Look at: http://en.wikipedia.org/wiki/Bertrand%27s_postulate
We have a famous theorem, stating "there is always a prime between n and two n",
(see http://en.wikipedia.org/wiki/Bertrand%27s_postulate)
and that means: we have: "always a prime between n**2 and (n+2)**2 (for n > 4)"
and that is a...
Yan: Number Theory for Computing
Shoup: A Computational Introduction to Number Theory and Algebra
Kumanduri: Number Theory with Computer Applications
Hard to find an written in German:
Forster: Algorithmische Zahlentheorie
I think, my Corollary helps to delete all 2{^b} - 1 with a composite b; but unfortunately, there is no help for sieving the Mersenne primes:
Theorem 18 by HW says (in short): 'If 2{^b} - 1 is a prime, then b is a prime'; and the 'other way round' is not valid
As a consequence of Theorem 18 from Hardy-Wright, we have the following
Corollary: For two natural numbers 1 < a and b: a{^b} - 1 is composite if a > 2 (because (a - 1) divides a^{b} - 1);
or in the case a = 2: if b = s * t (because 2^{s} - 1 divides 2^{s*t} - 1
Below you find my little algorithm (written in ARIBAS) to generate an simple-even magic square of side length n (ie n div 2 must be odd);
example for n = 6; the algorithm uses my 'MagicSquareOdd' (see above)
to form a matrix a and an auxiliary matrix 'aux' for the needed inter change of...
Below you find my little algorithm (written in ARIBAS) to generate an double-even magic square of side length n (ie 4 divides n);
example for n = 4; for simplicity of the algorithm, a 'vector' is used to store the 'square'
MagicSquareDoubleEven(4).
-: (16, 2, 3, 13, 5, 11, 10, 8, 9...
There is not one algorithm for all n (a natural number); I think, there are at least 3:
for odd numbers, for double even ( ie for numbers with 4 as factor) and for even numbers.
Below you find my little algorithm (written in ARIBAS) to generate an odd magic square;
example for n = 11; for...
x = -0.295905 is the first negative fixed point of the Riemann zeta, but it is not the only one: between x = (1.83 and 1.84) we find the only positive one and for example,
between x = (-24.0 and -24.01) or x = (-36.0 and -36.0000000001) we find others.
Proposition: We have fixed ponts of the...