Conditionally printing inside If[ ] produces NULLs?

drkirkby · April 2, 2021, 2:51pm

I’m trying to write a bit of code to find pseudoprimes - numbers for which (2^n -2)/n are integers, but n is not prime. I know the first 3 pseudoprimes are 561, 645 and 1105. So I wrote this below, which produces an output on the screen similar to that shown, except I don’t see the “During evaluation of ..” My screen just shows the numbers in a vertical column. Anyway, the main problem is there’s all these Nulls, but I don’t know why.
I’m using Mathematica 7.0, so quite an old version

n[51]:= Table[
 If[IntegerQ[(2^n - 2)/n] == True && PrimeQ[n] == False, 
  Print[n]], {n, 550, 1200}]

During evaluation of In[51]:= 561

During evaluation of In[51]:= 645

During evaluation of In[51]:= 1105

Out[51]= {Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, Null, \
Null, Null, Null}

mikebesso · April 2, 2021, 3:24pm

Try something like this:

Table[
 If[
  IntegerQ[(2^n - 2)/n] == True && PrimeQ[n] == False
  ,
  Print[n]; n
  ,
  Nothing
  ], {n, 550, 1200}]

Which prints and then returns:

{561, 645, 1105}

Remember, Print[] returns Null. Also, if you do not supply a third argument to If[], If[] will return nothing when the test expression is not True, so returning Nothing hides those Nulls.

Have a great weekend.

gianlucagorni · April 2, 2021, 4:00pm

Mathematica allows a shorter syntax:

Cases[Range[550, 1200],
 n_ /; IntegerQ[(2^n - 2)/n] && CompositeQ[n]]

drkirkby · April 2, 2021, 4:24pm

Unfortunately “Nothing” is not defined in my version of Mathematica, so the output contains a list of nothings.

drkirkby · April 2, 2021, 4:29pm

Unfortunately, CompositeQ is not defined in my version of Mathematica, but I modified your code to be

n[58]:= Cases[Range[550, 1200], 
 n_ /; IntegerQ[(2^n - 2)/n] && PrimeQ[n] == False]

Out[58]= {561, 645, 1105}

I find that syntax much harder to read than what I had before though. I guess its just my lack of knowledge of the language

rohitnamjoshi · April 2, 2021, 4:33pm

Range[550, 1200] // Select[IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &]
(* {561, 645, 1105} *)

rohitnamjoshi · April 2, 2021, 6:10pm

Hi David,

Unlike many other languages, WL syntax maps to an underlying symbolic expression. It may be helpful to look at that expression to understand it better

(n_ /; IntegerQ[(2^n - 2)/n] && PrimeQ[n] == False) // FullForm
(n_ /; IntegerQ[(2^n - 2)/n] && PrimeQ[n] == False) // TreeForm

(IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &) // FullForm
(IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &) // TreeForm

Define functions (with good names) to encapsulate logic and simplify complex expressions

pseudoPrimeQ[n_] := IntegerQ[(2^n - 2)/n] && Not @ PrimeQ @ n

Cases[Range[550, 1200], n_ /; pseudoPrimeQ[n]]

Cases[Range[550, 1200], n_?pseudoPrimeQ]

Range[550, 1200] // Select[pseudoPrimeQ]

drkirkby · April 2, 2021, 8:20pm

Thank you Rohit. Looking at the TreeForm and FreeForm is instructive.

Unfortuately

Range[550, 1200] // Select[IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &]

gives an error, about Select requiring 2 or 3 arguments, not 1.

mikebesso · April 2, 2021, 9:14pm

It would seem that the operator version of Select[] is a newer feature. Try:

Select[Range[550, 1200], IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &]

rohitnamjoshi · April 2, 2021, 10:52pm

David,

What version are you using? Operator form of Select (and many other functions) was added in V10. You can try the latest version for free (with some resource limitations) on the Wolfram Cloud.

drkirkby · April 3, 2021, 10:50am

Hi Mike,
I’m using version 7.0. That’s the latest that runs on Solaris, which is the OS I am using.

Select[Range[550, 1200], IntegerQ[(2^# - 2)/#] && Not[PrimeQ[#]] &]

works okay, and is just about readable! I’m not sure what the very last & does, but I will have to look at it.

mikebesso · April 3, 2021, 1:30pm

The last & makes the expression (the second argument to Select) an anonymous pure function.

Check out: Work with Pure Functions—Wolfram Documentation

Topic		Replies	Views
Why do I get Null when using my function? Questions computer-science , data-science , education , software-development	5	7772	May 16, 2015
Creating a list without Null entries Ideas mathematica	1	9204	July 24, 2013
Insert an "If...Then...Else" function into the following WL code? Questions	17	8657	April 6, 2017
Why does Select does not work with PrimeQ? Questions wolfram-alpha	6	13990	August 14, 2015
[?] Get proper format of a matrix , avoid matrix values with "Null" added? Questions	1	5806	July 24, 2018

Conditionally printing inside If[ ] produces NULLs?

Related topics