Here is a new prime 18-tuplet record (and a new 18 Simultaneous Primes record): 2152095346273291005088484977 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42,...
24705
Jens Kruse Andersen
jkand71
Dec 2, 2012 2:27 pm
... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen...
24706
paulunderwooduk
Dec 2, 2012 10:46 pm
Hi, I have a new composite test for odd n with any x and a: 2<x<(n+1)/2 1<a<(n+1)/2: kronecker(x^2-4,n)==-1 gcd(a^3-a,n)==1 gcd(a,x)==1 with sub-tests: ...
24707
WarrenS
warren_d_smi...
Dec 3, 2012 2:57 am
What is CCANT, for those of us too silly to know what RIES stands for (actually I unfortunately do know that)?...
Let pi(N) = number of primes p with p<=N. A well known question is whether pi(A)+pi(B) <= pi(A+B) always. Usually this is true, but Hensley & Richards...
... PDF answer: http://www.plouffe.fr/simon/math/A%20course%20in%20computational%20algebraic%20number%20theory%20-%20Cohen.pdf http://www.plouffe.fr/simon/math...
24713
paulunderwooduk
Dec 3, 2012 8:38 pm
... I notice these 3 have kronecker(x,n)==1. So I wriggle with this test: kronecker(x^2-4,n)==-1 kronecker(x,n)==-1 gcd(a,n)==1 (L+a)^(n+1)==a*x+a^2+1 (mod n,...
24714
paulunderwooduk
Dec 3, 2012 9:01 pm
... Last minute wriggle: gcd(a^3-a,n)==1 Paul...
24715
paulunderwooduk
Dec 3, 2012 9:31 pm
... n==3281 lead to the above wriggle. I could have used the following wriggle instead: gcd(x^2-1,n), which would allow a==1 Paul...
FYI ... From: Wolfram Research <info@...> Date: Mon, Dec 3, 2012 at 11:44 PM Subject: Mathematica 9 is now available To: saccuan.john@... ...
24719
djbroadhurst
Dec 4, 2012 1:48 pm
... leading to ... Well that's one way advertizing an over-priced commercial product. David...
24720
djbroadhurst
Dec 4, 2012 3:49 pm
... After I worked out to how to forge one counterexample, the gremlins were able to find more than 21,000: {tst(n,x,a)=2<x&&x<(n+1)/2&&1<a&&a<(n+1)/2&& ...
24721
paulunderwooduk
Dec 5, 2012 9:40 pm
Hi, my apology to the group and especially David Broadhurst if I have presented the following composite test before. For odd n find x: gcd(x,n)==1 ...
24722
paulunderwooduk
Dec 5, 2012 11:10 pm
... Of course x could be 1. So the fermat tests should be: (x-1)^n==x-1 (mod n) (x+1)^n==x+1 (mod n) And the light of n=513629;x=128921 I am adding the...
24723
James Merickel
moralforce120
Dec 8, 2012 10:02 am
Hello, group members. To a degree, I am able to locate and work with what I am interested in, but perhaps somebody can facilitate my efforts either with...
24724
pbtoau
Dec 8, 2012 10:52 am
The logarithmic integral and the Riemann approximation should get you within the square root of pi(x). I did not check if this is provenly so, but it works...
24725
paulunderwooduk
Dec 8, 2012 10:58 am
... I have found counterexamples in David's lists: ? {tstfile("underw65.txt");} 8120/12846 counterexamples left in underw65.txt ?...
24726
James Merickel
moralforce120
Dec 8, 2012 11:44 am
David: Well, I have details of the kind for getting the value exactly (though it may not be the clearest thing to read or implement in something akin to te way...
24727
James Merickel
moralforce120
Dec 8, 2012 11:44 am
David: Well, I have details of the kind for getting the value exactly (though it may not be the clearest thing to read or implement in something akin to te way...
24728
Luis Rodriguez
luiroto
Dec 8, 2012 3:02 pm
Sorry. You are searching the impossible. Not even if the Riemann's Hypothesis is demonsrated can one reduce the error below X^(1/2).Log(X). There is an...
24729
James Merickel
moralforce120
Dec 8, 2012 8:13 pm
Luis, The references I have find pi(x) faster than the sieve of Eratosthenes, and it is not that difficult to work out on one's own a means of computation...
24730
paulunderwooduk
Dec 9, 2012 2:04 am
Hi, here yet another composite test for a counterexample challenge, For n co-prime to 30 find x: gcd(x^3-x,n)==1 kronecker(x^2-4,n)==-1 and perform these...
24731
paulunderwooduk
Dec 9, 2012 12:50 pm
... n=396271;x=5042 is counterexample. I am now testing with the added wriggle: x^(n-1)==1 (mod n) Paul...
24732
paulunderwooduk
Dec 9, 2012 1:26 pm
... I dropped the above wriggle. The test I am now verifying is: gcd(x^3-x,n)==1 kronecker(x^2-4,n)==-1 (x-2)^((n-1)/2)==kronecker(x-2,n) (mod n) ...
