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Palm Jumeirah Island as an anlaogy to explain the Elliptic Curve Method

Palm Jumeirah Island as an anlaogy to explain the Elliptic Curve Method

3 comments

·October 7, 2025
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phkahler

Question for number theory folks. Is there a function (computable or not) that tells how many primes divide a number? Or more specifically the parity of the number of primes that divide a number?

I came up with such a parity function years ago and wondered if its worth writing up. I've googled and don't see such a thing talked about.

somezero

https://en.wikipedia.org/wiki/Prime_omega_function

https://en.wikipedia.org/wiki/Liouville_function

Deeptiman

A structured visualization of the Elliptic Curve Method (ECM), relating j-invariant classes and curve selection to Palm Jumeirah’s frond layout.

Imagine the Elliptic Curve Method as exploring Palm Jumeirah, Dubai’s iconic palm-shaped island. The island represents an elliptic curve y² = x³ + ax + b mod M, where M is the number to factor (a product of unknown primes). Fronds are j-invariants classifying curve shapes, points (x, y) are coordinates to probe, and the group order (number of points modulo a hidden prime p) is like the frond’s “explorable paths” bounded by Hasse’s theorem: |#E(Fₚ) — (p+1)| ≤ 2√p.