# `pupy.amazon_prime`¶

## Module Contents¶

`range`
`prime_gen`(plim=0, kprimes=None)

Infinite (within reason) prime number generator

My big modification is the pdiv_dictionary() function that recreats the dictionary of divisors so that you can continue to generate prime numbers from a (sorted) list of prime numbers.

Based on:
eratosthenes by David Eppstein, UC Irvine, 28 Feb 2002 http://code.activestate.com/recipes/117119/ and the thread at the url
Parameters: plim (int) – prime_limit; default=0 makes for an infinite generator kprimes (iter) – known_primes as an iterable (Default value = None)
`prime_factorization_gen`(n)

generates all numbers in the prime factorization of n

Parameters: n (int) – number to be factored
`prime_factors_gen`(n)

prime factors generator

Parameters: n (int) – number to be factorized
`is_prime`(number)

Checks if a number is prime

Parameters: number (int) – number to check if is prime -> True if number is prime bool
class `OctopusPrime`(plim=100)

Bases:`collections.MutableSequence`

OctopusPrime, the 8-leg autobot, here to help you find PRIMES

`_transform`(self, n=None)

TRANSFORM / grow the list

Parameters: n – (Default value = None)
`primes_below`(self, upper_bound)

Lists primes, p, such that p < upper_bound

Parameters: upper_bound (int) – exclusive upper bound -> primes less than upper_bound list
`primes_between`(self, lower_bound, upper_bound)

Lists primes, p, such that, lower_bound < p < upper_bound

Parameters: lower_bound (int) – exclusive lower bound upper_bound (int) – exclusive upper bound -> primes between lower_bound and upper_bound list
`__len__`(self)
`__getitem__`(self, i)
`__delitem__`(self, i)
`__setitem__`(self, key, value)
`insert`(self, index, object)
Parameters: index – object –
`__str__`(self)
`__repr__`(self)