3
votes
1answer
54 views

Factors of integers of the form $k^2-k+1$

Factorisation of arbitrary integers is of course a computationally hard problem. But what if the integers I'm interested in factorising are all of the form $k^2-k+1$ ? Is there some way to compute ...
1
vote
2answers
1k views

Notation : What is the meaning of the (mod n) in factoring algorithms?

Pretty much every thing is in the title, really! I'm trying to come up with an efficient algorithm to factorize large integer as an homework for a parallel programming course. I've seen a few pages ...
1
vote
0answers
69 views

lower bounds for maximum computing times for integer factorisation

Supposing that n were known to have two prime factors, and that the computer had a database of all the primes $<\sqrt{n}$. Then, unless n is square, one factor would be $<\sqrt{n}$. If an ...
2
votes
1answer
93 views

Factoring short intervals

There are algorithms (e.g., SIQS) that factor individual numbers. For large ranges of numbers, sieving is more efficient: for example, $(x^2,x^2+x)$ can be factored in time roughly linear in $x$. ...