20171231, 15:39  #56 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 

20171231, 15:40  #57  
Aug 2006
3·1,993 Posts 
Quote:
You’re learning! 

20171231, 15:55  #58 
Dec 2017
2×5^{2} Posts 
yes ... true  the original question was just the beginning and i am grateful for your mentioning the primorial function.
so let me continue with do you know a formula for p(i) not including all p(j) with j<i ? i would also be equally happy if you could come up with a formula for p(i) not including all p(k) witk k>n legendre came up with a "quick" algorithm as to how to find p(i+1) knowing p(i) ... but, that's not what i ask. Last fiddled with by guptadeva on 20171231 at 16:04 Reason: including legendre algorithm 
20171231, 16:03  #59  
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 
Quote:
Last fiddled with by science_man_88 on 20171231 at 16:11 Reason: Correcting typo/ fixed error in memory 

20171231, 16:28  #60  
Dec 2017
32_{16} Posts 
Quote:
one of his following joint papers with sato, wada and wiens is more understandable and very insightful https://www.maa.org/sites/default/fi...oWadaWiens.pdf 

20171231, 18:18  #61 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
38D_{16} Posts 
For primality:
For 64bit numbers, e.g. numbers less than 18446744073709551616, the BPSW test is deterministic and unconditionally correct. There are about 3 * log_2(n) steps, often less. It takes less than 200 steps (typically about 125) to give a correct answer for a 64bit prime. Pi(n) is on the order of 400,000,000,000,000,000. As I said a couple times, some tests meeting your requirements: * AKS * APRCL * ECPP No lookup tables, no use of O(sqrt(n)) primes, results faster than trial division. These aren't "simple formulas" but that's what we have. It seems we've moved on to the ubiqutous "formula for nth prime" discussion. We have algorithms that are quite fast. See, for example: https://math.stackexchange.com/a/961539/117584 https://math.stackexchange.com/a/775314/117584 People sometimes get upset that this isn't a "formula" or simple enough. Oh well. 
20171231, 21:51  #62 
Dec 2017
2×5^{2} Posts 
somehow i just stumbled upon another old paper by jones:
https://cms.math.ca/openaccess/cmb/v....04330434.pdf containing a simple formula for p(n) proved on the base of wilsons theorem and bertrands postulate ... so i'm happy now 
20180101, 03:45  #63 
Dec 2017
2×5^{2} Posts 
and even more happy after having found:
https://oeis.org/wiki/Formulas_for_primes yet the answer to the question if all p(j) with j<i are necessary to determine p(i) is probably: "we don't know" ? 
20180101, 03:56  #64 
Dec 2017
2×5^{2} Posts 
i will certainly look more deeply into these tests  some ecpp variants look promising

20180102, 07:44  #65  
Aug 2006
3·1,993 Posts 
Quote:


20180102, 07:57  #66  
Dec 2017
2×5^{2} Posts 
Quote:
I came across this on a Wikipedia Article an am trying to find a proof, but nonetheless, if this equation has its own article, then there must be a way of demonstrating the truth of this equation. If this is true, then there is another equation for prime numbers, but this looks like it was derived from the Almansa and Prieto formulas, or the Willans Formula (in particular, the reduced version from Neill and Singer). But overall, nice job :))) Last fiddled with by George M on 20180102 at 08:03 

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