There’s also quantum random:
And the latest is, I guess, the RDRAND opcode which is on x86 processors starting in 2015 and later?
Reading more closely, you have to trust the source of randomness, because if you don’t.. that’s a whole other level of security violations.
One of the things to check with all pseudo random number generators is the number of different random sequences. If you use a 16-bit seed for random number generator, you are limited to having only 65 thousand random sequences. If I collect a few of your “random” numbers, I can compare your sequence to my database of random number sequences to determine what number you used to seed it, and determine what the entire sequence will be. 32-bit is of course about 4 billion possible seeds, but the same theory applies. You seed it and generate a sequence, I can compare your sequence against my database of 4 billion random sequences and quickly determine what seed you used, and predict your next random numbers.
Not having a computer, let alone a calculator is going to make it very difficult. Even just writing down 1000 digits is going to take a long time.
Perhaps assign a bit to each of the 10 digits, counting in prime increments, do bitwise AND on the input digits, sum up the resulting digits, use the last digit of the sum. So, given: 0123456789 as input, and counting in prime 7 the random numbers would be:
111 → 789 → 4
1110 → 678 → 3
10101 → 579 → 3
11100 → 567 → 8
100011 → 489 → 1
…
That’s a fantastic mental exercise. People are also terrible random number generators! I’d probably use dice to generate the randomness. But what if you don’t have access to dice.. what can you make to help you be more.. er.. random? Did I link the “what people do in prison” article yet? It’s a good one:
In 2020 this was published:
https://www.wsj.com/articles/rand-million-random-digits-numbers-book-error-11600893049
Mr. Briggs, 40, creates Rand computer models for the U.S. Air Force. In his free time, he obsesses with puzzles and projects. He made a chain-mail hoodie to wear to a comic-book convention, taught himself to knit, learned to juggle.
In May, he attended an online presentation by Rand’s archivist, who said work on the million digits had stretched for years before publication in 1955. Mathematician Bernice Brown spent the late 1940s conducting mathematical tests to ensure the numbers contained no predictable patterns.
In her 1948 paper, “Some Tests of the Randomness of a Million Digits,” Mrs. Brown announced that “none of the tests contradicts the assumption of randomness.”
She died at 99 in 2003. Her analysis held until Mr. Briggs fixated on replicating her work, leading him down a three-month rabbit hole from which he hasn’t fully emerged.
Hmm. This is weird. It’s not an invalidation…
In a group of 50,000 random digits, mathematicians would expect 4,050 sequences of two identical digits in a row—77, for instance. They would predict 405 spots with three identical digits in a row, such as 555. There would be about 40 cases of four identical digits in a row. And four or five places with five identical digits together.
His results were “soul crushing,” Mr. Briggs says. The book contains 48 runs of four digits instead of 40, an astoundingly wide divergence in statistical terms that eluded any explanation he could conjure.
It’s not that the digits in the book aren’t random, he says. They just don’t seem to be exactly the right digits in exactly the right order, given the impulses the Douglas machine generated.
This is kinda pointless as a test (it’s still random, but not exactly in the “right order”? What?) and observation. It’s trivia at best?
To go one further, a sequence of three digits (i.e.: 555) appearing after a specific digit would be another test of randomness. Could this sequence be accurately predicted or simply appear at “random?” Then again, do we really need this?
Sounds like that is an example of random.