? 2+3
%1 = 5
? 2*3
%2 = 6
? gcd(53535,3737626)
%3 = 1
? bezout(53535,3737626)
%4 = [-1643201, 23536, 1]
? 53535*%4[1]+3737626*%[2]
%5 = 1
? 53535*%4[1]+3737626*%4[2]
%6 = 1
? 663636%7
%7 = 1
? Mod(663636,7)
%8 = Mod(1, 7)
? Mod(663636*565353,7)
%9 = Mod(5, 7)
? Mod(663636,7)*Mod(565353,7)
%10 = Mod(5, 7)
? Mod(663636^737737373737,7)
  ***   length (lg) overflow
? Mod(663636,7)^737737373737
%11 = Mod(1, 7)
? Mod(663633,7)^737737373737
  ***   Warning: large exponent in Mod(a,N)^n: reduce n mod phi(N).
%12 = Mod(5, 7)
? chinese(Mod(3,7),Mod(5,8))
%13 = Mod(45, 56)
? eulerphi(56)
%14 = 24
? factor(56)
%15 = 
[2 3]

[7 1]

? %15[1,2]
%16 = 3
? %15[2,1]
%17 = 7
? ?isprime
isprime(x,{flag=0}): true(1) if x is a (proven) prime number, false(0) if not. 
If flag is 0 or omitted, use a combination of algorithms. If flag is 1, the 
primality is certified by the Pocklington-Lehmer Test. If flag is 2, the 
primality is certified using the APRCL test. 

? ?
Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)
Extended help looks available:
  ??             (opens the full user's manual in a dvi previewer)
  ??  tutorial / refcard / libpari (tutorial/reference card/libpari manual)
  ??  keyword    (long help text about "keyword" from the user's manual)
  ??? keyword    (a propos: list of related functions).
? ?4

addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? ?ispseudoprime
ispseudoprime(x,{n}): true(1) if x is a strong pseudoprime, false(0) if not. 
If n is 0 or omitted, use BPSW test, otherwise use strong Rabin-Miller test 
for n randomly chosen bases.

? isprime(3747738784738274728877721)
%18 = 0
? ispseudoprime(3747738784738274728877721)
%19 = 0
? factor(3747738784738274728877721)
%20 = 
[3 1]

[289573 1]

[13439317 1]

[321005737627 1]

? for(n=1,100,if(isprime(n)&&n%8==1,print(n," ","hello")))
17 hello
41 hello
73 hello
89 hello
97 hello
? for(n=1,100,if(isprime(n)&&n%8==1,print(n," ","hello"),if(n==50,break)))
17 hello
41 hello
? for(n=1,100,if(isprime(n)&&n%8==1,print(n," ","hello"),if(n==50,print("goodbye");break)))
17 hello
41 hello
goodbye
? n=1000;while(!isprime(n),n++);n
%21 = 1009
? ?
Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)
Extended help looks available:
  ??             (opens the full user's manual in a dvi previewer)
  ??  tutorial / refcard / libpari (tutorial/reference card/libpari manual)
  ??  keyword    (long help text about "keyword" from the user's manual)
  ??? keyword    (a propos: list of related functions).
? ?11

addhelp     alias       allocatemem break       default     error
extern      for         fordiv      forell      forprime    forstep
forsubgroup forvec      getheap     getrand     getstack    gettime
global      if          input       install     kill        next
print       print1      printp      printp1     printtex    quit
read        readvec     reorder     return      setrand     system
trap        type        until       whatnow     while       write
write1      writebin    writetex    

? \rlesson.gp
? function(a,b)=for(n=a,b,if(n%2==1,if(Mod(3,n)^(n-1)==Mod(1,n),return(n);break)))
? ?function
function(a, b) = for(n=a,b,if(n%2==1,if(Mod(3,n)^(n-1)==Mod(1,n),return(n);break)))
? function(100,200)
%22 = 101
? \rlesson.gp
? function(a,b)=for(n=a,b,if(n%2==1&&!isprime(n),if(Mod(3,n)^(n-1)==Mod(1,n),return(n);break)))
? ?function
function(a, b) = for(n=a,b,if(n%2==1&&!isprime(n),if(Mod(3,n)^(n-1)==Mod(1,n),return(n);break)))
? function(100,200)
%23 = 121
? \rlesson.gp
? function(a,b)=for(n=a,b,if(n%2==1&&!isprime(n),if(Mod(3,n)^(n-1)==Mod(1,n),return(n);break)))
? function(1000,2000)
%24 = 1105
? \q
Goodbye!