In the 19 hundreds, many though that an explicit formula for the partition function was never going to be found. In 2011, finally, an explicit formula for the partition function was discovered.
For that reason, I am fascinated by how close do mathematicians think we are currently to discovering an explicit formula for prime numbers.
A new paper:
arxiv.org/abs/1802.10498
https://www.quantamagazine.org/a-chemist-shines-light-on-a-surprising-prime-number-pattern-20180514/
https://www.impactlab.com/2018/09/15/researchers-discover-a-pattern-to-the-seemingly-random-distribution-of-prime-numbers/
Regards,
Joachim
Dear Joachim Pimiskern ,
Thank you for this recommendation. I have taken a quick look at all 3. They discuss the same discovery related to primes. I will read the article more carefully when I find the time. But its seems very interesting: Making discoveries related to the primes from chemistry concepts.
Such an explicit formula was found by Riemann-in fact it's known under that name-cf. here: http://www-users.math.umn.edu/~garrett/m/mfms/notes_c/mfms_notes_02.pdf for instance. It's that formula that makes the Riemann hypothesis relevant. However proving the validity of the ``explicit formula'' did take some time.
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