Tagged Questions

48
votes
2answers
6k views

Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture

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 …
15
votes
0answers
519 views

Permutations of $(Z/pZ)^*$

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 …
4
votes
2answers
197 views

Are sums of the inverses of prime siblings finite?

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\ \}$ …
0
votes
0answers
119 views

What’s the missing number of this antiprimes sequence? [closed]

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 …
6
votes
6answers
519 views

Sequences equidistributed modulo 1

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 …
2
votes
1answer
294 views

p such that p+1 has a large prime factor, effectively

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 …
0
votes
1answer
202 views

A possible consequence of Dirichlet’s theorem about primes in arithmetic progression

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 …
2
votes
3answers
329 views

Is it true that $p^2+1$ is square free if $p>7$ is a Mersenne prime

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 …
-1
votes
0answers
287 views

Prove a+b+c+d is composite. [closed]

Let $a,b,c,d$ be natural numbers so that $ab=cd$. Prove that $a+b+c+d$ is composite.
5
votes
2answers
226 views

Does group of 4 equidistant successive prime exists ?

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 …
0
votes
1answer
205 views

Factorization of $p^2+1$ where $p$ is a Mersenne prime

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 …
7
votes
1answer
134 views

Composing two-term sums from the same primes

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 …
0
votes
4answers
266 views

The prime number $2$ [closed]

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 $>2$?
2
votes
1answer
189 views

To express $e^{\sum \limits_{k=0}^\infty q^{2^k}}$ as product terms of $(1-q^k)^{c(k)}$

$|q|\lt1$ $A(q)=\sum \limits_{k=0}^\infty q^{2^k}$ 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 …
3
votes
1answer
197 views

Least non primitive root

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 …

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