==(length$f(\a->mod(x)a==0)[1..x])
s=map(\(_,x)->x)$f(\(x,_)->p x)$zip[1..]$f(p)[2..]
r x=x`elem`(take x s)

answered Jul 7 '17 at 22:32

Sergii Martynenko Jr

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1

\$\begingroup\$ (\(_,x)->x) is snd, (\(x,_)->p x) is (p.fst). Both fst and snd are in Prelude, so no need for imports. \$\endgroup\$ – Laikoni Jul 7 '17 at 23:52
\$\begingroup\$ Don't use backticks too often: r x=elem x$take x s. However, in this case you can go pointfree (introducing backticks again) and omit the function name: elem<*>(`take`s). \$\endgroup\$ – nimi Jul 8 '17 at 12:32

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HyperNeutrino · Accepted Answer · 2017-07-08 02:30:11Z

1

Positron, 148 bytes

x=#(input@@)a=function{p=1;k=$1==2;f=2;while(f<$1)do{p=p*$1%f;k=1;f=f+1};return p*k}r=1;i=2;while(i<x)do{if(a@i)then{r=r+1}i=i+1}print@((a@x*a@r)>0)

Try it online!

answered Jul 8 '17 at 2:30

HyperNeutrino

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alephalpha · Accepted Answer · 2017-07-08 03:27:55Z

1

Pari/GP, 31 bytes

n->(p=isprime)(n)*p(primepi(n))

Try it online!

answered Jul 8 '17 at 3:27

alephalpha

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Leander Moesinger · Accepted Answer · 2017-07-08 20:00:43Z

1

Matlab, 36 34 bytes

Saved 2 bytes thanks to Tom Carpenter.

A very naive implementation using built-in functions:

isprime(x)&isprime(nzz(primes(x)))

edited Jul 8 '17 at 20:00

answered Jul 8 '17 at 7:18

Leander Moesinger

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1

\$\begingroup\$ For Octave only you can also save a further byte with (p=@isprime)(x)&p(nnz(primes(x))) \$\endgroup\$ – Tom Carpenter Jul 8 '17 at 17:28

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Chas Brown · Accepted Answer · 2017-07-09 20:29:45Z

1

Python 2, 89 bytes

def a(n):
 r=[2];x=2
 while x<n:x+=1;r+=[x]*all(x%i for i in r)
 return{n,len(r)}<=set(r)

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Constructs r, the list of primes <= n; if n is prime, then n is the len(r)'th prime. So n is a super prime iff n in r and len(r) in r.

edited Jul 9 '17 at 20:29

answered Jul 9 '17 at 19:41

Chas Brown

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miles · Accepted Answer · 2017-09-04 05:14:45Z

1

Python 2, 79 bytes

n=input()
s={2};p=i=1
while i<n:
 p*=i;i+=1
 if p*p%i:s|={i}
print{n,len(s)}<=s

Try it online!

answered Sep 4 '17 at 5:14

miles

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Tanj · Accepted Answer · 2017-07-16 15:11:15Z

0

Julia 0.6, 61 bytes

return 1 if x is a super-prime, 0 otherwise.

without using an isprime-kind function.

x->a=[0,1];for i=3:x push!(a,0∉i%(2:i-1))end;a[sum(a)]&a[x]

edited Jul 16 '17 at 15:11

answered Jul 10 '17 at 3:52

Tanj

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Is it a super-prime?

Background

Challenge

Test Cases

Scoring

20 Answers 20

Jelly, 5 bytes

How it works

Mathematica, 26 23 bytes

Jelly, 6 bytes

Japt, 13 11 bytes

Explanation

Python 3, 104 97 93 bytes

Jelly, 7 bytes

Haskell, 62 bytes

05AB1E, 6 bytes

Explanation

Pyth, 12 bytes

Explanation

Pyke, 8 bytes

Perl 6, 46 bytes

QBIC, 33 bytes

Explanation

Mathematica, 35 29 bytes

Haskell, 121 bytes

Positron, 148 bytes

Pari/GP, 31 bytes

Matlab, 36 34 bytes

Python 2, 89 bytes

Python 2, 79 bytes

Julia 0.6, 61 bytes

Your Answer

Not the answer you're looking for? Browse other questions tagged code-golf sequence number-theory decision-problem primes or ask your own question.

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Is it a super-prime?

Background

Challenge

Test Cases

Scoring

20 Answers 20

Jelly, 5 bytes

How it works

Mathematica, 26 23 bytes

Jelly, 6 bytes

Japt, 13 11 bytes

Explanation

Python 3, 104 97 93 bytes

Jelly, 7 bytes

Haskell, 62 bytes

05AB1E, 6 bytes

Explanation

Pyth, 12 bytes

Explanation

Pyke, 8 bytes

Perl 6, 46 bytes

QBIC, 33 bytes

Explanation

Mathematica, 35 29 bytes

Haskell, 121 bytes

Positron, 148 bytes

Pari/GP, 31 bytes

Matlab, 36 34 bytes

Python 2, 89 bytes

Python 2, 79 bytes

Julia 0.6, 61 bytes

Your Answer

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Not the answer you're looking for? Browse other questions tagged code-golf sequence number-theory decision-problem primes or ask your own question.

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