The munchkin seive is actually 2 analogous seives, one for 6n+1 primes (npp) and the other for 6n-1 primes (npm). The 6n + 1 seive Let a be a positive integer....
21555
kraDen
kradenken
Jul 5, 2010 6:56 am
Hi All, I noticed some "low hanging fruit" on Jens' "The Largest Known CPAP's" page. http://users.cybercity.dk/~dsl522332/math/cpap.htm - !!CPAP-5!! - (Gap...
21556
kraDen
kradenken
Jul 5, 2010 7:22 am
Again using cpapsieve Find_CPapn pfgw Primo Cheers Ken...
21557
djbroadhurst
Jul 6, 2010 10:49 pm
... Was this a mistake? It did not yet appear chez Jens: http://users.cybercity.dk/~dsl522332/math/cpap.htm#k5 David...
21558
Jens Kruse Andersen
jkand71
Jul 6, 2010 11:20 pm
... Yes, the announced CPAP-5 and CPAP-4 were both mistakes. They are AP-5 and AP-4 but my check found 14 and 7 other primes inside the AP's. It was caused by...
21559
kraDen
kradenken
Jul 7, 2010 1:25 am
... I thought I'd issued a retraction for both these yesterday but it appears that I replied to the poster (i.e. myself) and not to the list. Apologies to all...
21560
Ситников ...
chitatel2000
Jul 7, 2010 6:51 am
Given the value (m) p_n^2 < m < p_{n + 1}^2 p_n - primes n – prime number E – error in calculating the number of primes in the interval (p_n,m) By formula...
21561
djbroadhurst
Jul 7, 2010 1:36 pm
... Let n = 5. Then p_5 = 11 and p_6 = 13. I "give the value" m = 13^2 - 1, which lies between p_5^2 and p_6^2. Then m1 = m*13/(13 - 1) = 13^2 + 13, by the...
21562
Ситников ...
chitatel2000
Jul 7, 2010 3:10 pm
Given the value (m) p_n^2<m<p_n+1^2 p_n - primes n – prime number m*p_n+1/p_(n+1)-1=m_1 The interval (m, m_1) - one prime?...
21563
djbroadhurst
Jul 7, 2010 5:42 pm
In primenumbers@yahoogroups.com, ... http://chitatel2000.blogspot.com suggests that this condition might be something like m*prod(k=1,pi(sqrt(m)),1 -...
21564
djbroadhurst
Jul 7, 2010 6:36 pm
... It is rather easy to prove that the number of solutions to [1] is finite, in direct contradiction to a conjecture by Sergey. Consider the ratio R(m) =...
21565
djbroadhurst
Jul 7, 2010 11:15 pm
... It is interesting to see how Sergey fooled himself into making his false conjecture. His mistake was to believe that we may rely on the sieve of...
21566
Alberto Zelaya
albrtzlya
Jul 8, 2010 12:58 am
I'm Alberto Zelaya, lawyer and retired diplomat of the Argentine Foreign Service. I served in Algeria, Colombia and New Zealand. I write some fiction short...
21567
Journals IJI / IJAI /...
eic_iji
Jul 8, 2010 5:02 am
International Journal of Mathematics and Computation  ISSN 0974-570X (Online), ISSN 0974-5718 (Print), www.ceser.res.in/ijmc.html ...
21568
Ситников ...
chitatel2000
Jul 8, 2010 9:05 am
David, while I'll deal with your comment, look at the additional condition Additional condition (m) - Prime number m_p P_n^2<m_p<P_(n+1)^2 P_n - Primes n –...
P_n^2 <m <P _ (n+1) ^2 For the left restriction (P_n^2) value (m) can pass. It is a question of an error of calculation. For the right restriction it is...
21571
bhelmes_1
Jul 10, 2010 9:34 pm
A beautifull day Do you know whether there exists a fermat pseudoprime of the form p:=n^2+n+1 By the way i started a small collection of 1000 digit primes of...
21572
djbroadhurst
Jul 10, 2010 11:46 pm
... Yes. These [n, p] pairs make p = n^2 + n + 1 a Carmichael number: [2304, 5310721] [47735, 2278677961] [97944, 9593125081] [172799, 29859667201] [683808255,...
21573
djbroadhurst
Jul 11, 2010 1:01 am
... The largest has 208601 digits and was found by PrimeMogul himself: http://primes.utm.edu/primes/page.php?id=83711 David...
21574
Ситников ...
chitatel2000
Jul 12, 2010 1:59 pm
David. You are skeptical about my result. But look: If the value (m) equals the sum of primes. We have: The error calculation of the number of primes in the...
21575
djbroadhurst
Jul 12, 2010 4:56 pm
... Dorogoi chitatel' / Dear reader It's worse than that: you have no "result" for m > 40291. For real m and positive integer n let Q(m,n) = m*prod(k=1,n,1 -...
21576
djbroadhurst
Jul 13, 2010 2:01 pm
... How did you compute pi(x) with x > 10^15, please, David? Andrew Booker's programme hosted at http://primes.utm.edu/nthprime/ is restricted to pi(x) with x...
21577
Jens Kruse Andersen
jkand71
Jul 13, 2010 4:02 pm
... I don't know what David Baugh uses but there is something better. At http://mersenneforum.org/showthread.php?t=13210 I wrote: "Two years ago I searched for...
21578
djbroadhurst
Jul 13, 2010 4:40 pm
... Thanks, Jens! web.archive.org/web/20040125140056/http://www.cbau.freeserve.co.uk/ ... which seems to permit personal use. David...
21579
primenumbers@yahoogro...
Jul 14, 2010 10:59 am
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the primenumbers group. File :...
21580
John W. Nicholson
reddwarf2956
Jul 14, 2010 5:00 pm
pi(x) - pi(x/7) > sqrt(x) proved by N. Shapiro pi(x) > sqrt(x) + pi(x/7) let x = p_(n +1) and p_n so that pi( p_(n +1)) - pi( p_n) > sqrt( p_(n +1)) + pi( p_(n...
21581
Peter Kosinar
pkosinar
Jul 14, 2010 5:53 pm
... Yes, I do. While 10 is greater than 6 and 8 is greater than 3, (10-8) is not greater than (6-3). Peter...
21582
djbroadhurst
Jul 14, 2010 6:42 pm
... A proof, for integer x > 2, was given by Harold Shapiro in 1953 and may be found here: http://tinyurl.com/3yycvms The inequality is true by inspection for...
21583
John
reddwarf2956
Jul 14, 2010 7:00 pm
David thanks, Sorry I left off the "Harold" in Harold N. Shapiro. John W. Nicholson...
