Check that Euler's polynomial generates primes for the values 0 to 40.

euler.py

def isPrime(n):
   """Returns True if n is prime http://stackoverflow.com/a/1801446/2987382"""
   if n == 2 or n==3: return True
   if n < 2 or n % 2 == 0: return False
   if n % 3 == 0: return False

   i = 5
   w = 2
   while i * i <= n:
      if n % i == 0:
         return False
      i += w
      w = 6 - w
   return True

# Generate primes using Euler's polynomial x**2+x+41
# Optimized to avoid multiplications
primes = []
px = 41 # px contains the value of p(x) = x^2+x+41
x = 0
while isPrime(px):
	primes.append(px)
	px += 2*x+2
	x += 1

print len(primes), " primes generated by Eulers polynomial x**2+x+41"
print primes

# Output from 'python euler.py':
#
# 40  primes generated by Eulers polynomial x**2+x+41
# [41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 
# 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971,
# 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601]