The 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.

Aldrich