A sample of the conjectures discovered by the Ramanujan Machine is available here.
As mentioned in the paper, the Ramanujan Machine discovers mathematical conjectures without proving them. We highly encourage you to try and prove those conjectures and contribute to mathematics.
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Suggested Proofs
Showing ideas that are
- 1Pi and e are notches in a continuum all other fractions fall on.When mapping all fundamental constants and their 1-x counterparts, ^2,^3 & sqrt 1/nth above and below 1 a curve fit is found. Except for pi and e themselves. I call this the Smartacus conjecture... Read more...
- 1fundamental constant between pi and e raised to itselfIn between Pi^e and e&pi is a number raised to raised to itself that is in between these two #s,. That is also a fundamental # as a conjecture. That # is 2.9189056
- 1Odd numbers and square roots to infinityMy formula was discovered after I noticed that 3 times 3 plus 4 times 4 equals 5 times 5, an equation that I saw used in concrete construction when we set concrete forms and measured the corners to ma... Read more...
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- 1Some well-known resultsThese continued fractions are part of the automatically-found results, and are equivalent to a known result on e. They appear in the PDF file (not in the paper) given on the website. I have attache... Read more...
- 1Reccurence RelationsHere is some proofs via recurrence relations: https://www.overleaf.com/read/rhxybtcjxycj. The recurrence relations are found by wolfam alpha and relatively easily confirmed by hand.
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- 1Continued fraction for 64/pi^2I am stuck because what do I do with the because do I add it and continue with it or will this continued fraction will not work.
- 1Generalized Continued Fraction involving πThe proof of formula from the article: https://www.overleaf.com/read/xyxggjppqhvh
- 1Continued fraction for 64/pi^2I am stuck because what do I do with the because do I add it and continue with it or will this continued fraction will not work.
- 1Continued fraction for 64/pi^2I am stuck because what do I do with the because do I add it and continue with it or will this continued fraction will not work.
- 1Continued Fraction for 64/pi²What do I do here do I add the 0 and continue with it or will this not work. Also is this the correct way for a continued fraction for 64/pi².
- 1Continued Fraction for 64/pi²What do I do here do I add the 0 and continue with it or will this not work. Also is this the correct way for a continued fraction for 64/pi².
- 13rd formula1+\cfrac{n+1}{2+\cfrac{n+2}{3+\cfrac{n+3}{4+\cfrac{n+4}{...}}}}=\frac{\frac{d^n}{dx^n}\left ( xe^\frac{x}{1-x} \right )}{\frac{d^{n-1}}{dx^{n-1}}\left ( \frac{x}{1-x}e^\frac{x}{1-x} \right )} at po... Read more...
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