# Challenge

This is a simple one: Given a positive integer up to 1,000,000, return the closest prime number.

If the number itself is prime, then you should return that number; if there are two primes equally close to the provided number, return the lower of the two.

Input is in the form of a single integer, and output should be in the form of an integer as well.

I don't care how you take in the input (function, STDIN, etc.) or display the output (function, STDOUT, etc.), as long as it works.

This is code golf, so standard rules apply—the program with the least bytes wins!

# Test Cases

Input  =>  Output
------    -------
80     =>      79
100    =>     101
5      =>       5
9      =>       7
532    =>     523
1      =>       2
• Hi and welcome to PPCG!. To avoid down voting due to lack of quality I suggest you to post it to the sandbox first and after a couple of days post it here Mar 27 '19 at 15:17
• This is one of the outputs requested in this challenge. Mar 27 '19 at 15:24
• Very closely related but not quite identical. Mar 27 '19 at 15:35
• @Arnauld I saw that one, but I thought that they were different enough to warrant a new question. Mar 27 '19 at 15:37

# JavaScript (ES6), 53 bytes

n=>(g=(o,d=N=n+o)=>N%--d?g(o,d):d-1?g(o<0?-o:~o):N)

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### Commented

n => (            // n = input
g = (           // g = recursive function taking:
o,            //   o = offset
d =           //   d = current divisor, initialized to N
N = n + o     //   N = input + offset
) =>            //
N % --d ?     // decrement d; if d is not a divisor of N:
g(o, d)     //   do recursive calls until it is
:             // else:
d - 1 ?     //   if d is not equal to 1 (either N is composite or N = 1):
g(        //     do a recursive call with the next offset:
o < 0 ? //       if o is negative:
-o    //         make it positive (e.g. -1 -> +1)
:       //       else:
~o    //         use -(o + 1) (e.g. +1 -> -2)
)         //     end of recursive call
:           //   else (N is prime):
N         //     stop recursion and return N
)               // initial call to g with o = [''] (zero-ish)

# 05AB1E, 5 bytes

Åps.x

Try it online! or as a Test Suite

Inefficient for big numbers

• Too bad Ån is "In case of a tie, the higher prime is pushed" Didn't even knew we had this builtin, tbh. Mar 28 '19 at 7:51
• @KevinCruijssen: Neither did I until now :) Mar 28 '19 at 9:15

# Gaia, 3 bytes

ṅD⌡

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Rather slow for large inputs, but works given enough memory/time.

I'm not sure why D⌡ implicitly pushes z again, but it makes this a remarkably short answer!

ṅ	| implicit input z: push first z prime numbers, call it P
D⌡	| take the absolute difference between P and (implicit) z,
| returning the smallest value in P with the minimum absolute difference

# Octave, 40 bytes

@(n)p([~,k]=min(abs(n-(p=primes(2*n)))))

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This uses the fact that there is always a prime between n and 2*n (Bertrand–Chebyshev theorem).

### How it works

@(n)p([~,k]=min(abs(n-(p=primes(2*n)))))

@(n)                                      % Define anonymous function with input n
p=primes(2*n)      % Vector of primes up to 2*n. Assign to p
abs(n-(             ))    % Absolute difference between n and each prime
[~,k]=min(                      )   % Index of first minimum (assign to k; not used)
p(                                 )  % Apply that index to p

# Japt, 5 bytes

_j}cU
_j}cU     :Implicit input of integer U
_         :Function taking an integer as an argument
j        :  Test if integer is prime
}       :End function
cU     :Return the first integer in [U,U-1,U+1,U-2,...] that returns true

z-Ån

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# Wolfram Language (Mathematica), 31 bytes

Nearest[Prime~Array~78499,#,1]&

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& (*pure function*)
Prime~Array~78499       (*among the (ascending) first 78499 primes*)
1   (*select one*)
Nearest[                 ,#, ]  (*which is nearest to the argument*)

1000003 is the 78499th prime. Nearest prioritizes values which appear earlier in the list (which are lower).

