# Can logical operators be used with Cases?

Suppose I want all two digit primes between -75 and 100 inclusive.

a=Range[-75,100]

Select[Select[Cases[a, ?_Positive],(#>9&)],PrimeQ]


does it, but can't be the simplest way.

Cases[ a, _?Positive] and Cases[a, _?PrimeQ]


individually work but

Cases[a, _? Positive && PrimeQ]


fails, as do most of the variants I could think of using parenthesis and _? in from of both Positive and PrimeQ

Is there an elegant expression and is it possible to use logical operators with Cases in the way I am attempting?

• Select[Range[-75, 100], (Positive[#] && PrimeQ[#] &)] Mar 18, 2017 at 13:03
• Select[] is really much more preferable to Cases[] in this case. Mar 18, 2017 at 17:05

Generally I would use Condition:

Cases[Range[-75, 100], x_ /; Positive[x] && PrimeQ[x]]


For the specific case of And you can string PatternTest if you control grouping:

Cases[Range[-75, 100], (_?Positive)?PrimeQ]

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97}

• +1 for (_?Positive)?PrimeQ. Mar 23, 2017 at 8:46
• @Mr.Wizard +1 for showing me the use of a double pattern test Mar 23, 2017 at 9:28
• I hope I don't anger my initial responder whose answer was excellent,but Mr Wizard's response has, in my view, the elegant edge so I switched the green check! Mar 24, 2017 at 12:06
• @CMoller the short answer is: no you have not offended me because I am not here only for points. I consider Mr.Wizard as someone who I am learning from, I would suggest you to wait before making an accept. While I may not be here for points but removing accept does damage of points to the other person and shows up on their profile. You may offend someone else. Mar 24, 2017 at 19:58
• @CMoller For my part I do not mind losing the check-mark to a better answer posted later. To discourage that would be to discourage posting of better answers after an Accept has been given, and that would work against everyone's best interest. Just be sure you don't "move the goalposts" after asking your question; if you receive (and perhaps accept) an answer to the question you asked, but then realize you want something different or more, post a new question. Mar 24, 2017 at 21:37
Cases[Range[-75, 100], _?(Positive[#] && PrimeQ[#] &)]

(* or *)

Cases[Range[-75, 100], _?(Apply[And, Composition[Positive[#], PrimeQ[#]]] &)]
(* which is the same as the one below*)

Cases[Range[-75, 100], _?(Apply[And, Positive[#1]@*PrimeQ[#1]] &)]

(* or even more compactly *)
Cases[Range[-75, 100], _?(And @@ Positive[#1]@*PrimeQ[#1] &)]


a different way with Cases:

(Cases[#, _?Positive] ⋂ Cases[#, _?PrimeQ]) &@Range[-75, 100]

• @CMoller you are very welcome ! Mar 18, 2017 at 15:04
• @AliHashmi Since you have expressed interest in my coding style you may wish to see my answer below. Mar 23, 2017 at 5:06
• @Mr.Wizard I particularly enjoy your succinct way of coding style. Brief terse and enjoyable to read. I am trying to adopt a coding style which is a hybrid of yours and Leonid. I want to be able to switch to granularity when the need arises however being terse most of the times. Mar 23, 2017 at 20:33

You can use operator forms with Select:

Select[
Range[-75,100],
Through @* And[Positive, PrimeQ]
]


{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}