An anagram is the result of rearranging the letters of a word or a phrase to produce a new word of phrase, using all the original letters exactly once. Anagrams are sometimes used as pseudomyms (Leonardo da Vinci: o draconian devil; The Mona Lisa: oh lame saint).

A simple way to determine whether two words or phrases are anagrams, is to compute a hash value in such a way that only anagrams have an identical hash value. One way to compute such as hash value assigns each letter of the alphabet to the next prime number (a=2, b=3, …, z=101), and computes the hash as the product of all values corresponding to the letters of the word or phrase. In computing the hash value, only letters of the alphabet must be taken into account (no punctuation symbols, digits, etc.), and must be treated case insensitive. As such, the words callers, cellars and RECALLS all result in the same hash value 615461330, making them anagrams.

Hint: While working on this programming challenge you should take a break an watch the Monty Python sketch "The man who speaks in anagrams¹". You will hardly understand a single word of the conversation, unless you have a look at the transcript².

Assignment

Write a function nPrime that takes an optional integer argument $$n$$. The function must return a list containing the first $$n$$ prime numbers. If no argument is passed to the function, a list containing the first 10 prime numbers should be returned.
```
nPrime([n])
```
Write a function anagramHash that takes exactly two argument. The first argument is a phrase whose hash value must be returned by the function. The second argument is a list containing 26 (or more) integers that must be used to compute the hash value: the letter a corresponds to the first integer in the list, the letter b to the second number, and so on. The hash value is computed as the product of all integers that correspond to the letters in the phrase. When computing the hash value, only letters from the alphabet must be taken into account (no punctuation symbols, digits, etc.), and must be treated case insensitive.
```
anagramHash(phrase, integers)
```
Use the functions nPrime and anagramHash to write a function areAnagrams. The function takes two phrases as its argument, and must return a Boolean value that indicates whether the phrases are anagrams (return value True) or not (return value False). In determining whether the phrases are anagrams, the function must compute the hash values of both phrases. By default, the hash value is computed with mapping letters to the first 26 prime numbers. If a list of integers is passed as a third argument to the function, a mapping to these integers must be used to compute the hash values of the phrases.
```
areAnagrams(phrase1, phrase2[, integers])
```

Example

>>> nPrime()
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
>>> nPrime(5)
[2, 3, 5, 7, 11]
>>> nPrime(8)
[2, 3, 5, 7, 11, 13, 17, 19]

>>> anagramHash('Leonardo Da Vinci', nPrime(26))
4153036139030192260
>>> anagramHash('Leonardo Da Vinci', range(1, 27))
4073908608000
>>> anagramHash('Leonardo Da Vinci', nPrime(52)[-26:])
280080025163413341541861091223919
>>> anagramHash('O Draconian Devil', nPrime(26))
4153036139030192260

>>> areAnagrams('Leonardo Da Vinci', 'O Draconian Devil')
True
>>> areAnagrams('The Mona Lisa', 'Oh Lame Saint')
True
>>> areAnagrams('The Mona Lisa', 'Oh Lame Saint', range(1, 27))
True
>>> areAnagrams('The Mona Lisa', 'Oh Lame Saint', nPrime(52)[-26:])
True