• Nearest[Prime@Range@#,#,1]& for 27
– Ben
Mar 29 '19 at 16:10

# Brachylog, 7 5 bytes

;I≜-ṗ

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Saved 2 bytes thanks to @DLosc.

### Explanation

;I≜      Label an unknown integer I (tries 0, then 1, then -1, then 2, etc.)
-     Subtract I from the input
ṗ    The result must be prime
• @DLosc Mostly because I am stupid. Thanks. Mar 29 '19 at 8:26
• I think we just approached it from different directions. You were thinking about from the start, I assume, whereas I was thinking about pairing and subtracting and only later realized I'd need to make it work. :) Mar 29 '19 at 21:27

# Pyth, 10 bytes

Try it online here, or verify all the test cases at once here.

Trailing Q inferred
yQ   2 * Q
S     Range from 1 to the above
f         Filter keep the elements of the above, as T, where:
P_T        Is T prime?
D           Order the above by...
a Q          ... absolute difference between each element and Q
This is a stable sort, so smaller primes will be sorted before larger ones if difference is the same
h             Take the first element of the above, implicit print

# Jelly, 9 7 bytes

ḤÆRạÞµḢ

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Slow for larger input, but works ok for the requested range. Thanks to @EriktheOutgolfer for saving 2 bytes!

• Hey, that's clever! Save two by substituting _A¥ with (absolute difference). Oh, and can really be . Mar 27 '19 at 19:08
• @EriktheOutgolfer thanks. Surely using won’t always work? It means that only primes up to n+1 will be found, while the closest might be n+2. Mar 27 '19 at 22:39
• Hm, that's a concern. Mar 27 '19 at 22:40

# Python 2, 71 bytes

f=lambda n,k=1,p=1:k<n*3and min(k+n-p%k*2*n,f(n,k+1,p*k*k)-n,key=abs)+n

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A recursive function that uses the Wilson's Theorem prime generator. The product p tracks $$\(k-1)!^2\$$, and p%k is 1 for primes and 0 for non-primes. To make it easy to compare abs(k-n) for different primes k, we store k-n and compare via abs, adding back n to get the result k.

The expression k+n-p%k*2*n is designed to give k-n on primes (where p%k=1), and otherwise a "bad" value of k+n that's always bigger in absolute value and so doesn't affect the minimum, so that non-primes are passed over.

# C (gcc), 877674 72 bytes

Optimization of innat3's C# (Visual C# Interactive Compiler), 100 bytes

f(n,i,t,r,m){for(t=0,m=n;r-2;t++)for(r=i=1,n+=n<m?t:-t;i<n;n%++i||r++);}

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• Hello and welcome to PPCG. A few tips: r!=2 is equivalent to r-2, n%++i?0:r++ can most likely be n%++i||r++. Mar 29 '19 at 13:11
• I didn't immediately see that. Thanks. Mar 29 '19 at 15:13

# Tidy, 43 bytes

{x:(prime↦splice(]x,-1,-∞],[x,∞]))@0}

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## Explanation

This is a lambda with parameter x. This works by creating the following sequence:

[x - 1, x, x - 2, x + 1, x - 3, x + 2, x - 4, x + 3, ...]

This is splicing together the two sequences ]x, -1, -∞] (left-closed, right-open) and [x, ∞] (both open).

For x = 80, this looks like:

[79, 80, 78, 81, 77, 82, 76, 83, 75, 84, 74, 85, ...]

Then, we use f↦s to select all elements from s satisfying f. In this case, we filter out all composite numbers, leaving only the prime ones. For the same x, this becomes:

[79, 83, 73, 71, 89, 67, 97, 61, 59, 101, 103, 53, ...]

Then, we use (...)@0 to select the first member of this sequence. Since the lower of the two needs to be selected, the sequence which starts with x - 1 is spliced in first.

