Re: Length of sequence of consecutive primes starting at 2

From: Bob Silverman (rsilverman_at_draper.com)
Date: 07/19/04 

Date: Mon, 19 Jul 2004 15:57:44 +0000 (UTC)

On 16 Jul 2004, 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?

This question is very poorly posed. What do you mean by THE list
of consecutive primes?

(1) By specifying 'THE' list, you assume such a list, if it exists,
is unique. What makes you think so?

(2) What do you mean by "consecutive primes". Do you mean "twin
primes"? What does it mean for primes to be "consecutive"? If by
consecutive primes you mean "all primes starting with 2", then the
answer to your question about the list of consecive primes is:

INFINITE

The list of all primes starting with 2 is infinite. If instead, you
mean the largest list of all primes starting with 2 that has ACTUALLY
been published, that is a DIFFERENT question.

(3) If you mean that you are looking for a list of ALL primes below
a certain bound and you want the list with the largest bound that has
actually been calculated, I can tell you that such a list does not
 exist per se. Or rather, that such a list changes constantly, so you
 are asking for a moving target. It is also one thing to calculate
such a list, it is another to store and publish it.

(4) If you want a list of primes up to some bound B, it would be
faster to generate it via a sieve than to read it over the internet.
And storage for any reasonable B would be problematic. You are
talking terabytes.

(5) The answer to your last question is trivial. If B is the bound
on your list, then M41 - B is the number you are looking for.

(6) At one time or another, lists of all primes up to at least 10^12
have been generated. But I can't imagine anyone putting such a list
into permanent or even semi-permanent storage. It would be pointless.
Further, if at anytime someone did store such a list, extending it
a little bit would be trivial.

(7) If you tell me what you REALLY want, I can and will help. But
your questions are too imprecise for me to discern your real desire.
Please. If you are going to discuss mathematics, then you need to
learn how to pose your questions more precisely.

Relevant Pages

  • Re: Towards a Formula for Primes
    ... An Axiomatic Theorem on the Decidability of Primes. ... I was thinking in a Hilbert way. ... it would have given zero and 123 for the two lists. ...
    (sci.math)
  • Re: Tuple question
    ... totally bogus to me. ... Say I want to work with some primes and I have a primes generator. ... that keep screamign LISTS, ...
    (comp.lang.python)
  • Re: Chez Watt: Prime Idiocy
    ... figured criticism for slop was better than criticism for ommission. ... There is a disclaimer that the lists are only ... "primes" if you haven't got a clue what you are talking about. ...
    (talk.origins)
  • Re: Prime lists and Computation
    ... > Q2 Is their a complete list of primes to X Published? ... sufficient storage is available to store them all. ... prime lists for trial division. ... of digits by 3 would double the factoring time. ...
    (sci.math)
  • Re: sums of distinct primes redux
    ... > Every sufficiently large integer is the sum of *consecutive* primes. ... Would a prime itself be considered as a sum of consecutive primes? ... If a religion is defined to be a system of ideas that contains unprovable ...
    (sci.math)