On Tue, Dec 2, 2025, 10:28 AM Quan Tesla <[email protected]> wrote:
> John et al > > Apologies for my silence. Formalizing white papers. > > At least, there was a start: https://zenodo.org/records/17716858 > Help me understand this. The paper claims that p_k/p_k# approximates C to within 10^-30 for k ≈ 80, where p_k is the k'th prime, p_k# is the primordial, or the product of all primes up to p_k, and C is an irrational constant like pi, e, phi, ln 2, etc. for example, p_4 = 7, p_4# = 2x3x5x7 = 210, and p_k/p_k# = 1/30. This does not look right because p_k# grows much faster than p_k, so the ratio approaches 0 as k grows. Am I misunderstanding something? Any irrational number can be approximated to n digits of precision by a rational number a/b using a total of about n digits. For example, you can approximate pi to 3 digits as 22/7 or 6 digits as 355/113. Either representation takes about the same number of bits. Can you clarify? ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T7ff992c51cca9e36-M23c29acfb440cb21c70f05f3 Delivery options: https://agi.topicbox.com/groups/agi/subscription
