July 2021

[Xyzzy]

https://www.research.ibm.com/haifa/p.../July2021.html

[bsquared]

I've learned some things about Carmichael numbers from researching this puzzle, and unless I've misunderstood something 100 digit primary Carmichael numbers seem to be pretty easy to find. So far the largest I've found is a 620 digit primary solution.

[bsquared]

Originally Posted by bsquared

I've learned some things about Carmichael numbers from researching this puzzle, and unless I've misunderstood something 100 digit primary Carmichael numbers seem to be pretty easy to find. So far the largest I've found is a 620 digit primary solution.

A little more optimization and up to a 2470 digit solution. Not searching any more until I hear something from the puzzle admins about whether these solutions are correct.

[tgan]

did you also find b
"and b is the largest non-trivial square root of unity modulo n."

[Dr Sardonicus]

I submitted a solution on the 2^nd in the suggested format. I had never heard of "primary Carmichael numbers." Apparently a new thing. I learned something!

I only submitted a single example, a primary Carmichael number just greater than 10^100 and called it good. Inspired by this thread, I adjusted my script to find one just greater than 10^620.

In theory, my script could find solutions of any size, but in practice it's so mindless it would take a long long time to find a really large solution.

[bsquared]

Originally Posted by tgan

did you also find b
"and b is the largest non-trivial square root of unity modulo n."

Yes I'm finding them by construction so I know the factors, and knowing those it's straightforward to find the non-trivial roots of unity.

Originally Posted by Dr Sardonicus

I submitted a solution on the 2^nd in the suggested format. I had never heard of "primary Carmichael numbers." Apparently a new thing. I learned something!

I only submitted a single example, a primary Carmichael number just greater than 10^100 and called it good. Inspired by this thread, I adjusted my script to find one just greater than 10^620.

In theory, my script could find solutions of any size, but in practice it's so mindless it would take a long long time to find a really large solution.

Yeah I've also learned some things - the mark of a good puzzle. Also I lied earlier and kept my script running over night. This morning I saw that it found a solution of size 4936 digits.