So, this guy came up with a cool way to view primes, programmatically (ref pic):

https:/ /mathlesstraveled.com/2012/10/05/factorization-diagrams/

Some blogger picked up on it:

http:/ /www.datapointed.net/2012/10/animated-factorization-diagrams/

..and, here is what you want to watch:

http:/ /www.datapointed.net/visualizations/math/factorization/animated-diagrams/#

^^^THIS^^^

There is a version that goes above 10,000 but I don't think you'll need that. By 10K, it gets harder to see the detail.

Watch for the "X-Wing Factor" (pic attached). It's an upside down Y that tends to have a prime either side.

While watching, keep in mind the gaps between primes:

2 = twin primes

4 = cousin primes

6 = sexy primes (seriously!)

If you want some more triangles, same guy, here:

https:/ /mathlesstraveled.com/2012/10/20/visualizing-pascals-triangle-remainders/

You can play around with them, different mods, and create some neato pyramids here (pic attached):

http:/ /aleph.sagemath.org/?z=eJxlUU2L2zAQvedXzM1SKrtx6LaQIui1h5ZQ9mZCGMnjWIlsGX2Q9N9Xa3u7ZSuBBj3pvXkz01IHEwaN9mh0TJ6YEiM_bCAv7azzQTZNLfI-nf4Fl_ChaW4fldiX–1LrMt8nqBzHm5gRmjqqlLlK_PZGxwvlmSjjdeWGNtvr6URu7KuvjxtDc9ZgNoLzdqyUBb1rRAd6hVZcjZMmdENBi0z4sp5NbiWKX4SnbFWRp9IAIaJdDx7jMbJrIoPCrJDG4jP7syLO5_dEBsX5Dr73VWVWd1OMqSBvXrmM-Ypd2iEabP5ZsZIHnXctLmBZ6YwkDTjlOJZuQfLICYb5V6ARUVWFj9cm2wKh4KLWQpgAAn_M75n3Qt59vkTFyv1ZxoUeXAd_HL3AAwjDC5EqJ92_E0OU3TnNLUYaa10GWL0vw_rF4CjfDfrbFsM_O976N2dHZc7PTRN8Y3bx8Gy4rknT3DHADgCee_819wW3ZO-QexpqSgU_A_I37p3&lang=sage

>>4665 thanks!