How could I implement the equivalent of NextPrime

Question

I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.

Answer 1

(nextPrime[#1] = #2) & @@@ {{-3, 2}, {-2, 2}, {-1, 2}, {0, 2}, {1, 2}, {2, 3}};
nextPrime[n_Integer?EvenQ] := nextPrime[n - 1];
nextPrime[n_Integer] /; PrimeQ[n + 2] := n + 2;
nextPrime[n_Integer] := nextPrime[n + 2]
nextPrime[n_ /; n \[Element] Reals] := nextPrime[Floor@n]

Answer 2

For reference, here is the v7 code behind NextPrime, which is hard to read before stripping all the private context names.

NextPrime[1]; (* preload the definition *)
Unprotect[NextPrime];
ClearAttributes[NextPrime, ReadProtected];
$Context = "NumberTheory`NextPrimeDump`";
FullDefinition[NextPrime]

Yields:

Attributes[NextPrime] = {Listable}

NextPrime[-3] := -2

NextPrime[-2] := 2

NextPrime[-1] := 2

NextPrime[0] := 2

NextPrime[1] := 2

NextPrime[n_Integer] := Block[{res}, res = integerNextPrime[n]; res /; IntegerQ[res]]

NextPrime[r_] /; NumericQ[r] && ! IntegerQ[r] := 
 Block[{res, n}, 
  n = Quiet[Block[{$MaxExtraPrecision = 
           Max[$MaxExtraPrecision, 1 + Ceiling[Log[10., Abs[N[r]]]]]}, Floor[r]]]; (res = 
     NextPrime[n]; res /; IntegerQ[res]) /; IntegerQ[n]]

NextPrime[n_, k_Integer] /; NumericQ[n] && Positive[k] := 
 Block[{res}, res = Nest[NextPrime, n, k]; res /; IntegerQ[res]]

NextPrime[n_, k_Integer] /; NumericQ[n] && Negative[k] := 
 Block[{res}, res = Nest[PreviousPrime, n, -k]; res /; IntegerQ[res]]

NextPrime[n_?PrimeQ, 0] := n

NextPrime[n_, 0] := NextPrime[n]

NextPrime[n___] := (ArgumentCountQ[NextPrime, Length[{n}], 1, 2]; Null /; False)


integerNextPrime[n_Integer] := 
 Block[{res}, res = n + 1 + Mod[n, 2]; While[! PrimeQ[res], res += 2]; 
  res /; IntegerQ[res]]

integerNextPrime[___] := $Failed


PreviousPrime[n_] := Block[{res}, res = -NextPrime[-n]; res /; IntegerQ[res]]

PreviousPrime[___] := $Failed

Answer 3

Just a joke:

nextp[i_] := Prime[PrimePi[i] + 1]