Prime Spirals - Numberphile

I love his smile while talking about mathematics. That's a person who's loving the thing he's doing.

New primes, bigger primes, optimus primes

We've dug too deep The matrix is being unveiled

1:18 Ulam was bored by a lecture and was doodling. I like him.

Sad that he's name isn't James Prime.

Every once in a while, I come back to these numberphile videos to just listen to James Grime talk about his numbers. It just makes me feel so happy that he exists and that he's doing something he absolutely loves. I could never do what he does, but his enthusiasm and passion is inspiring:)

James showing his true 'attraction' for primes "Look at these curves."

thank you

You've got to love that ViHart reference😜

Like Ulam I was bored in my Math class a while ago and eventually wrote a Java program to generate his spiral. I found it really interesting to add color based on the relationships between the primes, like twin primes, primes that are 4 apart, 6 apart, and so on.

What I most like about numberphile is that they put subtitles in every single video. I really appreciate that ;D

keep an eye out for brown papers on ebay... I'll put this one up some time... best thing is to follow numberphile on twitter and facebook! :)

Half the diagonals have only even numbers, so only the diagonals with odd numbers have any prime numbers at all, with the exception of those that go through the number 2.

"Look at these cuuuurves" :D I love how this is used for once in a nonsexual way

You guys never cease to amaze me. You make even the most complex concepts in mathematics seems really easy. Keep up the great work guys :)

This is amazing. I thought they were all randomly spread out. I knew you can use find out the density of primes but not find patterns such as this. Beautiful.

I don't even see the code, all I see is blonde, brunette, redhead...

Ulam's Square produces the appearance of diagonal runs of primes because primes (other than 2) have to be odd and the odd numbers are restricted to a checkerboard pattern. If you run a random number comparison with that same checkerboard restriction in place (which Numberphile didn't do), then the randomized square will produce a similar appearance of diagonal runs. This is likely true for the spiral in the latter half as well, where I'd bet the "curves" come from the layout of even and odd numbers, and the "prime curves" are just artifacts of the even/odd curves. Note: While the whole even/odd checkerboard for the square is pretty obvious, I actually did bother to run some tests just to confirm it. I ran multiple tests on increasing size squares. Every test where the hits were restricted to a checkerboard resulted in the appearance of "diagonal runs" of hits.

Very interesting video. Many years ago, when taking a Number Theory course in graduate school, I mapped the integers onto a spiraling lattice and noticed that the twin primes tended to be found at the edges of the lattice. [This property of twin primes being at the edges only worked for the first few dozen twins.] I developed a crude recursive formula, but didn't have time to pursue the study. Years later, I noted that Stanislaw Ulam had discovered this and developed it at least a decade earlier. During the mid-60s, Scientific American had an article on Ulam's remarkable work.

What happens if you do an ulam spiral, but instead of circling primes, you circle random odd numbers with logarithmic spacing?