20080331, 04:50  #1 
Apprentice Crank
Mar 2006
2·227 Posts 
Connection between rank and digits on top5000 list
I was looking through the top 5000 primes list yesterday, and I found an interesting connection between a prime's rank and the number of digits it has. Let's call it "Moo's law".
Moo's law states that the rank of the prime to the power of 0.4 multiplied by the number of digits of the prime will always give rougly the same number. Let's see how it works: For the top 10 primes, Moo's law doesn't work too well. The top 5 primes are simply too big. Code:
Rank Prime Rank^0.4 Digits Rank^0.4 * Digits 1 2^325826571 1 9,808,358 9,808,358 2 2^304024571 1.3195 9,152,052 12,076,205 3 2^259649511 1.5518 7,816,230 12,129,582 4 2^240365831 1.7411 7,235,733 12,598,143 5 2^209960111 1.9037 6,320,430 12,031,011 6 2^134669171 2.0477 4,053,946 8,301,154 7 19249*2^13.. 2.1779 3,918,990 8,535,194 8 27653*2^91.. 2.2974 2,759,677 6,340,073 9 28433*2^78.. 2.4082 2,357,207 5,676,684 10 33661*2^70.. 2.5119 2,116,617 5,316,702 Code:
Rank Rank^0.4 Digits Rank^0.4 * Digits 15 2.9542 999,997 2,954,168 18 3.1777 909,526 2,890,175 25 3.6239 794,556 2,879,390 40 4.3734 644,179 2,817,283 50 4.7818 560,439 2,679,886 75 5.6237 464,957 2,614,793 100 6.3096 407,850 2,573,360 200 8.3256 301,252 2,508,083 500 12.0112 208,937 2,509,593 750 14.1262 192,241 2,715,630 1000 15.8489 169,014 2,678,691 2000 20.9128 126,660 2,648,814 3000 24.5951 112,619 2,769,875 4000 27.5946 108,344 2,989,709 4500 28.9258 101,539 2,937,094 
20080331, 05:00  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1101000010110_{2} Posts 
Any chance of a more mathematical description than "rougly"? Actually I don't even know what "rougly" means, maybe it is a mathematical term?
But I am sure you are on to something really really important there, can it be used to predict the upcoming 45th? Or maybe help towards an end global warming (if it is really warming that is)? 
20080331, 05:25  #3 
Apprentice Crank
Mar 2006
2×227 Posts 

20080331, 05:45  #4  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·3^{2}·7·53 Posts 
Quote:
Hehe, Firefox doesn't like the word "Firefox". Silly thing. 

20080331, 16:31  #5 
Oct 2005
Fribourg, Switzerlan
374_{8} Posts 

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