The following code represents a novel, ( and inefficient ) way to factor by trial division. def FactorByGCD(z,trace = 0): #{ steps = 0 if z < 4: #{ print "...
Hello group, Does anyone of you knows if there exists a C program to perform PRP tests (basic Fermat test or Rabin/Miller test) using the YEAFFT library that...
First order son primes (p, 3p+2 prime) are more common than Sophie Germains (p,2p+1 prime): approx 36% more common. Why? - If we look at mod 3 if p==1mod3 then...
... Other generalised relations have been looked at. However, with an exponent of 3 driving the size, these chains aren't likely to be longer than ones which...
... I seem to remember it comes with the ability to replace GMP multiplication routines. Get that working, and then just use the usual GMP exponentiation...
Are there numbers of specific form that you want to test? For example, if you want to test numbers of the form k*b^n+/-1, then there are options that don't...
... multiplication routines. ... routines, and it will use the YEAFFT multiplications. ... Hi Phil, If I can plug YEAFFT multiplication routines into GMP...
... there ... PRP ... Mersenne's ... Hello Mark, As mentioned in my previous reply to Phil, the numbers I want to check are (n+1)^p-n^p for which I don't know...
pfgw is your best bet. I don't know if YEAFFT will be faster than it for numbers of that form. ... [Non-text portions of this message have been removed]...
... exponent of 3 driving the size, these chains aren't likely to be longer than ones which are related to powers of 2. Have you tried looking for both? How...
... Can you write this in a way such that the task can be distributed over multiple machines? If so, and the code's portable, then I can stick 2*2 GHz of G5...
... They have. Many of them can be proved to have a maximum length. Teske & Williams' paper in LNCS 1838 is a nice treatment of consecutive prime values...
... Pythagorean Triplets must be of the form p = a^2 - b^2 = (a+b)*(a-b) p+k = 2ab q = a^2 + b^2 For p to be prime, a-b=1. Simple substitution finishes the...
Hello everybody. Im wondering about the state of the art about the class of compexity of the integer factorization problem. Could anybody comment something...
... It is trivial to prove that factoring is in NP. (Proof: guess the factors and use grammar-school multiplication, an O(N) algorithm to verify that the...
Hello all Diophantine Pythagorean theorem. Prove this Conjecture: “ If p is a ODD prime number then the following Diophantic Equation p^2+(p+k)^2=q^2 has...
Hello Sebastian, ... Proof: Rewrite the equation as p^2 = (q+(p+k)) * (q-(p+k)). We know that q+p+k > p and that p is a prime, so q+p+k = p^2 and q-(p+k) = 1. ...
Hola os envio un relato corto que se me ha ocurrido Espero que os guste ¡y que no sea una profecía! Atentamente Sebastian Martin ruiz [Non-text portions of...
Hola os envio un relato corto que se me ha ocurrido. Espero que os guste ¡y que no sea una profecía! Atentamente Sebastian Martin ruiz Ahora creo que si va...
Hola os envio un relato corto que se me ha ocurrido. Espero que os guste ¡y que no sea una profecía! Atentamente Sebastian Martin ruiz Los tres primeros...
Hello everybody: I wana to give a series of E-mails which contains an outline of the Proof of the Modularity of elliptic curves over rational numbers...
I offer a $50 prize to the first person who can submit a verifiable counterexample or proof by 10/1/8 for the following primality conjecture: x, A(x), B(x), k,...
Hello, Perhaps you may be interested to check out the conjecture, which I have made lately (and info on possible directions in proving it - see below) ? NO "n"...
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