To date, the Ramanujan Machine focused on four algorithms, variants of Meet-In-The-Middle (MITM) algorithm, Gradient Descent (GD), the Berlekamp-Massey algorithm, and a proprietary search algorithm, based on a phenomenon of factorial reduction. The algorithms are described in details in our publications.
If you are familiar with any of the results of the Ramanujan Machine we would love to know about it and give credit to the original discoverer, so please let us know.
New!
Conjectures using different orders of Riemann Zeta function
Using a new algorithm, The Ramanujan Machine discovered in June 2022 several conjectures that include different values of Riemann Zeta function. The results can be found here and all of them still unproven.
Conjectures for Apéry’s constant
We are excited to announce a few conjectures on the Apéry’s constant (Riemann Zeta function evaluated at 3). The results can be found here and two of which are still unproven.
Conjectures for Catalan’s constant
The Ramanujan Machine recently (May 2020) found a couple dozen conjectures on the Catalan constant, most of which are still unproven. Please see them here.
Conjectures for \(\pi^2\)
The Ramanujan Machine discovered about a dozen result on \(\pi^2\), most of which are still unproven and can be found here.
Conjectures for \(\log(2)\)
A continued fraction for log of 2 found after May 1st, 2020 is available here.
Conjectures by the community
Conjectures suggested by community members who contributed computational resources, along with credits, can be found here.
Previous results
The following results were obtained by the Ramanujan Machine. The PDFs below are computer generated, because of which they may appear in a different format than the most recent results provided above.
Conjectures for \(e\)
The following PDFs include conjectures that were generated for the number \(e\) by the MITM-RF algorithm. Please note that there are certain redundancies in the conjectures (if you want to help us improve this please contact us).
Conjectures for \(\pi\)
The following PDFs include conjectures that were generated for the number \(\pi\) by the MITM-RF algorithm. Please note that there are certain redundancies in the conjectures (if you want to help us improve this please contact us).
