Step by Step solution about How to resolve the algorithm Truncatable primes step by step in the Python programming language

The given Python code finds the longest left and right truncatable primes below a specified limit maxprime. A truncatable prime is a prime number that remains a prime when its digits are removed from either end.

The code uses a helper function primes(n) to generate a list of prime numbers up to n. It uses the Sieve of Eratosthenes algorithm to efficiently find prime numbers.

The main function truncatableprime(n) takes n as input and returns the longest left and right truncatable primes below n. It uses the list of prime numbers generated by primes(n) to find the longest truncatable primes.

The function iterates through the list of prime numbers in reverse order (largest to smallest) and checks if the prime number is a left truncatable prime. To check if a prime number is a left truncatable prime, the function generates a set of all possible truncations of the prime number (by removing digits from the left end) and checks if all the truncations are also prime numbers. If all the truncations are prime numbers, the function stores the prime number in the truncateleft variable.

The function then iterates through the list of prime numbers again in reverse order and checks if the prime number is a right truncatable prime. To check if a prime number is a right truncatable prime, the function generates a set of all possible truncations of the prime number (by removing digits from the right end) and checks if all the truncations are also prime numbers. If all the truncations are prime numbers, the function stores the prime number in the truncateright variable.

Finally, the function returns the truncateleft and truncateright values as a tuple.

The code prints the longest left and right truncatable primes below maxprime as a tuple.

maxprime = 1000000

def primes(n):
    multiples = set()
    prime = []
    for i in range(2, n+1):
        if i not in multiples:
            prime.append(i)
            multiples.update(set(range(i*i, n+1, i)))
    return prime

def truncatableprime(n):
    'Return a longest left and right truncatable primes below n'
    primelist = [str(x) for x in primes(n)[::-1]]
    primeset = set(primelist)
    for n in primelist:
        # n = 'abc'; [n[i:] for i in range(len(n))] -> ['abc', 'bc', 'c']
        alltruncs = set(n[i:] for i in range(len(n)))
        if alltruncs.issubset(primeset):
            truncateleft = int(n)
            break
    for n in primelist:
        # n = 'abc'; [n[:i+1] for i in range(len(n))] -> ['a', 'ab', 'abc']
        alltruncs = set([n[:i+1] for i in range(len(n))])
        if alltruncs.issubset(primeset):
            truncateright = int(n)
            break
    return truncateleft, truncateright

print(truncatableprime(maxprime))