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.
phkahler•3mo ago
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.
Deeptiman•4mo ago
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.