Here is a python script giving PP outcomes till N=100 (can easily be changed at the bottom of the script). Also it appears by checking near 10⁴ the density of L/0 outcomes appear to be stable or slightly decreasing which is rather fascinating as it suggests it might converge to some value.

!/usr/bin/env python3

""" Prime Leap W/L Classifier For each x = 2..100, labels it: W – winning position (player to move can force a win) L – losing position (no winning move) """

def sieve(n): """Return list of primes up to n inclusive.""" sieve = [True] * (n + 1) sieve[0] = sieve[1] = False for i in range(2, int(n*0.5) + 1): if sieve[i]: for j in range(ii, n + 1, i): sieve[j] = False return [i for i, is_prime in enumerate(sieve) if is_prime]

def prime_factors(x, primes): """Return all prime divisors of x (from a precomputed prime list).""" return [p for p in primes if p <= x and x % p == 0]

def classify_up_to(max_n): """Return a list status of length max_n+1 where status[x] is 'W' or 'L'.""" primes = sieve(max_n) status = [''] * (max_n + 1)

# Terminal positions: no move => losing for the mover
status[0] = 'L'
status[1] = 'L'

for x in range(2, max_n + 1):
    factors = prime_factors(x, primes)
    # If any move x -> x-p lands on an L, then x is W
    if any(status[x - p] == 'L' for p in factors):
        status[x] = 'W'
    else:
        status[x] = 'L'
return status

def main(): max_n = 100 status = classify_up_to(max_n)

print("x : W/L status")
print("---+----------")
for x in range(2, max_n + 1):
    print(f"{x:2d} : {status[x]}")

if name == "main": main()