The Joyous Structure of the Nature of Primes (Primitive Sets Theorem Proved!)

Reading the conjecture for the first time in Covid-19 locked-down Boston, I was sure it was true. There was a sense of deep vindication when I soon came across the proof of this conjecture by Erdős, years later, by a bright PhD student named Richard Duker Lichtman. This statement about the nature of primes was so beautiful it surely had to be true.

The original paper can be found here.

For anyone seeking to understand this proof, below we go into the thick of things

Into the Weeds

Conclusion

I hope in sharing this you are able to see some beauty in this wonderful proof about the nature of the primes.

Perhaps, one day, this sort of work will contribute to a proof of the Reimann hypothesis.

Will it be you, dear reader?

Hope so - :)

Further Reading

Jared Duker Lichtman Almost primes and the Banks-Martin conjecture

Paul Erdős, András Sárközy On the divisibility of sequences of integers

Tsz Ho Chan, Jared Duker Lichtman, and Carl Pomerance On the Critical Exponent for k-primitive Sets