20090214, 10:01  #1 
May 2005
2^{2}·11·37 Posts 
Other news

20090214, 12:20  #2  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
13761_{8} Posts 
Quote:
Is this me just being blind? 

20090214, 18:51  #3 
"Curtis"
Feb 2005
Riverside, CA
1011010101011_{2} Posts 
Well, if you click on the sieve reservation link from the link cruelty provided, they clearly state they are using sr1sieve right now. What makes you think they are using sr2 for singlek searches?
Curtis 
20090214, 20:14  #4  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
6129_{10} Posts 
Quote:
look at the second post a person gives a command including sr2sieve i suspect that the organizer has realized and is trying to sort it out 

20090510, 16:46  #5 
"Curtis"
Feb 2005
Riverside, CA
7·829 Posts 
http://science.slashdot.org/article..../05/10/1322207
I'm not sure how surprising this is, but such patterns are fun to discuss. 
20090511, 14:41  #6 
"Gary"
May 2007
Overland Park, KS
12172_{10} Posts 
Why would this be a new pattern? They've discovered nothing and I'm surprised that such a phenomon has a name. It's a simple matter of odds because we start counting at 1. As an example, let's take groups of 100, 200, 300, etc. people up to 1000 and have them number themselves. If you used only groups up to 500, the phenomon would be even more "biased" towards the #1.
If there are 100 people in the group and those people are numbered 1 thru 100, then the chance that any one given person's # begins with a 1 is: 1+10+1=12 out of 100 or 12%. For 200 people, it's 1+10+100=111 out of 200 or 55.55%!! For 300; 111/300 = 37%! 400; 111/400 = 27.75% 500; 111/500 = 22.2% 600; 111/600 = 18.5% 700; 111/700 = 15.86% 800; 111/800 = 13.88% 900; 111/900 = 12.33% 1000; 112/1000 = 11.2% The average of all percentages is 22.62%. Now...stopping the groups at 1000 is nearly the least favorable possible example for a leading digit of 1. Of course the most favorable would be 199, where 111/199=55.78% begin with the #1. The least favorable is technicaly 999, where 111/999=11.11% begin with the #1. Now, if you chose the average of the above groups between 0 and 1000 to stop your groups at...500; the average of those 5 percentages would be 30.89% and that is quite close to the log of 2, which is .30103. It's interesting that the LOWEST possible percentage for a leading digit of #1 is 11.11% or 1 in 9. If you assumed a random distribution of leading digits, that is the AVERAGE that you would expect (since a counting number cannot start with 0); not the lowest! I realize this is an overly simplistic example but easily demonstrates why a much higher percentage of anything that is tabulated, accumulated, or counted starts with a 1 instead of a 9. It's because we start counting at 1. Using the log method, you'd have: Leading digit of 1; log(2) = .30103 = 30.103% chance Leading digit of 2; log(3)log(2) = .17609 = 17.609% chance Leading digit of 3; log(4)log(3) = .12494 = 12.494% chance [etc. up to:] Leading digit of 9; log(10)log(9) = .04576 = 4.576% chance Note: log is base 10. I'm only speculating that the above would be close to correct. It appears that the pattern would fit. Regardless, you can't use such a thing to predict the stock market or electricity bills or primes or anything else. The random nature of anything that can potentially begin from the #1 (or a small fraction) such as prices of anything or the # of occurrences of something simply create such a phenomon. To me, it's all a bunch of grandstanding. The article even makes some comment that at the low end of the spectrum that the prime numbers leading digit is more "biased" towards a leading digit of the #1. Of course it is because the percentage of prime #'s drops so greatly when they are small! As they approach infinity, the chance of prime becomes almost uniform for any specific # of digits. Hence almost the same # of primes would occur with a leading digit of 1 as it would 9. Such stuff is interesting to discuss but otherwise generally useless information. Gary Last fiddled with by gd_barnes on 20090511 at 14:44 
20090511, 17:07  #7 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
Gary, your example for your argument is slightly misleading: if we count from 1 to 200, it's accurate, but we are only considering primes, so it's the same as saying 2 to 199 since 1 and 200 are automatically eliminated. Also, as you later state, that's the most extreme possible scenario.
Gary, see my prime counting here: http://www.noprimeleftbehind.net/for...?p=130#post130 My second table does indeed succumb to the problem you stated of ending our counting at an unfair location. pi(10,000,000) is 179,424,673, so everything from 100,000,000 (which is pi(5,761,455); finding all this at http://primes.utm.edu/nthprime/ BTW, a very useful page for finding this stuff ) up automatically starts with 1, similar to your worstcase scenario of 199. Indeed, for most fairly small round numbers x of pi(x), pi(x) is just above a power of 10 and so will give quite inflated figures But, if we instead count the primes between 10^a and 10^b, (a and b integers, whether a=0 or a=b1 or whatever) we are instead left with the most extreme scenario in the opposite direction, that of no artificial inflation. My first table counts between 10^6 and 10^7, and does show a small but definite preference toward lower starting values, for obvious reasons. And the article states that the researchers were counting between 1 and 10^d, so they avoided the problem you stated. (whether or not they recognized the problem of counting the leading digits in the first 10^x numbers and intentionally avoided it or just didn't think about it at all, I do not know) Last fiddled with by TimSorbet on 20090511 at 17:11 
20090519, 02:49  #8 
"Gary"
May 2007
Overland Park, KS
2^{2}·17·179 Posts 
But the article also referred to what, in effect, are counting numbers; i.e. electric bills, stock prices, population counts, etc. In that case, my calculations should be close. In the case of primes, the difference is much smaller between a starting digit of 1 and 9. That occurs for a similar reason: The primes starting with a 1 are smaller than the primes starting with a 9 and hence have a greater chance of being prime, albeit that amount of "greater chance" is relatively small; especially as the # of digits becomes large.
Last fiddled with by gd_barnes on 20090519 at 03:05 
20090519, 02:57  #9 
"Gary"
May 2007
Overland Park, KS
2^{2}×17×179 Posts 
I just wanted to say congrats to RPS for maintaining the top spot on # of primes! That was a lot of drives you guys have put out to maintain it. Barring a miracle (for us), it's doubtful that NPLB will be able to catch up now. As Carlos stated in another thread, likely PrimeGrid will pass us both; I'm thinking within 3 months or so. I think the top5000 site needs a separate listing for BOINC and nonBOINC projects. It would make things more interesting.
One thing that I, and I'm sure Karsten, would like to see is the nontop5000 portion of the k's that you're searching filled in. It certainly makes for less messy Rieselprime.de pages. Just thought I'd bring that up. I believe that Karsten does a lot of searching on his own to fill in range for various k's searched by individuals and drives so I'm sure he'd appreciate some help with it. Gary Last fiddled with by gd_barnes on 20090519 at 03:08 
20090519, 07:15  #10 
Nov 2003
2×1,811 Posts 
Thank you.
With limited resources, we are doing what we can. 
20090519, 18:17  #11 
Sep 2004
B0E_{16} Posts 

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