What is the prime factorization of this number : $$2510840694154672305534315769283066566440942177785613805158$$ $$3255420347077336152767157884641533283220471088892806902579$$ ?
If we concatenate the Mersenne-numbers $\ \ M(193)=2^{193}-1\ \ $ and $\ \ M(192)=2^{192}-1\ \ $ and divide by $5$, we get this $116$-digit composite number.
I tried to factor it with the $1.34$-version from yafu, but ecm did not give a result. The quadratic sieve is very time-consuming.
The smallest prime factor of this number probably has more than $40$ digits.
How can I factor this number ?
Best Answer
I factored this 116-digit composite, the factorization is $$C116=179870387995451933124857321125705471410636663412965107437\times139591664983685893216072195834659800165004530288592786103967$$
On my laptop with i3-5005U using yafu 1.34 and GGNFS, the factorization took about 14 hours.