Currently the sieve_of_eratosthenes method has an optimisation: all primes other than 2 are a multiple of 2, so that only odd numbers must be checked. This gives roughly a 2x speed up and reduces memory usage by about half.

We can add a similar optimisation by also treating multiples of 3 as a special case: only numbers of form 6n+1 and 6n-1 have to be checked, as all other numbers are multiples of 2 or 3. See https://www.quora.com/Why-do-prime-numbers-always-satisfy-the-6n+1-and-6n-1-conditions-Is-there-any-mathematical-logic-behind-it. This should reduce execution time and memory usage by about a third.

Examples (errors in bold):

primesUpTo(10, primesUpTo(20))
[2, 3, 5, 7, 11, 13, 17, 19]

primesUpTo(20, primesUpTo(10))
[2, 3, 5, 7, 5, 7, 11, 13, 17, 19]

Try using Hypothesis in unit tests

https://rhettinger.wordpress.com/2011/05/26/super-considered-super/

See collections (collections.py, _abcoll.py) for an example with OrderedDict and Counter. Combine to make OrderedCounter:

class OrderedCounter(Counter, OrderedDict):
    pass

Made some effort to do this but it doesn't seem to work properly yet

I added mutation testing on Travis in #9.

94/520 (18.1%) of the mutants survived. Analyse each one and determine whether it is equivalent or not.

If it is not equivalent, write a test to kill it.
If it is equivalent decide if the syntax of the program can be changed to prevent the mutant from being generated.

Implement the strong Lucas probable prime test. This would allow the isPrime function to become Baillie-PSW and therefore get rid of the expensive trial division step at the end.

https://doi.org/10.1090/mcom/3438

http://treyhunner.com/2019/04/why-you-shouldnt-inherit-from-list-and-dict-in-python/

Even if a list of primes is passed into primesUpTo, lst still uses memory to refer to all odd numbers 3 to n. This is not necessary - memory usage can be reduced by only listing odd numbers from primes[-1] to n