Re: really? (lame question about primes)

From	Richard Heathfield <rjh@cpax.org.uk>
Newsgroups	comp.programming
Subject	Re: really? (lame question about primes)
References	<5e5de47a-7353-4ffc-9f5d-ec083d1d63ba@googlegroups.com> <kt4Fx.394338$3n4.170027@fx35.am4> <44a165dc-8447-4ae0-8695-557a7ddf00cf@googlegroups.com> <ms3peh$o5v$1@dont-email.me>
Message-ID	<_RfFx.418341$bt.398932@fx32.am4> (permalink)
Organization	virginmedia.com
Date	2015-09-01 12:20 +0100

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On 01/09/2015 10:01, David Brown wrote:

<snip>

> Yes, you can factorise C by trying to multiply pairs A * B and see if
> they match.  The trouble is, with a 600 digit number there are quite a
> lot of such pairs to try!

Well, there aren't all that many really, and the OP specified two 
300-digit integers, so we needn't bother with lower numbers.

There are only 9*10^299 300-digit numbers, so we need to test 81*10^598 
= 8.1*10^599 pairs.

Let's further assume that we have a million million (10^12) computers at 
our disposal, and that each of these is capable of multiplying a million 
million pairs a second. So we can test 10^24 pairs per second, which 
means we will definitely find the result within 8.1*10^575 seconds. 
Assuming average luck, call that 4*10^575 seconds. This turns out to be 
1.267*10^468 as long as it takes for the universe to die of entropy.

Looking at it the other way, if we assume average luck and want the 
result within, say, a million seconds (11.5 days):

4*10^575 / 1000000 = 4*10^569

Square root of 4*10^569 is roughly 6.3*10^284.

So instead of a million million computers working at a million million 
pairs per second, we need

630,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 
computers each capable of multiplying

630,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 
pairs of 300-digit integers per second.

Power crisis? What power crisis?

<snip>

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

Thread

really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-08-31 12:07 -0700
  Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-08-31 23:23 +0100
    Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 01:18 -0700
      Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-01 11:01 +0200
        Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 12:20 +0100
          Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-01 15:48 +0100
            Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:26 -0700
              Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-09-02 02:12 -0500
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 08:38 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:03 +0200
          Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 13:24 -0700
            Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 22:27 +0100
              Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 15:02 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-01 23:20 +0100
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:22 +0200
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-01 17:18 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:19 +0100
                Re: really? (lame question about primes) James Dow Allen <gmail@jamesdowallen.nospam> - 2015-09-02 12:42 +0000
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 14:21 +0100
                Re: really? (lame question about primes) Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-09-02 17:45 +0200
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 18:06 +0100
                Re: really? (lame question about primes) James Dow Allen <jdallen2000@yahoo.com> - 2015-09-03 17:05 -0700
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-04 02:18 +0200
                Re: really? (lame question about primes) Chad <cdalten@gmail.com> - 2015-09-03 22:37 -0700
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-03 23:49 -0700
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-04 00:18 -0700
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-04 08:25 +0100
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 14:36 +0100
                Re: really? (lame question about primes) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-09-02 16:49 +0100
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 17:32 +0100
            Re: really? (lame question about primes) Kaz Kylheku <kaz@kylheku.com> - 2015-09-01 22:55 +0000
              Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 01:15 +0200
          Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 03:19 +0200
            Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 02:37 +0100
              Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 11:24 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 10:42 +0100
                Re: really? (lame question about primes) fir <profesor.fir@gmail.com> - 2015-09-02 03:01 -0700
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 12:28 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 14:12 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:19 +0100
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 14:56 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 15:47 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 16:27 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-02 16:37 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-02 17:01 +0200
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 10:55 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:05 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 11:49 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-03 10:54 +0100
                Re: really? (lame question about primes) David Brown <david.brown@hesbynett.no> - 2015-09-03 13:22 +0200
                Re: really? (lame question about primes) bartekltg <bartek@gmail.com> - 2015-09-03 13:58 +0200
                Re: really? (lame question about primes) Richard Heathfield <rjh@cpax.org.uk> - 2015-09-02 13:34 +0100
  Re: really? (lame question about primes) Robert Wessel <robertwessel2@yahoo.com> - 2015-08-31 23:10 -0500

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