[Ologn]

With Gemini 3, I wrote an Emacs Lisp which can tell if a number is prime or not using only primitive recursive functions. That was done at the end of last year, and none of the frontier LLMs were able to do it earlier in 2025.

I had some test functions where minimization could be optionally used, but wanted to do one where minimization was needed, like the Ackermann function. Most of the frontier models struggled with doing this, although I may have been prompting incorrectly. Although - if I had been prompting totally correctly, I probably could have gotten what I got out of a frontier LLM in early 2025 and before.

Incidentally the test function that tells you if a number is prime in Emacs Lisp with primitive recursion is

(defalias 'prime (c (c (c (r 's (c 'z (p 1))) (p 1) 'z) (c (r (p 1) (c 's (p 2))) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 1) (p 2))) (p 2) (p 1)) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 2) (p 1))) (p 2) (p 1)))) (c (c (r 'z (c (r (p 1) (c 's (p 2))) (c (c (r 'z (c (r (p 1) (c 's (p 2))) (p 2) (p 3))) (c (c (c (r 's (c 'z (p 1))) (p 1) 'z) (c (r (p 1) (c 's (p 2))) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 1) (p 2))) (p 2) (p 1)) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 2) (p 1))) (p 2) (p 1)))) (c (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (c (r 'z (c (r (p 1) (c 's (p 2))) (p 2) (p 3))) (p 2) (c (r 'z (c (r (p 1) (c 's (p 2))) (p 2) (c (c (r 's (c 'z (p 1))) (p 1) 'z) (c (r 'z (c (r 'z (c (r (p 1) (c 's (p 2))) (p 2) (p 3))) (c 's (p 2)) (c (c (r 's (c 'z (p 1))) (p 1) 'z) (c (c (c (r 's (c 'z (p 1))) (p 1) 'z) (c (r (p 1) (c 's (p 2))) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 1) (p 2))) (p 2) (p 1)) (c (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (c (r (p 1) (c (c (r 'z (p 1)) (p 1) 'z) (p 2))) (p 2) (p 1))) (p 2) (p 1)))) (c 's (p 2)) (p 3))))) (c 's (p 1)) (p 3))))) (p 1) (p 2))) (p 1)) (p 1) (p 2)) (c 'z (p 1))) (c (c (r 'z (c (c 's 'z) (p 1))) (p 1) 'z) (p 1))) (p 3) (c 's (p 1))) (p 2))) (p 1) (p 1)) (p 1)) (c 's (c 's 'z))))