mersenneforum.org New confirmed pi(10^27) prime counting function record
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2018-09-09, 17:25   #23
Till

"Tilman Neumann"
Jan 2016
Germany

5·79 Posts

Quote:
 Originally Posted by mikenickaloff 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/

I typed in a number that fits into the window, so the answer should definitely come instantly?

Code:
19700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000197
Unfortunately i do not see any response (couple of miutes waiting)

Last fiddled with by Till on 2018-09-09 at 17:26 Reason: typo

2020-05-01, 22:28   #24
rudy235

Jun 2015
Vallejo, CA/.

7×137 Posts

Quote:
 Originally Posted by kwalisch After roughly 5 months of computation David Baugh and myself have verified pi(10^27): pi(10^27) = 16,352,460,426,841,680,446,427,399 This time the computation took 20.35 CPU core years, this is 11.6% faster than our first computation. The speed up comes from primecount improvements, particularly I have added pre-sieving and wheel factorization to primecount's sieving algorithms. Below are the details of the verification: Code: x = 1000000000000000000000000000 y = 231112254739 pi(y) = 9199337709 P2 = 4743234949871865833944278 S1 = 45739379279637813150 S2_trivial = 42247262851521121201 S2_easy = 4453498620247012088893172 S2_hard = 16642108769824393833206446 S2 = S2_trivial + S2_easy + S2_hard pi(x) = S1 + S2 + pi(y) - 1 - P2 pi(x) = 16352460426841680446427399
Hello: The last post on this thread is a bit short of twenty months old. Is there any chance some new calculation has increased the size of the known π(x) ?
For instance π(290 is very close to π(1027) and while the next exponent (1028 is a difficult task I would think some progress might be there after almost 5 years. Last time it took about a year to go from 10^26 to 10^27

2020-05-06, 07:21   #25
kwalisch

Sep 2015

1610 Posts

Quote:
 Originally Posted by rudy235 Hello: The last post on this thread is a bit short of twenty months old. Is there any chance some new calculation has increased the size of the known π(x) ? For instance π(290 is very close to π(1027) and while the next exponent (1028 is a difficult task I would think some progress might be there after almost 5 years. Last time it took about a year to go from 10^26 to 10^27
primecount is still being actively used to compute new records by David Baugh and myself. primecount has been massively improved since our last pi(10^27) announcement i.e. I have now implemented Xavier Gourdon's algorithm and I have found an optimization that improves primecount's runtime complexity of the hard special leaves formula by more than a constant factor (see https://github.com/kimwalisch/primec...cial-Leaves.md).

I don't exactly know which values David is currently computing using primecount, but we will announce important new records here on the mersenneforum. I don't want to publicly disclose ongoing computations as this could give competitors a strategic edge. If you would like to contribute and use primecount to compute new records please send me an email and we can discuss privately and I can share more information.

 2020-05-24, 12:35 #26 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 2×11×41 Posts
2020-05-29, 18:49   #27
ixfd64
Bemusing Prompter

"Danny"
Dec 2002
California

29·79 Posts

Quote:
 Originally Posted by kwalisch I don't exactly know which values David is currently computing using primecount, but we will announce important new records here on the mersenneforum. I don't want to publicly disclose ongoing computations as this could give competitors a strategic edge. If you would like to contribute and use primecount to compute new records please send me an email and we can discuss privately and I can share more information.
Unless there's a prize involved, we should ideally be working together rather than competing against one another.

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