# function to generate random numbers between j<k
def random_between(j,k) :
   a=int(random()*(k-j+1))+j
   return a

# function to generate 1024-bit sophie germain prime
def SGP :
   boolean = false
   while boolean = false repeat
      p = random_between(2**1023, 2**1024-1)
      boolean = is 2p+1 in Primes()
   return p
    
# Working in Fp
p = SGP
G1 = FP(p)
g = G1.gen()​
︠de8b2318-c69e-4e91-987c-34d7ce7e39bci︠
%md 

Comments:
function random_between:
1) Use ZZ instead of int. It'll treat the number as an integer class and allow you to call methods on it.
2) random finds a number in the range [0.0,1.0). Try ZZ.random_element(lower_bound,upper_bound) instead to get an integer in the range [lower_bound, upper_bound)

function SGP:
1) You have forgotten the parentheses! SGP() =)
2) Sage true and false are True and False (note the capitalization). Not essential, but a good habit.
3) Instead of repeat, the while struct has the following format:

while condition:
    #Do stuff
#program continues after while loop

4) random_between should be ZZ.random, as in above point
5) no need for is. Remember to multiply! 2*p is a computation. 2p is not valid syntax.
6) x in Primes() is valid, but if you have an element of ZZ you can simply call the method num.is_prime() to get the same result