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86 results from messages in primenumbers

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  • --- In primenumbers@^$1, James Merickel wrote: > > I think that having gone through (at least) 5 editions and been scrutinized by all of the best number theorists in the world for the better part of a century makes this a safe assumption. > JGMÂ > Chapter 15 of Hardy/Wright looks to me like the basis for the issquare functions. Can the appropriate issquare for A = 14x^2 + 14xy...
    Aldrich Aug 11, 2012
  • --- In primenumbers@^$1, "djbroadhurst" wrote: > > I recommend > http://www.alpertron.com.ar/QUAD.HTM > for blow-by-blow solutions of such problems, > using continued fractions. > The presentation was beautifully done, but the calculations looked very difficult. A simpler approach (at least conceptually) should work for those integer binary quadratic forms where the number of...
    Aldrich Aug 11, 2012
  • > > I think its status will remain > > 'empirical observation' for quite some time. Since > > the qfbsolve procedure presupposes that it is true, > > and the good doctor declined to comment upon it..... > > There is no "presupposing" about qfbsolve(). The good doctor > David did provide a hint that qfbsolve() works for ALL primes > P of the form described above and also provided a...
    Aldrich Aug 7, 2012
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  • --- In primenumbers@^$1, "djbroadhurst" wrote: > > > > --- In primenumbers@^$2, > "Aldrich" asked: > > > if p was not known already known to be prime > > or even if it was a possible value of F(x,y), would the > > qfbsolve procedure prove it to be so straightaway? > > No. > > > If it had factors that were exclusively +/- 1 mod 10, would > > all of the locations of p be immediately...
    Aldrich Aug 6, 2012
  • --- In primenumbers@^$1, "Mark" wrote: > > If x and y are relatively prime, the conjecture would be modified to this: > > If A is the set of all numbers of the form 5x^2 + 5xy + y^2, with x and y relatively prime, then A contains *only* and *all* of those numbers which are +/- 1 mod 10 primes raised to an odd power, the prime 5 to the first power, and the composites that can be...
    Aldrich Aug 5, 2012
  • {A,x,y,F,m : positive integers} Consider for a moment the values of 'A' that are +/- 1 mod 10. Exclude all values of 'A' with Gcd(A,y) > 1, as well as all values that are powers of a prime. If one of the remaining 'A' values appears more than once it is composite, but if it appears once only then it is prime, and all of them will be composed solely of +1 mod 4 primes. Factors for...
    Aldrich Aug 5, 2012
  • --- In primenumbers@^$1, "djbroadhurst" wrote: > > Let > > F(x,y) = 5*x^2 + 5*x*y + y^2 > > Then for any prime p = +/- 1 mod 10 it is straightforward to > find integers [x,y] such that F(x,y) = p. In Pari-GP, simply use > > xyp5(p)=qfbsolve(Qfb(5,5,1),p); > > \\ Example: > > print(xyp5(100000000000000000039)); > > [5355540695, -1733283533] In this example, if p was not known...
    Aldrich Aug 2, 2012
  • {A,x,y : integers} 1) If A = 5x^2 + 5xy + y^2, then a subset of A is the complete set of all of the +/- 1 mod 10 primes and all of the composites that can be made exclusively from them. 2) If A = 2x^2 + 2xy + y^2 , then a subset of A is the complete set of all of the +1 mod 4 primes and all of the composites that can be made exclusively from them.
    Aldrich Aug 1, 2012
  • --- In primenumbers@^$1, "Phil" wrote: > > I discussed the Baillie-Wagstaff primality checker at my blog > > . Here's the latest version of source code, in Scheme, which differs > slightly from the original entry; it's more than "a few lines" of code, > but not too long: > (define (prime? n) (letrec ( (expm (lambda (b e m) (let ((times > (lambda (x y) (modulo (* x y) m)))) (cond...
    Aldrich Apr 24, 2011
  • --- In primenumbers@^$1, "Aldrich" wrote: > > It is my contention that the principle > of Primemine2 makes it a valid primality > test for all 8499 batches of outputs > produced. Since proof for this type of > en masse testing is unlikely to be found > anytime soon, I am seeking to find any > counterexamples among the four billion > integers on the list that I claim to be > prime...
    Aldrich Apr 12, 2011