Seeds above 1e10 appear to produce the same random seed function.

This is because the calculator exclusively uses floating point numbers in all of its calculations despite the fact that the z80 instruction set does not natively support floating point calculations. Floating point numbers represent smaller numbers more precisely than large numbers. The following will produce different outputs.

` ``3e10→rand rand 5e10→rand rand`

As for your second conjecture, you definitely need to formalize and revise it because 196164532 *kind of* outputs 1 one from **rand** and it is not divisible by 59. That was a value I was initially looking for with my code, because I didn't read the page close enough I wrote the code before finding it there, but there could be more than one so it's still useful. I say *kind of* because **randBin(** and **randNorm(** would have some sort of problem if the output was actually 1, according to the rand page anyway. This is the part that actually confused me when I posted this since **rand** doesn't use its own output as the next argument to itself(at least not by itself). I linked to this before but I think it's worth posting here again. I can't understand the C++ or Python very well since I haven't coded in them before but I probably wouldn't understand it if it was in Java either. A free PDF is also linked to on the page about rand. Reading it would really help in understanding how to make good conjectures and then how to prove them(again a bit hard to understand but not impossible).

` ``:S→rand :While 1 :10round(rand,1 :Ans→rand :Pause Ans :End`

for some starting integer S. It isn't too hard to prove that every integer S eventually leads to the loop (2,5,7), though the intermediate steps are a bit harder to track. I think the CE has a slightly varied PRNG, because I've seen 5's but no 4's and 10's but no 9's (i.e. just one off from your conjecture).

]]>N represents the first random number generated by an nonnegative integer seed S

The random seed function inputs a seed, and outputs the first random number that the generator returns with that given seed value.

Conjecture #1- the 9,7,4,2 pattern

For every value of S less than 13, round(10N,1) will always be approximately equal to either 9,7,4,2. The pattern oscillates until S=13, but the relationship remains reasonably approximate for much longer, slowly growing more inaccurate until it is almost completely flawed.

The following conjecture has been rewritten to better explain the point after a helpful comment by Deoxal

Conjecture #2- the largest gaps between the random seeds occur between numbers divisible by 58 and 59. For small seed values the 59 divisible seeds are (usually) the biggest, but since this pattern seems to shift downward over time, it probably isn’t an important way to find 1 valued random seed functions.