looking for tuples of n consecutive years with exactly n prime factors which are all distinct (turns out n>=4 is impossible because out of every four consecutive numbers, one must have 2**2 in its factorization, but I didn't realize this until the code was already written)

years.py

from subprocess import check_output

def factorize(n):
    if n == 0 or n == 1:
        return {}
    output = check_output(["factor", str(n)]).decode('utf-8')
    factors = list(map(int, output.split(": ")[1].split(' ')))
    factorization = {(f, factors.count(f)) for f in set(factors)}
    return factorization

def factors_all_distinct(fctn):
    for p in fctn:
        if p[1] != 1:
            return False
    return len(fctn)

successes = {}

previous_fact = None
year_fact = None
consecutive = 1
for year in range(1000, 3000):
    previous_fact = year_fact
    year_fact = factors_all_distinct(factorize(year))
    if year_fact:
        if year_fact == previous_fact:
            consecutive += 1
        else:
            consecutive = 1
        if year_fact >= 3 and consecutive == year_fact:
            run = tuple(y for y in range(year - year_fact + 1, year + 1))
            print(run)
            if year_fact in successes:
                successes[year_fact].append(run)
            else:
                successes[year_fact] = [run]
    else:
        consecutive = 1

print(successes)