6
votes
3answers
410 views

Smallest known unfactored composite number?

I'm trying to find examples of "small" numbers which are known to be composite, but for which no prime factors are known. According to this website the number $109!+1$ is a composite number of 177 ...
-1
votes
1answer
61 views

Efficient way to find lowest divisor of an integer.

I have followed the given way to find the lowest divisor of an integer, Let us assume n is the given integer. Check n is ...
8
votes
1answer
3k views

Pollard-Strassen Algorithm

I'm aware that the Pollard-Strassen algorithm can be used to find all prime factors of $n$ not exceeding $B$ in $O\big(n^{\epsilon} B^{1/2}\big)$ time. This is really useful because I need to find all ...
1
vote
0answers
138 views

A special factorization

Suppose that monic polynomial $f(x)\in\Bbb Z[x]$ such that for all $m\in\Bbb Z$, $m>1$, there's no integers $\langle r,r_1,\ldots,r_m\rangle$ such that $f(r)=f(r_1)\cdots f(r_m)$. Is there any ...