Python Set Comprehension

Question

So I have these two problems for a homework assignment and I m stuck on the second one     Use a Python Set Comprehension  Python s equivalent of Set Builder notation  to generate a set of all of the prime numbers that are less than 100  Recall that a prime number is an integer that is greater than 1 and not divisible by any integer other than itself and 1  Store your set of primes in a variable  you will need it for additional parts   Output your set of primes  e g   with the print function    Use a Python Set Comprehension to generate a set of ordered pairs  tuples of length 2  consisting of all of the prime pairs consisting of primes less than 100  A Prime Pair is a pair of consecutive odd numbers that are both prime  Store your set of Prime Pairs in a variable  Your set of number 1 will be very helpful  Output your Set of Prime Pairs     For the first one  this works perfectly    r   x for x in range 2  101   if not any x   y    0 for y in range 2  x       However  I m pretty stumped on the second one  I think I may have to take the Cartesian                       product of the set r with something but I m just not sure    This gets me somewhat close but I just want the consecutive pairs   cart      x  y  for x in r for y in r      if x  lt  y

User · Answer

You can get clean and clear solutions by building the appropriate predicates as helper functions. In other words, use the Python set-builder notation the same way you would write the answer with regular mathematics set-notation.

The whole idea behind set comprehensions is to let us write and reason in code the same way we do mathematics by hand.

With an appropriate predicate in hand, problem 1 simplifies to:

 low_primes = {x for x in range(1, 100) if is_prime(x)}

And problem 2 simplifies to:

 low_prime_pairs = {(x, x+2) for x in range(1,100,2) if is_prime(x) and is_prime(x+2)}

Note how this code is a direct translation of the problem specification, "A Prime Pair is a pair of consecutive odd numbers that are both prime."

P.S. I'm trying to give you the correct problem solving technique without actually giving away the answer to the homework problem.

User · Answer

You can generate pairs like this     x  x   2  for x in r if x   2 in r    Then all that is left to do is to get a condition to make them prime  which you have already done in the first example   A different way of doing it   Although slower for large sets of primes     x  y  for x in r for y in r if x   2    y

User · Answer

primes    x for x in range 2  101  if all x y for y in range 2  min x  11       I simplified the test a bit - if all x y instead of if not any not x y  I also limited y s range  there is no point in testing for divisors   sqrt x   So max x     100 implies max y     10  For x  lt   10  y must also be  lt  x   pairs     x  x 2  for x in primes if x 2 in primes    Instead of generating pairs of primes and testing them  get one and see if the corresponding higher prime exists

[python] Python Set Comprehension

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