# Variations on Ulam

Discussion in 'Number Theory' started by perotinus1983, Dec 18, 2021.

1. ### perotinus1983

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Hi, I'm new here and by no means a mathematician, but I got interested by primes and started doodling spirals like Ulam's.

I started working on different versions like omitting all even numbers, omitting 1, omitting even numbers and primes ending in 5 (including 5) etc. Latter is kind of nice, simply because there's less writing/cramp. Besides, patterns emerge earlier on paper this way. It's not really grounded in any formal idea, but I figured since 2 and 5 are the only primes ending in 2 or 5, I would chase primes more easily by only putting 1,3,7,9,11,13,17,19,21,23,37,29 etc. in the spiral. Not to say (1,) 2 and 5 are beneath me or anything...

There's some nice patterns emerging like 11,41,101,191,311,461,641, all prime numbers and found by adding 30 to 11, 60 to 41, 90 to 101 etc. The longest sequences I found like this were 13,43,103,193,313,463,643,853,1093,1363,1663,1993 (12 primes) and 17,41,107,197,317,467,647,857,1097,1367,1667,1997,2357 (13 primes). Patterns like this are common but usually break after 3 or 4 increments.

Anyway... can anyone tell me if there's some readily obtainable material available exploring this idea? Seems like a fun and intuitive thing to do, and people smarter than me could probably do much better. So I wouldn't be surprised.

P.S. (I also found 3163,3361,3613,3631 and 6133 are all prime numbers, so more than half of all possible odd numbers containing 1,3,3 and 6 are primes. Neat, no? Or scary?)

perotinus1983, Dec 18, 2021
2. ### MathLover1

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MathLover1, Dec 18, 2021
3. ### perotinus1983

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Thank you! I will probably have to learn some basic programming to devise a spiral of substantial size according to my own idea, but this still helps. It seems unlikely to me that I'm the first one toying with this, so... if you come across uneven number spirals and the like, I would be obliged if you mention them. Regards, Matt

perotinus1983, Dec 18, 2021
4. ### MathLover1

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MathLover1, Dec 18, 2021

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