20180718, 12:11  #12 
Jul 2018
100111_{2} Posts 
10^N:prime count ( < = 10^N)
================ 10^0:1 (many people say: 1 is not prime, but 1, there is a prime) 10^1:4+1=5 10^2:25+1=26 10^3:168+1=169 10^4:1229+1=1230 10^5:9592+1=9593 so other count must be +1 10^26:1699246750872437141327603+1 10^27:16352460426841680446427399+1 cumulative real count top lines. question: range count / before range count ? range count: 10^(N1){+0,1 if needed} to 10^(N):range prime count:(range prime count)/(before range prime count) =================================================================================================== 10^0+0,1 to 10^1:51=4:4/1=4 ** 10^1 to 10^2:265=21:21/4=5,25 ** 10^2 to 10^3:143:143/21=6,80952 ** 10^3 to 10^4:1061:1061/143=7,41958 ** 10^4 to 10^5:8363:8363/1061=7,88219 ** ... 10^17 to 10^18:22116397130086627:22116397130086627/2344318816620308=9,43404 ** ... 10^26 to 10^27:14653213675969243305099796:14653213675969243305099796/1522400441473293371915923=9,62507 ** ... real count top lines. 10^27 real cumulative count=16352460426841680446427399+1=16352460426841680446427400 10^27 kumalatif Rieamann count =16352460426841662907482112 (1635246042684168044642740016352460426841662907482112)/16352460426841680446427400=1,07e15 Riemann count very near real count! 163524604268416_80446427400 163524604268416_62907482112 last 11 digit! but last 11 digit not important for rate 10^38 cumulative Riemann count:1156251261026516892443946650513178624=1,156251261026516892443946650513178624e36 10^37 cumulative Riemann count:118788158912168252071104864537542656=1,18788158912168252071104864537542656e35 10^36 cumulative Riemann count:12212914297619365393344580861034496=1,2212914297619365393344580861034496e34 10^36 to 10^37:1,0657524461454888667776028367651e+35 10^37 to 10^38:1,0374631021143486403728417859756e+36 (Rieamann range prime count)/(before Rieamann range prime count) 1,0374631021143486403728417859756e+36/1,0657524461454888667776028367651e+35=9,73456 ** Rieman count limit: 10^37 question: 10^1001? lower limit for prime count=range / ln(middle_point_of_range) ln:logarithm_natural 10^1000 to 10^1001, range=9e1000 middle_point_of_range=5,5e1000 lower limit prime count=9e1000/ln(5,5e1000)=3,905758659e+997 10^1001 to 10^1002, range=9e1001 middle_point_of_range=5,5e1001 lower limit prime count=9e1001/ln(5,5e1001)=3,9018596861e+998 range count / before range count =3,9018596861e+998 / 3,905758659e+997=9,9900173 ** question: 10^(10001)? windows calculator limit < this calculation. obviously: 10>rate >9,99 question: 10^(9998)? ln:logarithm_natural 10^9997 to 10^9998, range=9e9997 middle_point_of_range=5,5e9997 lower limit prime count=9e9997/ln(5,5e9997)=3,909533749962e+9993 10^9998 to 10^9999, range=9e9998 middle_point_of_range=5,5e9998 lower limit prime count=9e9998/ln(5,5e9998)=3,909142747335e+9994 range count / before range count =3,909142747335e+9994 / 3,909533749962e+9993=9,99899987 ** question: Does it always get close to number 10? any proof of math? 
20180718, 13:29  #13  
Sep 2003
A12_{16} Posts 
Quote:


20180718, 14:32  #14  
Aug 2006
16E6_{16} Posts 
Quote:
https://oeis.org/A006880/b006880.txt which is referenced in the text you mention. There's not enough room for it in the main entry (generally we get only 270 characters there). 

20180818, 01:46  #15 
Sep 2003
A12_{16} Posts 
I wonder if they recorded the counts only at powers of 10.
It would be useful to record the counts at powers of 2 as well, and maybe other milestones. In particular OEIS sequence A059305 records Pi(mersenne_prime(n)), and it only shows 9 terms, up to 2^{61}−1 But... 2^{89} ≈ 6.1897 × 10^{26} So a new term could be added to A059305. Please tell me they didn't blow right past these milestones on their way to 10^{27} without pausing to record the value. Edit: also, new terms could be added to OEIS sequences A007053 and A086690, which also involve Pi(x) for x = powers of 2. Last fiddled with by GP2 on 20180818 at 02:11 Reason: only M89 is missing in A059305 
20180818, 02:27  #16 
Einyen
Dec 2003
Denmark
101100100101_{2} Posts 
They have at least calculated up to 2^{86}:
http://mersenneforum.org/showthread.php?t=19863 Post #15 has an answer to my similar question. http://oeis.org/A007053/b007053.txt Last fiddled with by ATH on 20180818 at 02:29 
20180818, 06:51  #17  
Jan 2008
France
17×31 Posts 
Quote:


20180819, 06:54  #18 
Aug 2005
2×3×19 Posts 
Ditto for Idesnogu post. Please get Walisch's primecount from GitHub and make some records.
To add to A059305 you will need to calculate pi(2^89). To add to A007053 you will need to calculate pi(2^87). To add to A086690 your new A059305 will do double duty. There are already 23 terms. They just do not show them all at the top of the page. Good luck GP2! Last fiddled with by dbaugh on 20180819 at 06:54 Reason: forgot a word 
20180819, 07:54  #19  
Sep 2003
2·1,289 Posts 
Quote:
Well, the good news is that AWS has R5 instances now, they are Skylake (versus R4's Broadwell and R3's Ivy Bridge). But obviously I was naive about the nature of the algorithm and imagined we could get the powersoftwo nearly for free. I don't think I can chase after this one. 

20180830, 04:38  #20 
Aug 2018
2_{16} Posts 
Why unpublished?
You shouldnt hide your work.. I created an algorithm that can get the number of primes up to 10^51227 instantly..
Maybe you should try using it to see if you can find how many there are up to a larger amount? https://www.datafault.net/primenumb...eryalgorithm/ 
20180830, 09:15  #21  
Dec 2012
The Netherlands
2^{7}×11 Posts 
Quote:
Mersenne numbers are identified by their exponent. The actual numbers are much too long to type. 

20180830, 12:47  #22  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3×5×547 Posts 
Quote:
I have shown that your algorithm does not work, at least as you have it deployed in your online implementation. 

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