On Mon, 22 Jul 2019 07:07:32 -0400, Robert J. Hansen stated: >> I went to an EFF (Electronic Frontier Foundation) meeting and a big >> and tall guy came to me and told me that he had a way of Breaking PGP >> and told me he had been working on a database program that made this >> possible and spouted off terms I had never heard before. > >Yeah, these conspiracy theorists always show up. > >> I went back inside, and I couldn't find him. I had questions. > >You're in the right place. > >Mathematicians have come up with different ways to estimate how many >primes there were under a certain value -- what we call the prime >counting function, or "π(x)" in mathematicalese. There are lots of >ways to do it, but they all give answers very close to each other: >these are estimates, not precise numbers. > >The first estimate for π(x) was "x divided by the natural logarithm of >x". > >Let x be 100. The natural log of 100 is about 4.6. 100 divided by 4.6 >is about 22. Thus, we expect there to be about 22 primes under 100. >There are in fact 25 -- so while this method isn't perfect it's >definitely enough to get us in the neighborhood. > >If we do that same equation for a 2048-bit key, it turns out there are >10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 >000 000 000 000 000 000 000 different prime numbers that could go into >it. > >Google's total data storage is about 10 exabytes. In 10 exabytes you >could store about 40 000 000 000 000 000 prime numbers. > >There's just no way anyone on earth has a list of prime numbers that >they're trying one after another. Not only isn't there enough hard >drive space, but the hard drives required would literally be bigger >than the entire Milky Way galaxy!
I am not sure about that. If a good data compression algorithm was employed, they might be able to save the space of a solar system or two. -- Jerry
pgp_kqZgIjIlX.pgp
Description: OpenPGP digital signature
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