Python prime number list wrong?

Question

I've tried with several different methods to get the 10001 prime number.

def isPrime(value):
  if ((2**value)-2)%value==0:
    return True

def nthPrime(n):
  count = 0
  value = 1
  while count < n:
    value += 1
    if isPrime(value):
      count += 1
  return value

When 10001 is the argument this returns 103903. When I'm expecting 104743.

I've tried:

primes = []
for i in range(2,105000):
  if ((2**i) - 2) % i == 0:
    primes.append(i)

print primes[10001] ---> 103903

Answer 1

I believe your prime sieve is wrong. Try using an isPrime function that takes that number mod each lesser prime. If any of these are 0 then the number is composite (not prime). To the best of my knowledge there is no single comparison that will tell you if a number is prime, as your isPrime function assumes.

Answer 2

Is this for Project Euler? It does seem familiar to me.

Your isPrime function is wrong, like TEOUltimus said, there is no one way to tell if a number is prime.

Simple Prime Generator in Python

This pretty much answers your question i guess.

Answer 3

You can make a function to generate primes, this might be slow but it will work.

Here's my function to do so :

def PrimesSieve(limit):
    np=set()
    p=[2]
    for i in xrange(1,limit+1,2):
            if i == 1: continue
            if {i} & np: continue
            beg=2 if i % 2 == 0 else 0
            for j in xrange(beg,int(limit)+1,i):
                    np.add(j)
            p.append(i)
    return p