I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.
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3 Answers
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7 (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] 
- 1$\begingroup$ There are only a few prime even integers. Perhaps you could take some advantage $\endgroup$Dr. belisarius– Dr. belisarius2013-01-18 04:37:05 +00:00Commented Jan 18, 2013 at 4:37
- 2$\begingroup$ There you go @belisarius $\endgroup$Rojo– Rojo2013-01-18 04:39:57 +00:00Commented Jan 18, 2013 at 4:39
- 1$\begingroup$ Ok. You got the NextPrime yellow belt +1 $\endgroup$Dr. belisarius– Dr. belisarius2013-01-18 04:41:14 +00:00Commented Jan 18, 2013 at 4:41
- $\begingroup$ @belisarius a few? $\endgroup$Mr.Wizard– Mr.Wizard2013-01-18 05:00:52 +00:00Commented Jan 18, 2013 at 5:00
- 3$\begingroup$ @Mr.Wizard Well, my first English teacher was proud of me. He was deaf. $\endgroup$Dr. belisarius– Dr. belisarius2013-01-18 05:03:38 +00:00Commented Jan 18, 2013 at 5:03
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1 Just a joke:
nextp[i_] := Prime[PrimePi[i] + 1] 
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somewhatNextPrime[x_] := FindInstance[\[FormalN] > x, \[FormalN], Primes]$\endgroup$Rojo– Rojo2013-01-18 04:54:32 +00:00Commented Jan 18, 2013 at 4:54
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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 
NextPrimeIS actually implemented in Mathematica. TryTrace[NextPrime[6]]. The core of it is quite similar to what I posted $\endgroup$