Large Number Limit Extravaganza
Your method of generating primes is horribly slow. Running your code takes on the order of 5 minutes on my machine.

Consider as an alternative a prime sieve, even a simple one like the Sieve of Eratosthenes will do (you don't need to go full Atkinson on it):

def prime_sieve(limit):
    a = [True] * limit
    a[0] = a[1] = False

    for i, isprime in enumerate(a):
        if isprime:
            yield i
            for n in xrange(i * i, limit, i):
                a[n] = False

if __name__ == "__main__":
    prod = 1
    for p in prime_sieve(240000):
        prod *= (1 - 1.0 / p)
        print prod
    primes_less_than = p - 1
    amta = 1 - prod

    print "The convergence:", primes_less_than
    print "All the way up to the number:", amta
    print "The amount of active inhibitors are:", prod * primes_less_than


This runs in less than a second.

Accuracy

In your question you said you want to calculate $$n \cdot \left(1-\left(\prod_{i=1}^n(1-p_i)\right)\right)$$ But in your code you implemented $$n \cdot \left(1-\left(\prod_{i=1}^n(1-1/p_i)\right)\right)$$.

You do amta = 1 -old and then later (1 - amta) * primeslessthan. Here you are needlessly loosing precision, because 1 - (1 - x) != x due to floating point precision. Better use old directly in the output.

Review:
Python has an official style-guide, which programmers are encouraged to follow, PEP8.

Your code violates it in the following points:


Always put the expression after an if in a new line
Use spaces around operators
Use lower_case names for variables and functions
old is a bad name for a variable, amta even worse


In addition, the following are discouraged for iterating in python:

l = [1, 2, 3, ...]

for i in range(len(l)):
    print l[i]

i = 0
while True:
    if i &gt; len(l) - 1:
        break
    print l[i]
    i += 1


Just use this simple syntax:

for x in l:
    print x


Note that the if does not need any parenthesis.

Finally, the print statement can take multiple expressions, separated by commas. Alternatively, you can use str.format:

print "The convergence: {}".format(primeslessthan)
print "All the way up to the number: {}".format(amta)
print "The amount of active inhibitors are: {}".format((1 - amta) * primeslessthan)