Mathematics

Question

Dear AskNSDL, I have question about calculating primes. Upon 'googling' "calculating primes" as keyword, I found the following information. (This is introduction to a more detailed discussion.) "Calculating Prime Numbers We now consider the question of how to find prime numbers. The prime number theorem shows that if we pick an integer n at random, it will be prime with probability [approximately = ] 1/ln(n). So even if n ~ 2^512, our random n is prime with probability 1/512ln(2) ~ 0.0028. This is perfectly reasonable; in principle then we can find primes quickly...." Does the expression here, n ~ 2^512, mean n is an odd number near 2^512? Thanks, ml

Answer

Michael, Actually, n ~ 2^512 in this case merely means that n is an integer near 2^512. Of course, if n is even in that range, it can't be prime, so if it's odd, it's prime with probability about 2/512ln(2) ~ .0056 prime probability http://vrd.askvrd.org/services/answerschema.xml