new_contents: # euler discoverd the remarkable quadratic equation
  #
  # n**2 + n + 41
  #
  # It turns out that the formula will produce 40 primes for the consecutive values n=0 to 39
  #
  # howver, when n = 40, the result is not prime
  # 
  # n**2 - 79n + 1601 produces 80 consecutive primes for the consecutive values n=0 to 79. the produce of the coefficients -79 and 1601 is -126479
  #
  # considering quadratics of the  form n**2 + an + b where abs(a) < 1000 and abs(b) < 1000, find the product of the coefficients a and b for the quadratic expression which produces the maximum number of primes for consective values of n starting with 0
  
  import p007
  
  
  def f(b, c, n):
      return n**2 + b*n + c
  
  primes = p007.primes(10000)
  
  maximum = {'prime': 0}
  for b in range(-1000, 1001):
      for c in range(-1000, 1001):
          #print b,c
          for n in xrange(0, 10000):
              res = f(b, c, n)
              if res not in primes:
                  if n > maximum['prime']:
                      maximum['prime'] = n - 1
                      maximum['b'] = b
                      maximum['c'] = c
                  break
  
  print maximum
  print maximum['b'] * maximum['c']            
  
subject: add 27