January 20th, 2014, 08:08 PM  #1 
Senior Member Joined: Nov 2013 Posts: 246 Thanks: 2  primes and twin primes: Number between powers of 10
I have been curious about prime and twin prime distribution. So now lets explore primes and twin primes. 1100: Primes: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61, 67,71,73,79,83,87,91,97 1100: Twin Primes 3,5,7,11,13,17,19,41,43,71,73 1001000: Primes: 101,103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823,827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 1001000: Twin Primes 101,103,107,109137,139,191,193,197,199,227,229,281 ,283,311,313,347,349431,433,461,463,521,523,641,64 3,827,829,857,859,881,883 Now why is it that as you go from 1 power of ten to another power of ten the number of primes increases but the percent primes decreases? now do twin primes and primes have a constant ratio or does the ratio change? 
January 20th, 2014, 11:32 PM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: primes and twin primes: Number between powers of 10 Quote:
 
January 21st, 2014, 09:03 AM  #3  
Senior Member Joined: Nov 2013 Posts: 246 Thanks: 2  Re: primes and twin primes: Number between powers of 10 Quote:
thats only approximate not exact like you would get if you counted all the primes and all the twin primes and divided the twin primes by the primes(the actual number of them not the primes themselves).  
January 21st, 2014, 09:16 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: primes and twin primes: Number between powers of 10 Quote:
 
January 21st, 2014, 11:48 AM  #5  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: primes and twin primes: Number between powers of 10 Quote:
 
January 21st, 2014, 08:50 PM  #6  
Senior Member Joined: Nov 2013 Posts: 246 Thanks: 2  Re: primes and twin primes: Number between powers of 10 Quote:
counting the primes and twin primes and dividing the number of twin primes by the total primes like this: # of twin primes/ # of primes gives you an exact ratio. It might give you repeating decimals but that is still exact. c/log(n) (I think that is what you said) gets closer and closer to the exact ratio but still doesn't get to it exactly. thus you have this: lim x(where x is c/log(n)) > ? = # of twin primes/ # of primes It is an approximate that equation you have. Simply counting the number of primes and twin primes gives you the exact ratio.  
January 22nd, 2014, 01:07 AM  #7  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: primes and twin primes: Number between powers of 10 Quote:
 
January 22nd, 2014, 05:20 AM  #8  
Senior Member Joined: Nov 2013 Posts: 246 Thanks: 2  Re: primes and twin primes: Number between powers of 10 Quote:
by simply counting I don't mean just looking at the numbers and add 1 to 1 every time you come across a primes(that would mean much fewer primes than ?). I mean doing trial division and figuring out it is prime and than adding 1 to the number of primes you have so far.  
January 22nd, 2014, 06:25 AM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: primes and twin primes: Number between powers of 10 Quote:
 
January 22nd, 2014, 06:40 AM  #10  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: primes and twin primes: Number between powers of 10 Quote:
 

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