20081012, 20:41  #1 
May 2004
New York City
3×17×83 Posts 
PrimeEmpty Century
The first primeempty decade (x0 thru x9 composite) occurs for
x=20, since 200 to 209 are composite. What is the first primeempty century (x00 thru x99 composite)? What about the first primeempty millenium? 
20081012, 22:18  #2 
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Could we adopt more optimistic terminology by referring to "compositeful [to coin a word] centuries", or simply "composite centuries"?
Or at least "primefree centuries" rather than "primeempty centuries"? 
20081012, 22:52  #3 
Aug 2002
Ann Arbor, MI
433 Posts 

20081012, 23:18  #4 
"Richard B. Woods"
Aug 2002
Wisconsin USA
1111000001100_{2} Posts 
offby1
There are no primes between 1671781 and 1671907. I find no composite millenium below p[sub]1000000[/sub] = 15485863. Getting those results required using only the searchandreplace and duplicatelinedeleting functions of a text editor, plus visually comparing a few line numbers to line content, on a file listing the first million primes in order. I need to generate some larger lists. Last fiddled with by cheesehead on 20081012 at 23:40 
20081013, 00:00  #5 
Aug 2002
Ann Arbor, MI
433 Posts 
Blame Maple for incrementing the counter on a forwhile loop even when the while condition isn't met (and me for screwing up the double check because I used the wrong letter).

20081013, 00:17  #6 
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
[I]Classic[/I] offby1 example!

20081013, 04:25  #7 
Aug 2002
Ann Arbor, MI
110110001_{2} Posts 
No primefree centuries x000x999 up to x=27414773

20081013, 08:41  #8 
(loop (#_fork))
Feb 2006
Cambridge, England
13·491 Posts 
http://www.trnicely.net/gaps/gaplist.html
suggests that the first primefree millennium will be somewhere around 10^16, so naive search techniques are unlikely to be very useful. 1100 CNC Be.Nyman 2001 29.02 17 28907866922785967 indicates that 28907866922786xxx is a primefree millennium, and, if you trust that the list of kilogaps below 5e16 is complete, it's probably the first one. 
20081013, 08:43  #9 
Dec 2003
2^{3}·3^{3} Posts 

20081013, 09:09  #10  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Quote:
   Edit: However, there's that joke about imaginary numbers and onehalf piece of chalk, to illustrate that the number onehalf may not exist in certain contexts ... Last fiddled with by cheesehead on 20081013 at 10:04 

20081013, 09:14  #11  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
However, I do thank you for that estimate. Saves me a lot of disk space. :) Quote:
1050 CFC Be.Nyman 2000 28.25 17 13893290219203981 Last fiddled with by cheesehead on 20081013 at 09:33 

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