Re: Length of sequence of consecutive primes starting at 2
From: Hugo Pfoertner (nothing_at_abouthugo.de)
Date: 07/16/04
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Date: Fri, 16 Jul 2004 20:40:13 +0200
Joseph Weinberg wrote:
>
> Hello
> I would like to know how long the list of consecutive primes (i.e. not
> skipping any primes in between) is and can I find it somewhere. Also,
> how far apart are the current largest prime (41st Mersenne prime?) and
> the last prime in the above sequence?
> Best regards,
> Joe
The lenght of this list is only dependent on how much money you are
willing to spend to buy disk space. Let's assume you have two 250GByte
disks (400 bucks are not too much for possessing such a list ;-). If you
don't apply any tricks (e.g. the 30 numbers/Byte technique or something
similar) it might be convenient to store 8byte integers. You can then
store 500*10^9/8=6.25*10^10 prime numbers. The largest element of this
list will be somewhere between 1.692*10^12 and 1.754*10^12, using the
Dusart and Rosser/Schoenfeld bounds for the k-th prime.
The 41st known Mersenne Prime
http://mersenne.org/prime7.txt is approximately
2.994104294..*10^7235732,
so you need a few more disks to store the primes in the remaining gap.
Hugo
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