Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville : “The big experts in the field had already tried to make this approach …

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$. Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of per …

PART I (Initial version) Let   $P$   be the set of all primes   $2\ 3\ \ldots$.   Let $$P_d\ \ :=\ \ \{\ p\in P\ :\ \exists_{q\in P}\ \ 0 < |p-q|\le d\ \}$ …

Composite numbers $n$ such that $A179382((n+1)/2)=(n-1)/(2^c)$ for some $c > 0$. I named this numbers "antiprimes". $a(1-5):92673, 143713, 3579553, 4110529, 28688897$ $a(6) > 68 …

Let $\alpha$ be any positive irrational and $\beta$ be any positive real. We have the following results. H. Weyl (1909): The fractional part of the sequence $\alpha n$ is equidist …

I was reading the Boneh-Franklin IBE paper, and it seemed rather conspicuous to me that they didn't address the question of how to find primes $p$ and $q$ satisfying what they nee …

EDIT : I copy-paste the beginning of a previous question since Gerry Myerson suggested this question should be self-contained. "let's consider a composite natural number $n$ great …

For a problem in group Theory I need some information about the Mersenne primes: Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime. Is it true that $p^2+1$ is square …

Let $a,b,c,d$ be natural numbers so that $ab=cd$. Prove that $a+b+c+d$ is composite.

For example Group of 2 equidistant successive primes 3,5,7 distance 2 151,157,163 distance 6 Group of 3 equidistant successive primes 251,257,263,269 distance 6 1741,1747,1 …

Let $p=2^a-1$ be a Mersenne prime and so $a$ is an odd prime if $p>7$. We know that if $p=7$, then $(p^2+1)/2$ is equal to $5^2$. Can we prove that if $p>7$ , then $(p^2+1)/2$ is …

The following is an old result of Erdős and Turán (American Mathematical Monthly, 1934): Given a set of $2^n + 1$ distinct positive integers, all of its two-term sums cannot be co …

Possible Duplicate: Why is 2 so odd? I have read few books and articles, almost all of them refer that any prime $p>2$. Just wondering why it has to be $>2$?

$|q|\lt1$ $A(q)=\sum \limits_{k=0}^\infty q^{2^k}$ Easily We can see that $$A(q)=q+A(q^2)\tag 1$$ Let's assume we redefine $A(q)$ as below $A(q)=-\sum \limits_{k=1}^\infty c …

There is an abundant literature, and even here on MO no shortage of questions, on the question of the smallest prime primitivee root modulo $q$ (where $q$ is a prime, or more gener …