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Old 2018-07-18, 12:11   #12
hal1se
 
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Quote:
Originally Posted by kwalisch View Post

pi(10^27) = 16,352,460,426,841,680,446,427,399
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^(N-1){+0,1 if needed} to 10^(N):range prime count:(range prime count)/(before range prime count)
===================================================================================================
10^0+0,1 to 10^1:5-1=4:4/1=4 **
10^1 to 10^2:26-5=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
(16352460426841680446427400-16352460426841662907482112)/16352460426841680446427400=1,07e-15
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?
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Old 2018-07-18, 13:29   #13
GP2
 
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Quote:
Originally Posted by CRGreathouse View Post
Fantastic! I've updated the OEIS entry https://oeis.org/A006880.
But this sequence only displays 26 terms. The newer 27th term is mentioned only in the notes below that.
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Old 2018-07-18, 14:32   #14
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Quote:
Originally Posted by GP2 View Post
But this sequence only displays 26 terms. The newer 27th term is mentioned only in the notes below that.
More importantly, it's in the b-file
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).
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Old 2018-08-18, 01:46   #15
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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 261−1

But...

289 ≈ 6.1897 × 1026

So a new term could be added to A059305.

Please tell me they didn't blow right past these milestones on their way to 1027 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 2018-08-18 at 02:11 Reason: only M89 is missing in A059305
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Old 2018-08-18, 02:27   #16
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They have at least calculated up to 286:
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 2018-08-18 at 02:29
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Old 2018-08-18, 06:51   #17
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Quote:
Originally Posted by GP2 View Post
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 261−1

But...

289 ≈ 6.1897 × 1026

So a new term could be added to A059305.

Please tell me they didn't blow right past these milestones on their way to 1027 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.
The computation is not incremental, so you have to choose the x you want and launch the run.
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Old 2018-08-19, 06:54   #18
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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 2018-08-19 at 06:54 Reason: forgot a word
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Old 2018-08-19, 07:54   #19
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Quote:
Originally Posted by dbaugh View Post
Ditto for Idesnogu post. Please get Walisch's primecount from GitHub and make some records.

...

Good luck GP2!
Heh.

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 powers-of-two nearly for free. I don't think I can chase after this one.
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Old 2018-08-30, 04:38   #20
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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/prime-numb...ery-algorithm/
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Old 2018-08-30, 09:15   #21
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Quote:
Originally Posted by mikenickaloff View Post
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/prime-numb...ery-algorithm/

Mersenne numbers are identified by their exponent.
The actual numbers are much too long to type.
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Old 2018-08-30, 12:47   #22
Uncwilly
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Quote:
Originally Posted by mikenickaloff View Post
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/prime-numb...ery-algorithm/
In the thread that you started: http://mersenneforum.org/showthread.php?t=23618
I have shown that your algorithm does not work, at least as you have it deployed in your on-line implementation.
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