Sstrhsrtj

1. 
   

   The primes macro in Knuth's TeXBook (Version 3.0 1996) in Chapter 20: Definitions (also called Macros) page 218, produces a stray space after the 3, as in 2, 3 , 5, 7, 11, .... I have given up finding where it comes from.

   
   
   

   documentclass{article}
   
   % RN. 13 Dec 2018
   
   begin{document}
   
   newififprime newififunknown % boolean variables 
   
   newcountn newcountp newcountd newcounta % integer variables
   
   defprimes#1{2,~3% assume that #1 is at least 3 
   
   n=#1 advancen by-2 % n more to go 
   
   p=5% odd primes starting with p 
   
   loopifnumn>0 printifprimeadvancep by2 repeat} 
   
   defprintp{, % we will invoke printp if p is prime 
   
   ifnumn=1 and~fi % ‘and’ precedes the last value 
   
   numberp advancen by -1 } 
   
   defprintifprime{testprimality ifprimeprintpfi} 
   
   deftestprimality{{d=3 globalprimetrue 
   
   looptrialdivision ifunknownadvanced by2 repeat}} 
   
   deftrialdivision{a=p dividea byd 
   
   ifnuma>d unknowntrueelseunknownfalsefi 
   
   multiplya byd 
   
   ifnuma=p globalprimefalseunknownfalsefi}
   
   
   
   defN{10}
   
   The first N prime numbers are: primes{N~}.
   
   
   
   end{document}
   
   

   
   


2. 
   

   To enhance my ability to read code (including my own) without the help of yellow, green and blue texters and a fat black permanent marker, I am in a habit of formatting it for logical clarity, mainly by using indentation. In the case of Saint Knuth's primes this results in the following, but any hopes to spot the renegade space that way were ill-founded:

   
   
   

   documentclass{article}
   
   % RN. 13 Dec 2018
   
   begin{document}
   
   %%%%%%%%%%%%%%
   
   %   variables:
   
   %%%%%%%%%%%%%% 
   
   % boolean:
   
   newififprime
   
   newififunknown 
   
   % integer: 
   
   newcountn
   
   newcountp
   
   newcountd
   
   newcounta
   
   %%%%%%%%%%%%%%
   
   %   the macros:
   
   %%%%%%%%%%%%%% 
   
   defprime#1%
   
   {
   
       n=#1 advancen by -2 % n more to go 
   
       p=5% odd primes starting with p 
   
       loop ifnumn>0 
   
           printifprimeadvancep by 2 
   
       repeat
   
   } 
   
   
   
   defprintp
   
   {%
   
       , % we will invoke printp if p is prime 
   
       ifnumn=1 and~fi  % ‘and’ precedes the last value 
   
       numberp advancen by -1 
   
   } 
   
   
   
   defprintifprime
   
   {%
   
       testprimality 
   
       ifprime 
   
           printp 
   
       fi
   
   } 
   
   
   
   deftestprimality
   
   {%
   
       {%
   
           d=3 globalprimetrue 
   
           loop
   
               trialdivision 
   
               ifunknown advanced by 2 
   
           repeat
   
       }%
   
   } 
   
   
   
   deftrialdivision
   
   {%
   
       a=p dividea by d 
   
       ifnuma>d 
   
           unknowntrue
   
       else
   
           unknownfalse
   
       fi 
   
       multiplya by d 
   
       ifnuma=p 
   
           globalprimefalseunknownfalse
   
       fi
   
   }
   
   
   
   defN{10}
   
   The first N prime numbers are: primes{N~}.
   
   
   
   end{document}
   
   

   
   

NOTE: In formatting the code I introduced % characters as required to achieve the desired expansion purely by trial and error. Any general advise or guidelines for the indentation of plain-TeX code which will avoid making a complete mess of the final printed output are welcome.

primes{N~} That's your spurious space right there. Remove the ~. This is not expl3, i.e. ~ is not a regular space but def~{penalty@M }.

When you request primes{N~} this expands to

2,~3% assume that #1 is at least 3

n=N~ advancen by-2 % n more to go

...

which further expands to

2,~3% assume that #1 is at least 3

n=10penalty@M   advancen by-2 % n more to go

...

which is exactly the space you see after the 3.