Dear Mr. Brennen, if I thought that the factors for each f1, f2, etc. were all prime, even for a second, then I wouldn't have considered the notion of proof...
Hi all, Consider the set of natural numbers and filtering them by 3,5 and 7 (but not 2!) Within an interval of 105 I will find 15 pairs of numbers that differ...
** Proprietary ** ** High Priority ** Sir, your so-called proof is utterly incomprehensible. In order to avoid further linguistic "chaos" you are kindly...
(i) Does the following series converge or diverge? 1/a[1]+1/a[2]+1/a[3]..... Where a[n] is the nth prime in the series of primes p[1],p[2]..that have...
... According to the Artin conjecture, the sum diverges. ... {cp(n)=local(c=0.,pmax=prime(n));forprime(p=3,pmax, if(znorder(Mod(2,p))==p-1,c=c+1/p));c} \p15 ...
4a. Convergent or divergent series? Posted by: "robert44444uk" robert_smith44@... robert44444uk Date: Sat Oct 24, 2009 12:52 am ((PDT)) (i) Does the...
One thing I have often thought about is trying to build a quasi-alternating series out of the reciprocals of the primes, so that: - the reciprocal of every...
... Here's some data: For primes up to 10^3 : sum =~.166803 10^4 : sum =~.166329 10^5 : sum =~.165365 10^6 : sum =~.165021 10^7 : sum =~.165036 10^8 : sum...
Hi all, a notion occurred to me that has probably been explored, so I'm looking for references to it. Of the numbers n# +1 or n# -1 (n Primorial plus 1, or...
Re ... I can easily see that the positive terms would converge. However, there is a problem with showing that the series noted above converges absolutely. Term...
... The sum is a variation on sum (9) at http://mathworld.wolfram.com/PrimeSums.html It starts (1/3)-(1/5)+(1/7)+(1/11)-(1/13)-(1/17) and equals 0.3349813253...
Is it a known fact that the sum of primes of a twinprime pair is always divisible by 12 ? (divisible by 4 is evident) or is there a counterexample? gr. Rob ...
... Yes it's a known fact. All primes > 3 have the form 6n +/- 1. Thus a twin prime is always of the form (6n-1,6n+1) . The sum is 12n, which is divisible by...
... Rats, my computer doesn't know what to do with a dvi file. While in my ignorance, I can't fathom how it can take merely 174 milliseconds to compute 300...
... I used only primes p < 400 {ans(A,N)=local(S=1/2.,L); forprime(p=3,A,S=S+if(p%4==1,1,-1)/p); for(s=1,N,L=if(s==1,Pi/4,if(s%2==0,zeta(s)*(1-1/2^s), ...
... To obtain, 70 good decimal digits, in 9 milliseconds, it suffices to use only the first two odd primes p = 3,5. This is so fast that, to time it...
... Your intuition was good, Julien. The key to the proof of finiteness (and also to the very fast evaluation) is that you were using a Dirichlet character: ...
... In fact, polling the odd primes really helps: I found 10,000 good digits in 7 minutes, by consulting the 24 odd primes p < 100. The result is in ...
A Ramanjan Prime Corollary: 2*p_(i-n) > p_i for i > k where k = primepi(p_k) = primepi(R_n). That is, p_k is the n'th Ramanujan Prime, R_n, and the k'th prime....
... Others will correct me if I am wrong, but I think they use the same arithmetic engine now. Of course prp.exe does not prove primality. LLR might be the...
... For base 2, I recommend LLR, since it will automatically do a Proth test for k*2^n+1 numbers. You could also use PFGW, but you would need to force a...
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