All Questions

In this and this question we show that if $p=27a^2+27a+7$ is prime, then the order of the elliptic curve $y^2=x^3+2$ modulo $p$ is either $p$ or $p+2$. Q1 Can we unconditionally show that the order ...

We got argument and strong experimental support that integers of the form $n=p q^2$ can be factored using elliptic curves easier than general integers Q1 Is this known? Added This is known since at ...

If a composite integer resembles a prime too closely, it must pass algorithmic tests designed to find primes and in addition avoid nontrivial factorization. Given an integer $p$, assume it is prime ...

I've been running a search for Mordell curves of rank >=8 for about 12 months and have identified approximately 280,000 curves in our archivable range, amongst many millions that aren't. For this ...