Number Theorem

[retina]

Originally Posted by R.D. Silverman

If you want to discuss a subject you need the pre-requisites.

But there are no such statements made on this forum stating any pre-requisites. I think it is fair for herege to find a math forum and ask a question. I also think it is fair for me to try to ask for clarification and answer whatever I can. You suggested I keep quiet but where would herege be now if I did?

Without knowing the upbringing or background of the posters it is not fair to judge so quickly. Perhaps it is a simple English language barrier thing, maybe herege was born in some-poor-country and is trying his/her best to learn something to improve his/her life with a better (or any) job. There could be a thousand other reasons why people post and I see no reason to keep quiet when I might be able to help.

But, never mind, I think I might have caught you on a bad day. Perhaps tomorrow will be a better day.

[cheesehead]

Originally Posted by R.D. Silverman

If you want to discuss a subject you need the pre-requisites.

Perhaps you recall exchanges you and I had a while back about the differences between this public forum and a formal classroom. As retina points out, no prerequisites (other than simple mersenneforum.org registration) have been placed on participation in this forum by the forum administration.

If you are unwilling to do background reading then you should not get involved.

I remind you that your background reading should have included the rules, regulations, and prerequisites of this forum, and that, therefore, you should be aware that no prerequisites of the sort you seem to demand here actually pertain to this forum.

So it looks like you are the one who is here deficient in prerequisites. I write "looks like" because I'm sure you actually have been aware of all forum prerequisites, including the absence of any required reading, knowledge, and so forth, in the past, but have just temporarily forgotten some of that recently.

Your attitude stinks.

Ahem.

Yet another instance of the "instant gratification" generation.

That's a mistaken attribution.

retina and you obviously have some differences in worldview along the lines of those I have not yet summarized from George Lakoff (a project in progress). It's not a generational matter.

[ewmayer]

Closing this thread before it devolves into yet another neverending snipe and countersnipe fest -- if anyone has anything further to add regarding the substance of the original thread topic, PM me.

[xilman]

Originally Posted by R.D. Silverman

What we can say is that the probability that the
MR test is in error is 4^-n. (and yes, it is 4^-n, not 2^-n).

Bob, if you're going to require precise statements from all participants, then you must also allow me to be pernickety.

Your statement quoted above is just plain wrong. I'm certain you've already done your background reading so I'll have to assume you failed to proof-read your post carefully enough.

The probability of the result of a single MR test on integer N to base b, where 1 < b < N, being in error is at most 1/4. For provably most integers, the probability of error is much less than 1/4.

It took me ages to get this concept over to the PGP developers in the mid-90s. They kept wanting to run numerous tests, even though one or two MR tests are easily sufficient for the purpose. (In the early 90s I spent even longer persuading them that a MR-test was better than the Fermat test they were then using --- it's faster, has a lower probability of failure in the average case and a much much better reliability in the worst case.)


Paul