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I understand how to make lists with the Select function and NestList, but these are only for one dimensional lists. Is it possible to make lists of all points that satisfy a constraint? For example, all points {x,y} that satisfy PrimeQ[x*y+1]==True.

Sorry if this is really amateur, I only recently started Mathematica and I'm trying to teach myself the functions.

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  • $\begingroup$ Like Select[pts, PrimeQ[Apply[Times, #] + 1] &]? $\endgroup$
    – J. M.'s missing motivation ♦
    Commented May 17, 2017 at 13:35

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There are many ways to do this. I will show one with SparseArray.

matrix = SparseArray[{x_, y_} /; PrimeQ[x y + 1] -> 1, {100, 100}]

Now try these:

MatrixPlot[matrix]

ArrayRules[matrix]

Keys@Most@ArrayRules[matrix]

The last one just gives a list of {x,y} pairs.

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  • $\begingroup$ f@x is just alternative notation for f[x]. $\endgroup$
    – Szabolcs
    Commented May 17, 2017 at 13:38
  • $\begingroup$ What does the ->1 mean? $\endgroup$
    – volcanrb
    Commented May 17, 2017 at 14:40
  • $\begingroup$ @volcanrb , You might be interested in this thread. $\endgroup$
    – N.J.Evans
    Commented May 17, 2017 at 15:15
  • $\begingroup$ @volcanrb It depends on the context. For this use, look up SparseArray. $\endgroup$
    – Szabolcs
    Commented May 17, 2017 at 16:46

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