[LibWhacker]

Just for fun.

[dp0622]

you gonna talk about my weight, have the guts to do it to my face. :)

[Perchant]

Divided by itself and 1 without a remainder? All numbers are like that as far as I can tell. 4 divided by 4 is 1 and 4 divided by 1 is 4 so why isn’t 4 a prime number?

[Perchant]

Oh I see it could by divided by another number as well. I’m not seeing the amazing significance.

[jpsb]

bump for a read later.

[ShadowAce]

[Hot Tabasco]

First - and this begins to get technical - note that if a number is a composite, such as n=ab, then a and b cannot both exceed √n. For example, with the composite "21" - 21=3x7 - only 7 is bigger than √21 = 4.58. Therefore, he determined that any composite integer n is divisible by a prime p that does not exceed √n.

Wow, talk about coincidence, me and my buddies were discussing this very topic last Friday night in the bar......

[NoDRodee]

I don’t understand unlucky 13 relationship to Judas.
Judas was one of the 12. How would he make 13?

[Lonesome in Massachussets]

Just for fun.

Yes, it is. Probably the worst explanation of the Sieve of Eratosthenes I ever read, overall not bad. I recall the first programming problem I ever had in school was to find the prime numbers below 100 using Fortran. I didn't know about the Sieve of Eratosthenes, but did know that any composite number had to have at least one factor less than or equal to its square root.

If you pick a number, N, "at random" from the set of all integers, what is the approximate likelihood that it is prime? Curiously enough, 1/ln(N). (ln(*) is the natural logarithm of *). The expected number of primes in the interal M to N is equal to the integral from x = M to x = N of dx/ln(x). The approximation gets relatively better as M get large. (Limit as M -> Inf and M-N -> Inf of the integral over the count of primes approaches unity.)

[golux]

Thanks for the post! I am no mathematician but...
iI am surprised to see so little about primes in this “primer!”

[IronJack]

I have a minor in math and I have never understood the fascination mathematicians have with primes. Okay, they’re only divisible by themselves and one. So what???

[zeugma]

I've run a GIMPS client for a while. The numbers are so huge now though, that it takes weeks if not months to test a single number. Personally, I think it's astounding that they can factor a number like 2^74207281-1. That number is so large that it is pretty much imaginary. There is nothing in the universe that there is that many of.

I wish my drivers license or SSN were prime. Sadly, they are both divisable by 2. Yup.I'm a nerd.

[2 Kool 2 Be 4-Gotten]

Awesome - I’ll make this my number my next password at work.

[CodeToad]

22 million digits is still small by cryptography standards.

It isn’t the logic behind a prime that is the hard part. Advanced logic must be created to shortcut the processing needed to find the prime. These numbers cannot be calculated directly and must be processed in chunks. That processing takes a looong time. So, the advanced math is about finding the next prime using math instead of processing.