Sunday, March 6, 2022

Obsessing about numbers an expression of the current insanity or a therapy for it? maybe both

UPDATE: Added more at bottom, couldn't stop obsessing

Of all two-digist numbers ending in 1, 21 and 81 are not prime, beubg duvusubke by other nubmers than thesmevles and 1.

Of all two-digit numbers that end in 3, 33, 63 and 93 are not prime

Of all the two-digit numbers that end in 7, 27 and 77u are not prime.

Of all the two-digit numbers that end in 9, 39, 69 snf 99 are not prime..

So that's roughly a quarter to a third of numbers in this group that are not prime; all the rest are prime numbers.

If you'd like to work it out for three-digit numbers be my guest. Happy obsessing.

But I kept on obsessing myself.

There are 360 three-digit numbers that end in 1, 3, 7, or 9. If the proportions of prime to nonprime numbers in this group are comparable to the two-digit group, about 100 will be nonprime and 260 will be prime, but this will be discovered by working them out.

ALLTHREE-DIGIT NUMBERS ENDING IN 1:
101, 111, 121,131, 141, 151, 161, 171, 181, 191
202, 211, 221. 231. 241. 251. 261. …
301, 311, 321, 331, 341, …
401, 411, 421, 431, …
501, 511, 521 …
601, 611 …
701 …
801…
901 …

ALL THREE-DIGIT NUMBERS ENDING IN 3
103, 113, 123, 133, 143, 153, 163, 173, 183, 193
203, 213, 223, 233, 243, 253 …
303, 313, 323 …
403…503… 603… 703 …803 … 903 …

ALL THREE-DIGIT NUMBERS ENDING IN 7:
107, 117, 127 …
207 … 307 … 407 … 507 … 607… 707… 807 … 907

ALL THREE-DIGIT NUMBERS ENDING IN 9: 109, 119, 129 …
209 … 309 … 409 etc etc.

In the group ending in 1, those will be nonprime which are divisible by 3, 7 or 9
Here are some of the nonprimes

111 (3x37), 141 (3x47), 171 (3x57) br> 201 (3x67, 231 (3x77 and 7X33), 261 (3x87), 291 (3.97)
321 (3x107)) >br? … and we have a pattern in the diviers too. Fun, huh? ,br> Looks like the percentage is holding up, about a third are noprime