tag:blogger.com,1999:blog-24378736.post8488007512010963372..comments2018-01-13T14:32:54.107-06:00Comments on Beck's blog: Why finding big prime numbers? why study weird arithmetic sequences?beckhttp://www.blogger.com/profile/15394216344733862200noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-24378736.post-77193524466123351752017-08-16T10:50:26.440-05:002017-08-16T10:50:26.440-05:00And according to your proposed proof of primality ...And according to your proposed proof of primality to check if n is prime I need to stop dividing by k and checking if my division is whole number for all k<Sqrt(n).<br /><br /><br />Imagine that the number you want to test has smallest prime factor 2^74,207,281 − 1 (This is the Mersenne 49), this number has 22 million digits, so your method would not finish even with a quantum computer. <br /><br />What you are describing is a sieve to identify primes less than n by checking if they are divisible by all the k < sqrt(n). But this sieving doesn't work in practice to decide if an arbitrary integer is prime.<br /><br />beckhttps://www.blogger.com/profile/15394216344733862200noreply@blogger.comtag:blogger.com,1999:blog-24378736.post-76269668260863597022017-07-14T22:55:27.928-05:002017-07-14T22:55:27.928-05:00To prove whether a number is a prime number, first...To prove whether a number is a <a href="http://nuclearstrategy.co.uk/prime-number-distribution-series" rel="nofollow">prime number</a>, first try dividing it by 2, and see if you get a whole number it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 and so on.primenumbershttp://nuclearstrategy.co.uk/prime-number-distribution-seriesnoreply@blogger.com