Rare numbers: Difference between revisions

=={{header|Python}}==

===naive===

A simple implementation, just to show how elegant python can be. Searches up to 10^11 in about 3hours w/ pypy on my Intel Core i5.

<lang Python>

# rare.py

# find rare numbers

# by kHz

from math import floor, sqrt

from datetime import datetime

def main():

start = datetime.now()

for i in xrange(1, 10 ** 11):

if rare(i):

print "found a rare:", i

end = datetime.now()

print "time elapsed:", end - start

def is_square(n):

s = floor(sqrt(n + 0.5))

return s * s == n

def reverse(n):

return int(str(n)[::-1])

def is_palindrome(n):

return n == reverse(n)

def rare(n):

r = reverse(n)

return (

not is_palindrome(n) and

n > r and

is_square(n+r) and is_square(n-r)

)

if __name__ == '__main__':

main()

</lang>