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 November 21st, 2009, 03:47 PM #1 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 354 Thanks: 7 Math Focus: primes of course # of primes Easy one. I realize the count is infinite, but in terms of certified primes, excluding specialized form ones, is the certified number tracked and updated anywhere by anyone? Maybe a few years ago it was one number, today is a few million more, whatever. [I presume certified xcludes pseudoprimes?] Thanks
November 21st, 2009, 07:59 PM   #2
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Re: # of primes

Quote:
 Originally Posted by billymac00 Easy one. I realize the count is infinite, but in terms of certified primes, excluding specialized form ones, is the certified number tracked and updated anywhere by anyone?
Surely not. Here's a prime
Code:
1732171865069032155779794045187
and its Pocklington-Lehmer certificate
Code:
[2 2 1]

[17 2 1]

[443 2 1]

[38401050773 2 1]
bit the prime is 'so large' that almost surely no one before has ever certified this to be prime. (There are ~3 billion billion smaller primes for each person on Earth, for example.) But since it's so easy to certify this as a prime -- Pari did it in microseconds -- who could possibly keep track?

 November 22nd, 2009, 05:12 AM #3 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: # of primes Perhaps you are thinking of Mersenne primes. Forty-seven are known. They are the ronin of math. Okay, maybe not.
 November 22nd, 2009, 10:01 AM #4 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 354 Thanks: 7 Math Focus: primes of course Re: # of primes yes I meant normal primes. CRG, are you saying to merely use isprime of Pari? To help me learn, how xactly was that certificate retrieved out of Pari? thanks ...
November 22nd, 2009, 04:05 PM   #5
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Re: # of primes

Quote:
 Originally Posted by billymac00 yes I meant normal primes. CRG, are you saying to merely use isprime of Pari? To help me learn, how xactly was that certificate retrieved out of Pari? thanks ...
isprime(p,1) gives a certificate for p. Other flags may give other certs; I don't recall the settings.

Edit: As of the current build, 1 is the only flag that gives a certification. If you want a better method, try Primo or François Morain's ECPP.

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