Journal

Exceptional Primes and the Number 31


I’m a bit tired. So I’m going to mention a project I’m thinking about tackling in unity sometime. Why Unity? Well because I like doing shit in it. I could probably make this in something much smaller. Anyways, let’s get into the finer details. As mentioned in the title of the previous post, my age is now a prime number. It will not be prime again until I am 37. But that got me wondering. Is the sum of prime’s including my age, also a prime? So I got checking. One thing to consider that I didn’t last time I thought about this was that 1 is not prime. It has a single factorization, not two, and prime numbers have two.

Anyways. Let’s check out the idea a bit.

I’m going to make this simple, the number first, the sum of primes including that number, and whether or not it fits my rule.

2 : 1 – No3 : 2 – Yes, 5 : 3 – Yes, 7 : 4 – No11 : 5 – Yes, 13 : 6 – No, 17 : 8 – No, 19 : 9 – No, 23 : 10 – No, 29 : 11 – Yes, 31 : 13 – Yes, 37 : 15 – No, 41 : 16 – No!

So as you can see, up until 41 years of age there are a number of exceptionally prime years. 3, 5, 11, 29, and 31! The next one is at…67 (17)! That’s so far from now!

I actually wrote the program tonight and here are my initial findings!

2 : 1 – NO!, 3 : 2 – YES!, 5 : 3 – YES!, 7 : 4 – NO!, 11 : 5 – YES!, 13 : 6 – NO!, 17 : 7 – YES!, 19 : 8 – NO!, 23 : 9 – NO!, 29 : 10 – NO!, 31 : 11 – YES!, 37 : 12 – NO!, 41 : 13 – YES!, 43 : 14 – NO!, 47 : 15 – NO!, 53 : 16 – NO!, 59 : 17 – YES!, 61 : 18 – NO!, 67 : 19 – YES!, 71 : 20 – NO!, 73 : 21 – NO!, 79 : 22 – NO!, 83 : 23 – YES!, 89 : 24 – NO!, 97 : 25 – NO!, 101 : 26 – NO!, 103 : 27 – NO!, 107 : 28 – NO!, 109 : 29 – YES!, 113 : 30 – NO!, 127 : 31 – YES!, 131 : 32 – NO!, 137 : 33 – NO!, 139 : 34 – NO!, 149 : 35 – NO!, 151 : 36 – NO!, 157 : 37 – YES!, 163 : 38 – NO!, 167 : 39 – NO!, 173 : 40 – NO!, 179 : 41 – YES!, 181 : 42 – NO!, 191 : 43 – YES!, 193 : 44 – NO!, 197 : 45 – NO!, 199 : 46 – NO!, 211 : 47 – YES!, 223 : 48 – NO!, 227 : 49 – NO!, 229 : 50 – NO!, 233 : 51 – NO!, 239 : 52 – NO!, 241 : 53 – YES!, 251 : 54 – NO!, 257 : 55 – NO!, 263 : 56 – NO!, 269 : 57 – NO!, 271 : 58 – NO!, 277 : 59 – YES!, 281 : 60 – NO!, 283 : 61 – YES!, 293 : 62 – NO!, 307 : 63 – NO!, 311 : 64 – NO!, 313 : 65 – NO!, 317 : 66 – NO!, 331 : 67 – YES!, 337 : 68 – NO!, 347 : 69 – NO!, 349 : 70 – NO!, 353 : 71 – YES!, 359 : 72 – NO!, 367 : 73 – YES!, 373 : 74 – NO!, 379 : 75 – NO!, 383 : 76 – NO!, 389 : 77 – NO!, 397 : 78 – NO!, 401 : 79 – YES!, 409 : 80 – NO!, 419 : 81 – NO!, 421 : 82 – NO!, 431 : 83 – YES!, 433 : 84 – NO!, 439 : 85 – NO!, 443 : 86 – NO!, 449 : 87 – NO!, 457 : 88 – NO!, 461 : 89 – YES!, 463 : 90 – NO!, 467 : 91 – NO!, 479 : 92 – NO!, 487 : 93 – NO!, 491 : 94 – NO!, 499 : 95 – NO!, 503 : 96 – NO!, 509 : 97 – YES!, 521 : 98 – NO!, 523 : 99 – NO!, 541 : 100 – NO!, 547 : 101 – YES!, 557 : 102 – NO!, 563 : 103 – YES!, 569 : 104 – NO!, 571 : 105 – NO!, 577 : 106 – NO!, 587 : 107 – YES!, 593 : 108 – NO!, 599 : 109 – YES!, 601 : 110 – NO!, 607 : 111 – NO!, 613 : 112 – NO!, 617 : 113 – YES!, 619 : 114 – NO!, 631 : 115 – NO!

Anyways, I’m going to look even deeper into the math behind this in the coming week and graph out the results. See what we are looking at here. I’m sure some math dork has already worked this out and given it a name. But I’m still going to swoop in like a peregrine penguin and give it my own name as well. I don’t know what it will be yet. Exceptionally prime does sound kinda funny though.

Edit: For fun I went up to 101 since that’s a pretty likely “end” point for a lot of folks. That or sooner. We’ve got 73 (19) and 97 (23)!