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## Takes an image and finds a prime that looks like that image
## Usage: python [Image path] {image_width} {image_height}
## Miller-Rabin implementation code from:
import math
import copy
import os
import random
from PIL import Image
import sys
def ipow(a,b,n):
#calculates (a**b)%n via binary exponentiation, yielding itermediate
#results as Rabin-Miller requires
A = a = long(a%n)
yield A
t = 1L
while t <= b:
t <<= 1
#t = 2**k, and t > b
t >>= 2
while t:
A = (A * A)%n
if t & b:
A = (A * a) % n
yield A
t >>= 1
def MillerRabinTest(test, possible):
# Output:
# - True if not prime
# - False if the number can be prime
return 1 not in ipow(test, possible-1, possible)
smallprimes = (3,5,7,11,13,17,19,23,29,31,37,41,43,
def test_prime(p, k=None):
if k==None:
bits = math.log(p,2)+1
k = int(2*bits)
for i in smallprimes:
if p % i == 0:
return False
for i in xrange(k):
if i>20:
print "These are likely to be prime, test ",i, "of", k
test = random.randrange(2, p)|1
if MillerRabinTest(test, p):
return False
return True
if len(sys.argv)<=3:
print "Missing arguments, to use the script:",sys.argv[0],"[Image path] {width} {height}"
#gets the real size of the image
basefn = sys.argv[1]
img =
w,h = img.size
W,H = int(sys.argv[2]),int(sys.argv[3])
def convert_image(img,W,H):
# converts image into a sequence of 1's and 8's
w,h = img.size
img = img.resize((W,H), Image.ANTIALIAS)
img = img.convert('L')
avr = sum(img.getdata()) / (W*H)
bw = img.point(lambda x: 0 if x<avr else 255,'1')
ps ="".join( map( lambda c: "1" if c>128 else "8",bw.getdata()))
ps = ps[:-1]+"1"
# prints the image as a sequence of 1's and 8's
print "The image will look like this (warning: this number is not prime yet!)."
for i in range(H):
print ps[i*W: i*W+W]
return ps
def change(ps):
#changes a random position in the image
ran_pos = random.randrange(len(ps))
c = ps[ran_pos]
if c == "1":
n = "7"
n = random.choice(["0","9","6","4","5","2","3"])
newps = ps[:ran_pos-1] + n + ps[ran_pos:]
return newps
def find_prime(ps):
#does random changes until a prime is found
if test_prime(int(ps),50):
return ps
i = 1
print "Finding Prime"
while True:
if (i%50)==0:
print " "
P = change(ps)
if test_prime(int(P),50):
return P
if __name__ == "__main__":
number_image = convert_image(img,W,H)
prime_image = find_prime(number_image)
print "PRIME FOUND!"
for i in range(H):
print prime_image[i*W: i*W+W]
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