Ja I did mean n = p*2^kp or n=(2^k)*p as Lloyd points out. I have discovered a cool property of those numbers, altho surely not an original discovery. All my mathematical discoveries fall into two sets: those notions that have been known since before the Permian extinction, and those notions that are original with me but are wrong.
I was looking at Goldbach's conjecture, that any even number above 2 can be expressed as the sum of two primes. So I wondered how many different ways can a number be expressed as the sum of two primes? Let P(n) be the number of ways, assuming the number 1 as not prime, but twice a prime counts in P(n). So for instance P(14)=2 because of 3+11 and 7+7 but not 13+1. So Goldbach conjectures that P(n)>0 for all even integers more than 2. There may be a standard terminology for this concept, I just don't know what it is. I calculated P(n) for all evens up to 800,000 and found that in general P(n) increases as a constant times n^.75 but if one graphs P(n) against n, one sees a cool almost fractal pattern. The numbers separate into apparent layers. The lowest layer, corresponding to about .12*n^.75 contains most of the numbers, but a second layer forms above that one. I found that that second layer is made up of factors of 6. another layer above that contains numbers that are a factor of 30. Not surprisingly, a fourth layer contains factors of 210. I guessed that still another layer would contain factors of 2310 (check) and that P(30030) should be still another layer. Altho I have only one example, the P(factors of 510510) soar still higher. I know this is correct, therefore it must be ancient knowledge. Is this cool or what? spike > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > Behalf Of Lloyd Miller > Sent: Friday, October 20, 2006 12:26 PM > To: The Great Internet Mersenne Prime Search list > Subject: Re: [Prime] name please for n = 2^kp > > > erm I think he means n=(2^k)*p _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
