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Bertrand's postulate states that there is always at least 1 prime number between n and 2n for all n greater than 1.
Your task is to take a positive integer n greater than 1 and find all of the primes between n and 2n (exclusive).
Any default I/O method can be used. Whoever writes the shortest code (in bytes) wins!
n 2n primes
2 4 3
7 14 11, 13
13 26 17, 19, 23
18 36 19, 23, 29, 31
21 42 23, 29, 31, 37, 41
ôU Åfj
ôU Åfj
U // Implicit input 7
ôU // Inclusive range [Input...Input+U] [7,8,9,10,11,12,13,14]
Å // Remove the first item [8,9,10,11,12,13,14]
fj // Filter primes [11,13]
declare
n number:=7;
p number;
v number:=0;
begin
for i in (n+1)..(n*2)-1 loop
p:=0;
for j in 2..trunc(sqrt(n*2)) loop
if mod(i,j)=0 then p := 1;
exit;
end if;
end loop;
if p =0 then
dbms_output.put_line(i);
v:=v+1;
end if;
end loop;
end;
·ÅPʒ‹
·ÅPʒ‹ || Full program.
||
· || Double the input.
ÅP || Lists all the prime lower than or equal to ^.
ʒ‹ || Filter-keep those which are greater than the input.
param($n)(2*$n-1)..++$n|?{'1'*$_-match'^(?!(..+)\1+$)..'}
Takes input $n, constructs a range from 2*$n-1 to ++$n (i.e., excluding the endpoints), and feeds that range into a Where-Object cmdlet. The clause is the regex pattern match against unary numbers. Thus, those numbers where that clause is true (i.e., they are prime) are filtered out of the range and left on the pipeline. Output is implicit.
Saved 1 bytes thanks to @Arnauld
f=(n,q=n,x)=>n?q%x?f(n,q,x-1):f(n-1,q+1,q).concat(x<2?q:[]):[]
{⍵≤1:⍬⋄(0πt)/t←(⍵+1)..2×⍵}
Perhaps better the range in Axiom: When a>b than a..b is the void set. Test
g←{⍵≤1:⍬⋄(0πt)/t←(⍵+1)..2×⍵}
g 7
11 13
g 9
11 13 17
g 0
g 1
g 2
3
g 6.3
DOMAIN ERROR
{grep &is-prime,$_^..^2*$_}
{ # bare block lambda with implicit parameter ｢$_｣
grep # find all values
&is-prime, # that are prime
# from the following
$_
^..^ # create a Range that excludes both endpoints
2 * $_
}
⎕CY'dfns'⋄
{1↓(10pco(⍵+0⍵))/(-⍵)↑⍳⍵+⍵-1}
The characters B← are not counted towards the byte count because they're unnecessary and are added to TIO so it's easier to call the function. Also, ⍎'⎕CY''dfns''⋄⍬' is the equivalent to ⎕CY'dfns'⋄, but TIO doesn't accept the usual APL notation for that, so the extra characters are needed.
Thanks to @ErikTheOutgolfer for 1 byte.
⎕CY'dfns'⋄ ⍝ Imports every direct function. This is needed for the primes function, 'pco'.
{1↓(10pco(⍵+0⍵))/(-⍵)↑⍳⍵+⍵-1} ⍝ Main function, prefix.
(10pco ) ⍝ Calls the function 'pco' with the modifier 10, which lists every prime between the arguments:
(⍵+0⍵) ⍝ Vector of arguments, ⍵ and 2⍵.
⍝ The function returns a boolean vector, with 1s for primes and 0s otherwise.
1↓ ⍝ Drops the first element of the vector (because Bertrands postulate excludes the left bound).
/ ⍝ Replicate right argument to match the left argument.
⍳⍵+⍵-1 ⍝ Generate range from 1 to 2⍵-1 (to exclude the right bound)
↑ ⍝ Take from the range
(-⍵) ⍝ The last ⍵ elements.
0 ⍵.
\$\endgroup\$
Jan 8, 2018 at 15:29
xŸ¦ʒp
xŸ¦ʒp Full Program
x double top of stack
Ÿ inclusive range
¦ remove first element (pop a: push a[1:])
ʒ filter to keep
p prime elements
-1 byte thanks to Mr. Xcoder
This is fairly straightforward: within the range of (n+1,2n), select numbers that are primes.
Range[#+1,2#]~Select~PrimeQ&
Example
Range[#+1,2#]~Select~PrimeQ&[7]
(* {11, 13} *)
Select[#+Range@#,PrimeQ]&
\$\endgroup\$
Jan 8, 2018 at 15:07
fṗtS…D
fṗtS…D -- example input: 7
S… -- range from itself (inclusive) to itself..
D -- | .. doubled
-- : [7,8,9,10,11,12,13,14]
t -- tail: [8,9,10,11,12,13,14]
fṗ -- filter primes: [11,13]
fṗ§…→D
fṗ§…→D -- example input: 7
§… -- range from ..
D -- | .. itself incremented to
-- | .. itself doubled
-- : [8,9,10,11,12,13,14]
fṗ -- filter primes: [11,13]
Prime related functions wered moved to a package in Julia 0.5, so this would require using Primes in newer versions, and also TIO doesn't have that package installed.
n->primes(n+1,2n)
q->{for(int n=q,i,x;++n<2*q;){for(x=n,i=2;i<x;x=x%i++<1?0:x);if(x>1)System.out.println(n);}}
-3 bytes thanks to @ceilingcat.
Explanation:
q->{ // Method with integer parameter and no return-type
for(int n=q,i,x;++n<2*q;){
// Loop `n` in the range (q,2q):
for(x=n, // Set `x` to `n`
i=2;i<x // Loop `i` in the range [2,n):
; // After every iteration:
x=x%i++<1? // If `x` is divisible by `i`:
0 // Set `x` to 0
: // Else:
x); // Leave it unchanged
if(x>1) // If `x` is larger than 1 at the end of the inner loop
// (which means it's a prime):
System.out.println(n);}}
// Print this prime `n`
n = 1for which there are no prime in (excluded) range (1, 2)? \$\endgroup\$