How long does your algorithm take to prove that 2^33219281-1 (the smallest
prime exponent Mersenne number with at least 10 million digits) is prime?
The chance that a number about this size will be prime is about 1 in 23
million. You would therefore expect to examine about 23 million candidates to
find a 10 million digit prime. OK you can cut that by a large amount by
eliminating candidates with small factors but you're still going to be left
with a large number of "awkward" candidates - I'd guess at least one million.
So unless your algorithm can prove primality of a 10 million digit number in
the order of 30 seconds you're unlikely to find a prime in about 30 million
seconds - one year is "only" 31,536,000 seconds.
If your primality proving method is rigorous and anything like as fast as
that, you've made a major discovery - our best methods are several decimal
orders of magnitude worse, even for special numbers like Mersennes. So please
tell us about it, even if you have to write it up for a maths journal and/or
patent the algorithm first.
Actually, if you've discovered an algorithm that can do that, please
don't patent it!
Soo Reams
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