---------------------------------------------------------------------- [Previous post by Allen Poapst follows]
Hi, my name is Allen Poapst, attending Brock University, St. Catharines ON, Canada. I was searching up prime sequence formula on the internet, and happened to find your name and e-mail. Some sort of GIMPS 10,000$ thing, I have no clue what this is, is it a reward for finding the formula? If so, I have found a formula for the prime sequence which I am trying to get published through the university I am attending. Yes I know this is a hotmail account and an informal letter, but it is just for inquiry purposes. Though the formula I have works in the following manner: f(x) = x.... x f(x) 2 1 3 2 5 3 7 4 11 5 13 6 . . . . . . 200,000,093 -> 11,078,945th prime (using my program that simulates my formula, this calculation on my notebook takes 11 seconds) etc... until infinite, although I have only tested my formula to approximately 5 million, using a computer simulation, the logic of the formula makes sense for all numbers, since I found a pattern that my formula exploits. So if you give a prime number into my formula, it will pop out where it is in the prime sequence, though I have not found a formula that works the other way around, where you give the position in the sequence and the formula pops out the prime number. A professor that is helping me publish my formula at the university I am attending says that he knows of no formula that is known for what I have found. Can you confirm this? And also would my formula acctually be worth 10,000$, that would be great if it was actually worth money. A response ASAP would be appreciated, and thank you for your time, I am really excited about this formula if it is unknown and I discovered it. Thank you, Allen Poapst, Brock University My e-mails: [EMAIL PROTECTED] [EMAIL PROTECTED] [EMAIL PROTECTED] ..................................................................................................................................................................... [Response by [email protected] listmember Robert Betts] The actual distribution of the prime numbers along the real line is still unknown, that is, as far as I know. In fact if the actual distribution was known, I believe perhaps it indeed might be possible to write a computer algorithm or a "formula" such as you state, but to predict the probability any given prime had a certain sequence number such as you say your formula does, given that these sequence numbers are assigned for each prime, for example sequence number 1 for 2, sequence number 2 for 3, sequence number 3 for 5..... Let x be a positive real number. What is known for sure about where a certain number of primes are, is known from the Prime Number Theorem, which says that the number of primes less than x, denoted by pi(x), is pi(x) = x/ln(x). So if I am not mistaken, (and perhaps a listmember who is a bona fide mathematics professor can help me here because I am just a graduate student), for your formula really to work would require knowledge on the actual distribution of the prime numbers along the real line. Also it would depend on someone actually proving the Riemann Hypothesis, that the Riemann zeta function has all its nontrivial zeroes along the line Re(z) = 1/2 in the complex plane. If you'd like to read up on this (like I have), you might want to obtain: 1. Riemann's Zeta Function, H.M. Edwards, Dover Publications, NY, 2001. (You'll find a proof of the Prime Number Theorem and an appendix with Riemann's notes on this topic, in this book) 2. The Art of Computer Programming, Volume II, Donald Knuth (excellent book! unfortunately I cannot remember the publisher for this, but the book is in my alma mater university library. You should be able to find it at your school's library). It's nice to hear your professor is helping you with publication. I'm envious. I wish I was so lucky. Robert Betts Graduate Student, Mathematics (Alumnus, 2002): University of Massachusetts Department of Mathematics and Science Science Building 100 Morrissey Blvd. Boston, MA USA 02125 _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