Note: Only one of x and x - 1 can be prime, so it is okay that the spliced sequence starts with x - 1. Though the sequence could be open on both sides ([x,-1,-∞]), this would needlessly include x twice in the sequence. So, for sake of "efficiency", I chose the left-closed version (also because I like to show off Tidy).

# Factor, 91 bytes

: p ( x -- x ) [ nprimes ] keep dupd [ - abs ] curry map swap zip natural-sort first last ;

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# APL (Dyalog Extended), 20 15 bytesSBCS

Tacit prefix function inspired by Galen Ivanov's J answer.

⊢(⊃⍋⍤|⍤-⊇⊢)¯2⍭⍳

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ɩndices one through the argument.

¯2⍭ nth primes of that

⊢() apply the following tacit function to that, with the original argument as left argument:

the primes

indexed by:

the ascending grade (indices which would sort ascending)
of
| the magnitude (absolute value)
of
- the differences

pick the first one (i.e. the one with smallest difference)

# Perl 6, 35 bytes

{$_+=($*=-1)*$++until .is-prime;$_}

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This uses Veitcel's technique for generating the list of 0, -1, 2, -3 but simplifies it greatly to ($*=-1)*$++ using the anonymous state variables available in P6 (I originally had -1 ** $++ *$++, but when golfed the negative loses precedence). There's a built in prime checker but unfortunately the until prevents the automagically returned value so there's an extra $_ hanging around. • I'd usually use a sequence operator approach to something like this, but comes out to one byte longer, so nice work finding a shorter method – Jo King Mar 29 '19 at 0:39 • @JoKing good catch. The things that happen when I golf too quickly after getting a working solution. I had a similar one but the damned lack of [-1] haha Mar 29 '19 at 0:49 # C, 122121 104 bytes p(a,i){for(i=1;++i<a;)if(a%i<1)return 0;return a>1;}c(a,b){for(b=a;;b++)if(p(--a)|p(b))return p(b)?b:a;} Use it calling function c() and passing as argument the number; it should return the closest prime. Thanks to Embodiment of Ignorance for 1 byte saved a big improvement. Try it online! • But c() receives two parameters... Also, you can probably shorten the while(1) to for(;;) (untested, since I don't get how to run your code Mar 28 '19 at 5:03 • @EmbodimentofIgnorance I wrote it and tested it all on an online c compiler, I could call c() passing only the first parameter. And you are right, for(;;) saves me a byte, only 117 left to get first place :) Mar 28 '19 at 11:30 • 110 bytes: #define r return p(a,i){i=1;while(++i<a)if(a%i<1)r 0;r a>1;}c(a,b){b=a;for(;;b++){if(p(--a))r a;if(p(b))r b;}}. Here is a TIO link: tio.run/… Mar 28 '19 at 21:06 • 106: tio.run/… Mar 28 '19 at 21:12 • 101: tio.run/… Mar 28 '19 at 21:17 # Wolfram Language (Mathematica), 52 bytes If[PrimeQ[s=#],s,#&@@Nearest[s~NextPrime~{-1,1},s]]& Try it online! • You have an extra space that can be removed to save a byte. – Ben Mar 29 '19 at 16:03 • @Ben you are right. thanx Mar 29 '19 at 23:08 # APL(NARS), 38 chars, 76 bytes {⍵≤1:2⋄0π⍵:⍵⋄d←1π⍵⋄(d-⍵)≥⍵-s←¯1π⍵:s⋄d} 0π is the test for prime, ¯1π the prev prime, 1π is the next prime; test: f←{⍵≤1:2⋄0π⍵:⍵⋄d←1π⍵⋄(d-⍵)≥⍵-s←¯1π⍵:s⋄d} f¨80 100 5 9 532 1 79 101 5 7 523 2 # J, 19 15 bytes (0{]/:|@-)p:@i. Try it online! # MathGolf, 10 bytes ∞╒g¶áÅ-±├Þ Try it online. Explanation: ∞ # Double the (implicit) input-integer ╒ # Create a list in the range [1, 2*n] g¶ # Filter so only the prime numbers remain áÅ # Sort this list using the next two character: -± # The absolute difference with the (implicit) input-integer ├ # Push the first item of the list # (unfortunately without