Velocity Reviews > Re: A different take on finding primes

# Re: A different take on finding primes

Dave Angel
Guest
Posts: n/a

 11-15-2009
Vincent Davis wrote:
> Out of pure curiosity I would like to compare the efficiency of different
> methods of finding primes (need not be consecutive). Let me be clear, given
> 2min, how many primes can you find, they need not be in order or
> consecutive. I have not seen any examples of this. I am assume the solution
> is different depending on the time give, 2min or 2 hours. I assume a sieve
> solution would be best for larger times. When the numbers get really large
> checking to see if they are a prime gets costly.
> So what do you think?
>
> *Vincent Davis
> 720-301-3003 *
> http://www.velocityreviews.com/forums/(E-Mail Removed)
> my blog <http://vincentdavis.net> |
>
>

The sieve can be very efficiently written, but you have to decide
whether to optimize for memory size or for speed. At a minimum for size
you need an object for each prime currently found, and you will be
looking through that list for each new candidate. Incidentally this
approach can be done without any division. If you have memory to burn,
you make a bit array equal in size to the largest prime you expect to
encounter.

There are also good algorithms for deciding whether a number of a
particular form is prime. For example, there's a test for numbers of
the form 2**n + 1.

And don't forget the Miller-Rabin test.

DaveA

Tobiah
Guest
Posts: n/a

 11-16-2009

>> Let me
>> be clear, given 2min, how many primes can you find, they need not be in
>> order or consecutive.

Do they have to go from low to high? )

Anh Hai Trinh
Guest
Posts: n/a

 11-18-2009
> 1) google list of prime numbers
> 2) see "Prime numbers list" in the results (number 3 in the results)
>
> I found 455042511 prime numbers in approx 15 seconds.

Python).

sage: time primes_first_n(10^7);
CPU times: user 4.36 s, sys: 2.43 s, total: 6.79 s
Wall time: 6.88 s

That used 3G of RAM, you could certainly go higher if you have more
memory.

----aht