JREF Forum General Topics Science, Mathematics, Medicine, and Technology PDA View Full Version : Prime numbers: dumb question allanb 6th February 2007, 04:50 AM I'm interested in primes although I know almost nothing about them: I understand Euclid's proof that there is an infinite number of them, and that's the extent of my knowledge.
So here's the question. If the largest known prime is N, does that imply that all primes smaller than N are known, or can there be a prime smaller than N which hasn't yet been found? Firestone 6th February 2007, 04:59 AM I don't think so.
Here (http://primes.utm.edu/primes/download.php) you can find a list af the largest known prime numbers. There is no reason I'm aware of to assume that we found all smaller primes.
(Although in theory it could be done of course.) Paul C. Anagnostopoulos 6th February 2007, 04:59 AM Excellent question. I'd guess that there can be holes in the sequence, because primes are found using various algorithms that yield classes of primes. However, primes found using the sieve of Atkin (or whatever the current best sieve is) would not have gaps in the sequence.
~~ Paul DeviousB 6th February 2007, 07:37 AM | |
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