Palindrome Test With Candidates

pal_cands_01.py

import functools
import time

def timer(func):
    @functools.wraps(func)
    def wrapper_timer(*args, **kwargs):
        tic = time.perf_counter()
        value = func(*args, **kwargs)
        toc = time.perf_counter()
        elapsed_time = (toc - tic)*1e6
        print(f"{elapsed_time:0.6f}")
        return value
    return wrapper_timer

def paltest(p):
    P = str(p*(p+1))
    if P != P[::-1]:
        return False
    Q = str( (p+22)*(p+23) )
    if Q == Q[::-1]:
        return True

def candidates():
    cands = []
    for m in range (5,10):
        ## 4mn7, p+1 odd
        n = m + 7 - 4
        if n < 10:
            p = 4*10**3 + m*10**2 + 10*n + 6
            cands.append(p)
        ## 4mn1, p odd
        n = m + 1 - 4
        if n < 10:
            p = 4*10**3 + m*10**2 + 10*n + 1
            cands.append(p)

    for s in range (0, 5):
        ## 5st6, p+1 odd
        t = s + 7 - 5
        if t < 10:
            p = 5*10**3 + s*10**2 + 10*t + 6
            cands.append(p)
        ## 5st1, p odd
        t = s + 1 - 5
        if t < 0:
            t += 11
        if t < 10:
            p = 5*10**3 + s*10**2 + 10*t + 1
            cands.append(p)
    return cands

@timer
def run():
    print ( [p for p in candidates() if paltest(p)] )

run()