The Archimedes, Ulam, and Sacks Spirals, Euler's Prime Formula, and the Non-random Distribution of Prime Numbers

Found this by chance the other day: The Sacks Spiral, an interesting variant of the Ulam spiral. 

sources: 

https://naturalnumbers.org/sparticle.html

https://math.osu.edu/sites/math.osu.edu/files/EulerPrimeGeneratingPolynomial.pdf

Euler's Prime Formula is the n^2 + n + 41 curve. 

As the last constant term becomes at increasing large prime number, I suspect the proportion of prime numbers in the curve asymptotically approaches 1.