21868Prime Mine Update
- Oct 6, 2010The program to find large numbers of primes
appearing on A = 5x^2 + 5xy + y^2 seems to work
pretty well. It is based, as you may recall from
some of my earlier postings on the topic, upon the
observation that primes and squares of primes ending
in one or nine seem to appear only once as values of
A, whereas composites will appear more than once.
A simple stepwise iteration and storage system finds
and records eligible integers, and the composites among
them are eliminated when they appear a second time.
For a sample of small 13 digit numbers, the program
found 18086 primes in 5.5 seconds. As the sample
numbers grew the rate slowed for 18 digit numbers
to 4,037,5243 primes located in 2500 seconds. The
results for 13 and 14 digit numbers were all verified
by trial division. Only a few of the the larger
numbers were verified this way.
It has occurred to me that some of you out there
might be able to use similar methods to find 100 times
as many primes per second as I have on my old Pentium3
running Pascal software. I have heard that some low-end
encryption systems may be vulnerable to this blizzard of
primes even at these low levels (just above 10^18). Of
course, encryption need not depend on large primes to
be effective. If you're so inclined, check out my
programming toy at the US copyright office (enxxxxx4a.rtf)
for a really different concept.Still, medium term, I don't
think our friends at BlowCash or SloShark systems have
anything to worry about.