Derpetology

Wednesday, August 5, 2026

The Collatz Conjecture, the Goldbach Conjecture, the integer factorization problem, and prime numbers

Today I noticed that if you use the Collatz Conjecture with a prime as a seed, the first odd result greater than 1 that is not a multiple of 5 (greater than 5) will be prime or semiprime. Here are examples with the primes between 1 and 100

2 1

3 10 5...

5 is prime.

5 16 8 4 2 1

7 22 11...

11 is prime.

11 22 34 17...

17 is prime.

13 40 20 10 5...

5 is prime.

17 52 26 13...

13 is prime.

19 58 29...

29 is prime.

23 70 35 106 53...

53 is prime.

29 88 44 22 11...

11 is prime.

31 94 47 142 71...

71 is prime.

37 112 56 28 14 7...

7 is prime.

41 124 62 31...

31 is prime.

43 130 65 196 98 49...

49 is semiprime.

47 142 71...

71 is prime.

53 160 80 40 10 5...

5 is prime.

59 178 89...

89 is prime.

61 184 92 46 23...

23 is prime.

67 202 101...

101 is prime.

71 214 107...

107 is prime.

73 220 110 55 166 83...

83 is prime.

79 238 119...

119 is semiprime.

83 250 125 376 188 94 47...

47 is prime.

89 268 134 67...

67 is prime.

97 292 146 73...

73 is prime.

skipping a bit

997 2992 1496 748 374 187...

187 is semiprime with factors of 11 and 17.

9973 29920 14960 7480 3740 1870 935 2806 1403...

1403 is semiprime with factors 23 and 61.

By combining this with the Goldbach Conjecture, we have a new primality test and a way of generating primes. Start with a large even number (100 digits or more) and divide by 2 until you get an odd number. Then use that odd number as a seed for the Collatz conjecture. The first odd result that isn't a multiple of 5 will be either prime or semiprime. I suspect that as for large seeds, the first odd result is more likely to be semiprime than prime.

In this way, it is possible to build up a library of large semiprimes, which eases the integer factorization problem.

What happens if the seed is semiprime?

187 562 281...

281 is prime.

1403 4210 2105 6316 3158 1579...

1579 is prime.

So if we start with a semiprime, we can get an actual prime in a few iterations.

For any given range, there will be somewhat more semiprimes than primes.

Tuesday, August 4, 2026

my favorite cowboy songs

Blues Saraceno - Grave Digger [ Lyrics Video ]

Marty Robbins - El Paso (Audio)

[Ghost] Riders in the Sky

The Good, the Bad and the Ugly • Main Theme • Ennio Morricone

The Blues Brothers (1980) - Rawhide Scene (5/9) | Movieclips

Horse Soldier, Horse Soldier

The Highwaymen - Highwayman (Official Video)

knowledge as a social cue

An educated native speaker of English has a vocabulary of about 25,000 words even though only about 6,000 of them account for 95% of what they say. So what is the value of knowing the other 19,000 words? A large vocabulary is a reliable signal that someone has read a lot, because that is the usual way someone comes to know many words. People who read a lot are usually smart; thus, the use of rare words is a signal to other intelligent people that they are alike and should interact. The fact that we have dictionaries (and can instantly look up the definition of words online) does not negate the advantage of having a large vocabulary.

It's similar to the way people wear certain clothes in order to fit into a group. There's a reason why businessmen always wear suits. It's an advertisement about who they are and wish to associate with.

Indeed, the most common way people try to ingratiate themselves into a group is by changing their appearance and sometimes their speech. People who move to a different country or region often adopt the accent there in order to be accepted.

Knowledge also works as a social cue. Most knowledge, especially the kind from formal education, has little direct utility, especially today when almost everyone has the internet in their pocket. The amount of practical knowledge a typical adult needs is surprisingly small. Almost all the rest functions as way to show interests and status. For example, knowing how to change a tire is a lot more useful than being able to read Latin, yet knowing Latin is a clear indicator that someone is inquisitive, well-read, and probably intelligent. I suspect this is the reason the high IQ society Mensa uses a Latin word for its name.

Someone who is very knowledgeable and demonstrates it is showing (unintentionally or not) who they are and who they want to associate with. This is why people should be careful about what knowledge they share. If you talk about astronomy all the time, people will wonder why you aren't working at a planetarium or a member of a stargazer club. Sharing knowledge on different topics sends mixed signals, sort of like switching from one language to another. If you want to speak English, it does no good to go around speaking Spanish or any other language.

Still, being knowledgeable on many topics is generally respected. Scholars hundreds of years ago were respected precisely because it was known to take a lifetime of study to learn so much. The key to avoid being called a know-it-all is to say little. Sile et philosophus esto is Latin for "be silent and you will pass for a philosopher". In any case, know-it-all refers to someone who pretends to be more knowledgeable than they are. Someone who really does know a lot on many topics is a polymath.

I say be a renaissance man if you can. The world can always benefit from another genius.

I should add that jokes are the most useful thing to memorize if you want to make friends and get people to like you.

Saturday, August 1, 2026

How many books should you read?

The short answer is the more, the better. But as in all other things, there are diminishing returns to reading.

It's better to read many short books than one long one. Nonfiction is more informative and often more enjoyable.

Here is a short reading list that provides a good education:

1. Bullfinch's Mythology

2. The Cartoon History of the Universe

3. Man's Search for Meaning

4. Animal Farm

5. Slaughterhouse 5

6. The Art of War

7. Ecclesiastes

8. Proverbs

9. Alice in Wonderland

10. The Hobbit

Anyone who reads all of those will have a pretty good grasp of life, the universe, and everything.

Should you go to college? Should you study engineering?

I think it is a bad idea to borrow a lot of money for college, though most who study law or medicine pay back their loans with no problem.

I was not enthusiastic about college. I went because I got a full scholarship and couldn't think of anything better to do. I don't regret going to college, but it made me realize that I did not want to spend any more time in school, though that ended up happening anyway.

My scholarship required that I study science, engineering, or technology. I picked chemical engineering because I liked chemistry in high school and the starting salaries were good. At the time, I wasn't sure if I wanted to get a PhD, so I thought engineering was a practical choice that would let me go to work right away if I wanted. As it turned out, after four years of studying engineering, I wanted to do something completely different for a while. So I joined the Peace Corps because I wanted to travel, learn another language, and have an adventure. That was probably the best decision I ever made.

In order to be a successful engineer, you have to be focused and driven. You have to care a lot about getting the design or process right. If you find the work boring, as I did, engineering will not work out for you as a career. Engineers usually work in teams, so they have to be sociable. If you're an introvert, avoid engineering unless you're really interested in the technology involved.

If I had to live my life over again knowing everything I know now, my life would be about 90% the same. That's a sign I don't have too many regrets and made mostly the right decisions.

suggested movies for homeschoolers and gifted/talented students

Many are available for free on YouTube.

The War of the Worlds (1953)

Some are family friendly, others not so much. Sex, violence, and profanity are parts of adulthood. Movies are a safe way to introduce them. Forbidden fruits are excellent incentives for good behavior.

1. The Lion, The Witch, and The Wardrobe (1979)

2. Jaws

3. Star Wars (original trilogy)

4. The Thing (1982)

5. Saving Private Ryan

6. The Blues Brothers

7. Robocop

8. The Terminator

9. The Matrix

10. Patton

11. Tora! Tora! Tora!

12. Braveheart