Factor RSA-1024

Definitions and mathematical statement

Shared notation.

$\mathbb N=\{1,2,\ldots\}$, and $\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$ denote the integers, rationals, reals and complex numbers. Any other conventions are specified locally.

Let $N$ be RSA-1024, the following fixed integer. Its decimal digits are obtained by concatenating the displayed lines in order: \[\begin{gathered} 1350664108659952233496032162788059699388814756\\ 0566702752448514385152651060485953383394028715\\ 0571909441798207282164471551373680419703964191\\ 7430464965892742562393410208643832021103729587\\ 2576235850964311056407350150818751067659462920\\ 5563685529475213500852879416377328533906109750\\ 544334999811150056977236890927563 \end{gathered}\] A prime factorization is an expression $N=\prod_{j=1}^{t}q_j^{e_j}$ with distinct primes $q_j$ and positive integer exponents $e_j$.

Statement recorded in the supplied source.

Find the prime factorization of this exact 309-digit integer $N$. [S2]

Short English statement

Factor the fixed RSA-1024 challenge number, rather than solve a general factoring problem.

Sources

• S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9300005 (AMR-092-0005). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 Tim S. Roberts, Unsolved problems in number theory, logic, and cryptography RSA problem statement. https://unsolvedproblems.org/index_files/RSA.htm.