## My problems

I need to fully understand Siegel’s, Chebyshev, Riemann’s, Poincare’s work, especially part of works connected with PNT and Zeta, and nonvanishing L-series for arithmetic progressions. I recently suggested a problem, and received an answer that there is the same number of primes starting with 123 and ending with 3 as those starting with 123 and ending with 7. I was given the following  article as the proof to the very claim:

http://www.math.umass.edu/~isoprou/pdf/primes.pdf

But, according to my matrix and the probabilities of numbers appearing in each column of the matrix this seems very interesting case to pore over.

Thus, I introduced two following tasks:

1. Let $S_{i}$ be set of numbers with $i$ nondistinct consecutive prime divisors, where $n$ denotes the greatest of nondistinct prime divisor used. Let $M(i)$ denote number of elements of $S_{i}$. Find ${{M(i)}\over{K(i)}}$, where $K(i,n)=max(S_{i})$ and $n$ is i-th prime number.

2.p1- prime number;np1, np2 – odd numbers;u($a_{1}^{k_{1}}*a_{2}^{k_{2}}...a_{n}^{k_{n}}$)=$k_{1}+k_{2}+..+k_{n}$ for prime $a_{i}$ and  natural $k_{i}$

Knowing that u(np1-p1) = u(x – np2), is this true that $\forall np1,np2$ $\exists p1$: x is prime?