Bram Cohen posted an interesting programming challenge.

After some puny attempts at some kind of proof, I gave up and wrote a search to find candidate exponents - here's my brute-force search 'solution':

#!/usr/bin/env python

def baseconvert(x, base):
        result = []
        while (x/base > 0):
                result.append(x%base)
                x = x/base
        result.append(x)
        resultstring = ""
        for digit in result:
                resultstring = "%d" % digit + resultstring
        return resultstring

for exp in range(0, 100000):
	if exp%1000 == 0:
		print "waypoint", exp
        power = pow(2,exp)
        based = baseconvert(power, 7)
        if based.find("000") < 0:
                print exp, "no triplezeroes", based

In the comments on his original entry, Bram says, "[t]here's a bit of a joke with regards to the correct answer - it's in a field of mathematics where we basically can't prove anything, so what you do is test numbers up to a high enough value that you're convinced there couldn't possibly be any higher ones".