Is there any integer multiple of N=2^2004 that includes no zeroes in its decimal representation?
... on probability
For n = 1 to 377 (where I stopped the program), such representation is always found in a "short" time, comparatively speaking in regard to the size of the numbers.
At n=375, for example, 2^n = 76957043352332967211482500195592995713046365762627825523336510555167425334955489475418488779072100860950445293568, which, multiplied by 1258101, gives a number with no zeros: 96819733198613458381733344978575743499579345812327829918735187265966692981332836264513476151439389165262616174283194368.
That is, 2^375 is a 113digit number, and the number of possibilities for the last 113 digits of its multiples is a cycle of values whose cardinality is a 79digit number, and we've looked through only about 1 and a quarter million to find what we're looking for.

Posted by Charlie
on 20040827 15:41:52 