popping the list itself, so:) Þ # Discard everything from the stack except for the top # (which is output implicitly as result) • @JoKing Thanks! I knew Max thought about changing it, but didn't knew he actually did. The docs still state the old one. Mar 28 '19 at 8:53 • Ah, I use the mathgolf.txt file as reference, since it seems to be more up to date – Jo King Mar 28 '19 at 23:21 • @JoKing Yeah, he told me yesterday about that file as well. Will use it from now on. :) Mar 29 '19 at 7:23 # Python 2 (Cython), 96 bytes l=lambda p:min(filter(lambda p:all(p%n for n in range(2,p)),range(2,p*3)),key=lambda x:abs(x-p)) Try it online! • Might be able to save a couple bytes via r=range;... Mar 28 '19 at 20:33 • @Arnauld, it now works for x=1 Mar 29 '19 at 8:20 ## C# (Visual C# Interactive Compiler), 104 100 bytes n=>{int r=0,t=0,m=n;while(r!=2){n+=(n<m)?t:-t;t++;r=0;for(int i=1;i<=n;i++)if(n%i==0)r++;}return n;} Try it online! Explanation: int f(int n) { int r = 0; //stores the amount of factors of "n" int t = 0; //increment used to cover all the integers surrounding "n" int m = n; //placeholder to toggle between adding or substracting "t" to "n" while (r != 2) //while the amount of factors found for "n" is different to 2 ("1" + itself) { n += (n < m) ? t : -t; //increment/decrement "n" by "t" (-0, -1, +2, -3, +4, -5,...) t++; r = 0; for (int i = 1; i <= n; i++) //foreach number between "1" and "n" increment "r" if the remainder of its division with "n" is 0 (thus being a factor) if (n % i == 0) r++; } return n; } Console.WriteLine(f(80)); //79 • 88 bytes Sep 9 '20 at 0:40 # Java 8, 88 87 bytes n->{for(int c=0,s=0,d,N=n;c!=2;s++)for(c=d=1,n+=n<N?s:-s;d<n;)if(n%++d<1)c++;return n;} Port of @NaturalNumberGuy's (first) C answer, so make sure to upvote him!! -1 byte thanks to @OlivierGrégoire. Try it online. Explanation: n->{ // Method with integer as both parameter and return-type for(int c=0, // Counter-integer, starting at 0 s=0, // Step-integer, starting at 0 as well d, // Divisor-integer, uninitialized N=n; // Copy of the input-integer c!=2; // Loop as long as the counter is not exactly 2 yet: s++) // After every iteration: increase the step-integer by 1 for(c=d=1, // (Re)set both the counter and divisor to 1 n+=n<N? // If the input is smaller than the input-copy: s // Increase the input by the step-integer : // Else: -s; // Decrease the input by the step-integer d<n;) // Inner loop as long as the divisor is smaller than the input if(n%++d // Increase the divisor by 1 first with ++d <1) // And if the input is evenly divisible by the divisor: c++; // Increase the counter-integer by 1 return n;} // Return the now modified input-integer as result # Java (JDK), 103 bytes n->{int p=0,x=0,z=n,d;for(;p<1;p=p>0?z:0,z=z==n+x?n-++x:z+1)for(p=z/2,d=1;++d<z;)p=z%d<1?0:p;return p;} Try it online! • Umm.. I had already create a port of his answer.. ;) Although yours is 1 byte shorter, so something is different. EDIT: Ah, I have a result-integer outside the loop, and you modify the input inside the loop, hence the -1 byte for ;. :) Do you want me to delete my answer?.. Feel free to copy the explanation. Mar 29 '19 at 12:50 • @KevinCruijssen Oops, rollbacked! Mar 29 '19 at 12:59 • Sorry about that (and thanks for the -1 byte). I like your version as well, though. Already upvoted before I saw NaturalNumberGuy's answer. Mar 29 '19 at 12:59 # Haskell, 79 74 bytes (thanks to Laikoni) 72 bytes as annonymus function (the initial "f=" could be removed in this case). f=(!)(-1);n!x|x>1,all((>0).mod x)[2..x-1]=x|y<-x+n=last(-n+1:[-n-1|n>0])!y Try it online! ### original code: f=(!)(-1);n!x|x>1&&all((>0).mod x)[2..x-1]=x|1>0=(last$(-n+1):[-n-1|n>0])!(x+n)

