The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 26972593−1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2p−1, have been found which contain more digits. However, in 2004 there was found a …
A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1. Considering natural numbers of the form, ab, where a, b < 100, what is the maximum digital sum? …
The bot doesn’t do much but tell fortunes, give a pong response to a ping, and log the chatroom. Will probably add to is as I get bored. The fortunes text file can be found here if interested. import socket import random from config import * def processChat(sock, buff): buff = buff.strip() …
Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5: 22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=3125 If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms: 4, …
The series, 11 + 22 + 33 + … + 1010 = 10405071317. Find the last ten digits of the series, 11 + 22 + 33 + … + 10001000. This problem was solved easily with Python, due to arbitrary length constraints on numbers. import math foo = 1 total …
A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are: 012 021 102 …
The Fibonacci sequence is defined by the recurrence relation: Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 …
n! means n × (n − 1) × … × 3 × 2 × 1 For example, 10! = 10 × 9 × … × 3 × 2 × 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 …
This is a basic port scanner implementation in Python; it attempts to connect to the given ports of the specified host (all ports, if none indicated), and outputs to a text file and to the console if a given port is open – if it is, it then attempts to …
The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule above and starting with 13, we generate the following sequence: 13 → 40 → 20 → 10 → 5 → 16 …