def A( n ):
if is_probable_prime( n ) or gcd( n, 10 ) != 1: return None
r, k = 11111, 5
while True:
if not r % n: break
r = r * 10 + 1
k += 1
return k
def primedSpiral():
'''
Returns the side length of the first spiral for which the number of primes along the diagonals are less than 10%
'''
primes_count, n = 0, 2
while( True ):
length = ( n << 1 ) - 1
sq = length ** 2
for i in xrange( 0, ( n - 1 ) << 3, ( n - 1 ) << 1 ):
if is_probable_prime( sq - i ): primes_count += 1
if primes_count * 10 < ( ( length << 1 ) + 1 ): return length
n += 1
def getSmallestPrime():
for num in range( 11, 1000, 2 ):
if num % 5 == 0: continue
numDigits = getDigitsIn(num)
for pattern in getPattern5() if num < 100 else getPattern6():
numbers = generateNumbers( pattern, numDigits )
size = len( numbers )
for number in numbers:
if not is_probable_prime( number ):
size -= 1
if size < 8: break
if size == 8:
return numbers[0]
'''
Created on Jul 27, 2012
@author: anuvrat
'''
from utils.prime_utils import totient, is_probable_prime
max_ratio, max_number = 0.0, 0
for n in xrange( 1, 10 ** 6, 1 ):
if is_probable_prime( n ): continue
ratio = n * 1.0 / totient( n )
if ratio > max_ratio:
max_ratio = ratio
max_number = n
print max_number
def can_be_written( odd_composite ):
for square in squares:
if is_probable_prime( odd_composite - square ): return True
'''
Created on Jun 30, 2012
@author: anuvrat
'''
from utils.prime_utils import is_probable_prime
squares = [2 * x * x for x in range( 1, 1000000 )]
def can_be_written( odd_composite ):
for square in squares:
if is_probable_prime( odd_composite - square ): return True
for odd_composite in xrange( 9, 10 ** 9, 2 ):
if not is_probable_prime( odd_composite ) and not can_be_written( odd_composite ): break
print odd_composite
