Hello: Let C(n)=n!!+Sum[(Floor[n/i])!!,{i,1,n}] C(1)=2 C(2)=5 Which is the next prime number? for n>2 are all C(n) composite? or find a countraexample. There...
i am in desperate need of a ubasic expert. i need to find an algorithm in ubasic where i can find x,y,z for the equation ax^4+by^4=z^2. i need a fast...
... Took a nice sabbatical from numbers, namely the primes. The things drive me crazy. But in a momement of weakness/boredom, perhaps abit of seasonal...
in which so many of the possible prime factors are used as in the gap between 1327 and 1361. If you factorise all the numbers not divisibel by 2, 3, or 5...
the following program tries to determine the primality of a number by combining two tests into one, avoiding the usual pseudo-prime situ- ation: 10 cls 20...
... Ahem. http://hjem.get2net.dk/jka/math/primegaps/maximal.htm lists the known maximal gaps. The largest ratio between the starting prime of successive...
... The "unusuality" could be measured dividing the gap length by log(p)*log(p)*sqrt(log(log(p))), where p is the prime after the gap. Thus, the most "unusual"...
... Hopefully for Bertrand, he didn't say that. If I'm supposed to be finding counterexamples and errors today, that single sentence contains a treasure...
Given a,b solve ax^4+by^4=z^2. With a,b>0? Rewrite to: ak^2+bl^2=m with k=x^2, l=y^2, m=z^2. Forgetting the conditions on k,l,m it's easy to see that k,l ->m. ...
I have had a look at your factorisation of all the 1132 composites after 1693182318746371 and it still does not seem as "efficient" in using all the primes...
... after ... all the primes below ... as I did in my ... divisible by 2, 3 or 5 and ... and that is as little as ... from a situation where ... Even with the...
Hello Bill, ... Slightly less programatic description of the test: If both 1) N must not be divisible by 5, and 2) 2^N - 3^((N-1)/2) = 1 or 3 (mod N), then N...
http://www.csail.mit.edu/timeline/timeline.php/timeline.php?query=event&id=197 google for primes is in NP and you must be able to get it ... From: Kermit Rose...
In a previous post I discussed how every prime up to 43 was used to factor numbers in the gap of 33 composites between 1327 and 1361. Clearly, then, what we...
not trying to sound like a text book, but... let Q= k*2^n +1, where 'n'/is prime/ and k<= 2^n +1. I can't find a counter-example... using... if 2^((Q-1)/4) ==...
Hello group, Do you have any idea why openpfgw systematically crashes on systems with xeon processors ? I have 2 servers, one linux box and one windows box...
Bill, just to clarify something for myself.. For even n: T(n) = T(n/2)^2 - 2 (MOD 47) T(n + 1) = T(n/2) * T((n+2)/2) - 3 (MOD 47) I was figuring out where the...
Below I print out prime n, (not required to be prime) k, non-prime value Q, factorization of Q, given that 2^((Q-1)/4) == 1 mod Q. 7, 65, 8321, (53) (157) 7,...
... yes!, if n is even... ... don't know about that complicated mess, but if m IS odd, say 15... then T15 = T8 * T7 - 3 mod N it's that simple!; the author...
here's how to catch a 2-pseudoprime... off the cuff... if `I' is already prime, then the algorithm lets it slip through; but... if `I' is a pseudo-prime, then...
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