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November 21st, 2009, 03:47 PM   #1
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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?]

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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?
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November 22nd, 2009, 05:12 AM   #3
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Re: # of primes

Perhaps you are thinking of Mersenne primes. Forty-seven are known.

They are the ronin of math. Okay, maybe not.
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November 22nd, 2009, 10:01 AM   #4
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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 ...
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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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