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Explanation:

f x = (-1)!x

isPrime x = x > 1 && all (\k -> x mod k /= 0)[2..x-1]
n!x | isPrime x = x            -- return the first prime found
| n>0       = (-n-1)!(x+n) -- x is no prime, continue with x+n where n takes the
| otherwise = (-n+1)!(x+n) -- values -1,2,-3,4 .. in subsequent calls of (!)
• Inside a guard you can use , instead of &&. (last$...) can be last(...), and the second guard 1>0 can be used for a binding to save parenthesis, e.g. y<-x+n. Mar 30 '19 at 10:57 • Anonymous functions are generally allowed, so the initial f= does not need to be counted. Also the parenthesis enclosing (-1+n) can be dropped. Mar 30 '19 at 11:22 • Thanks for the suggestions. I didn't know "," and bindings are allowed in function guards! But i don't really like the idea of an annonymous function as an answer. It doesn't feel right in my opinion. Mar 31 '19 at 2:58 • You can find more tips in our collection of tips for golfing in Haskell. There is also a Guide to Golfing Rules in Haskell and dedicated chat room: Of Monads and Men. Mar 31 '19 at 22:13 # VDM-SL, 161 bytes f(i)==(lambda p:set of nat1&let z in set p be st forall m in set p&abs(m-i)>=abs(z-i)in z)({x|x in set{1,...,9**7}&forall y in set{2,...,1003}&y<>x=>x mod y<>0}) A full program to run might look like this - it's worth noting that the bounds of the set of primes used should probably be changed if you actually want to run this, since it will take a long time to run for 1 million: functions f:nat1+>nat1 f(i)==(lambda p:set of nat1&let z in set p be st forall m in set p&abs(m-i)>=abs(z-i)in z)({x|x in set{1,...,9**7}&forall y in set{2,...,1003}&y<>x=>x mod y<>0}) ### Explanation: f(i)== /* f is a function which takes a nat1 (natural number not including 0)*/ (lambda p:set of nat1 /* define a lambda which takes a set of nat1*/ &let z in set p be st /* which has an element z in the set such that */ forall m in set p /* for every element in the set*/ &abs(m-i) /* the difference between the element m and the input*/ >=abs(z-i) /* is greater than or equal to the difference between the element z and the input */ in z) /* and return z from the lambda */ ( /* apply this lambda to... */ { /* a set defined by comprehension as.. */ x| /* all elements x such that.. */ x in set{1,...,9**7} /* x is between 1 and 9^7 */ &forall y in set{2,...,1003} /* and for all values between 2 and 1003*/ &y<>x=>x mod y<>0 /* y is not x implies x is not divisible by y*/ } ) # MATL, 6 bytes t:YqYk Try it online! List the first n primes and find the one closest to n. # Perl 5, 57 bytes$a=0;while((1x$_)=~/^.?$|^(..+?)\1+$/){$_+=(-1)**$a*++$a}

Try it online!

/^.?$|^(..+?)\1+$/ is tricky regexp to check prime

(-1)**$a*++$a generate sequence 0,-1, 2,-3 ...

# C# (Visual C# Interactive Compiler), 112 bytes

g=>Enumerable.Range(2,2<<20).Where(x=>Enumerable.Range(1,x).Count(y=>x%y<1)<3).OrderBy(x=>Math.Abs(x-g)).First()

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Left shifts by 20 in submission but 10 in TIO so that TIO terminates for test cases.