Re: Prime lists and Computation

Carl Parkes:

> Q1. Given a large integer {x} . If it is proved to be prime, what other
> information is generated?
>
> 1. Complete Prime list to x^(1/2)?

No.

> Q2 Is their a complete list of primes to X Published?
> X~ 10^20? X~10^30. X= 10^??

I have seen one up to 10^7 several years ago, published at the end of the
19th century. Since then, such lists have become uninteresting, at least
after the advent of computers. You can easily check a number less than
10^7 for primeness in a few minutes with a hand-held, non-programmable
pocket calculator which is less heavy than the book - and you save the way
to the library.

> Q3 Storage: When does it become more efficient to store the prime list than
> to generate/calculate it.

Never. Up to 10^k, there are about 3/7k * 10^k primes--too many for a list.

> Q4 What would be the expected time to factor a 1 MB file, if it was
> interpreted as a very integer.

Quite some time--you won't see the end of the computation.

Helmut Richter
.

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: Length of sequence of consecutive primes starting at 2
    ... >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. ... lists of all primes up to at least 10^12 ... into permanent or even semi-permanent storage. ...
    (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)