https://twitter.com/kyasmt/status/1413786372628914178

pm.scm

(use srfi-42)
(use math.prime)

(define (solve N)
  (let* [[v (make-vector N)]
         [%%solve (^ (n k) (let [[x (vector-ref v k)]
                                 [y (vector-ref v (- n k 1)) ]]
                             (max (+ x y) (* x y))))]
         [%solve (^ (n) (if (zero? n) 1
                          (max-ec (: k n) (%%solve n k))))]
         ]
    (do-ec (: n 0 N)
           (vector-set! v n (%solve n)))
    (vector-ref v (- N 1))))

(define (main args)
  (let1 answer ($ solve $ string->number $ cadr args)
    (print answer)
    (print (mc-factorize answer))
    0))

result.txt

ル╹ヮ╹ルɔ MIKA:~/work
% gosh pm.scm 100
7412080755407364
(2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3)
ル╹ヮ╹ルɔ MIKA:~/work
% gosh pm.scm 101
11118121133111046
(2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3)
ル╹ヮ╹ルɔ MIKA:~/work
% gosh pm.scm 102
16677181699666569
(3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3)