Theory Behind RSA
... of p1, p2, …, pk, so must be divisible by a prime not on the list. The largest known prime is 213,466,917-1, which has 4,053,946 digits Primality: Simply start checking for divisibility by 2, 3, 4, 5, 6, 7, … A number n is prime if it isn’t divisible by any number up to n Determining whether ...
... of p1, p2, …, pk, so must be divisible by a prime not on the list. The largest known prime is 213,466,917-1, which has 4,053,946 digits Primality: Simply start checking for divisibility by 2, 3, 4, 5, 6, 7, … A number n is prime if it isn’t divisible by any number up to n Determining whether ...
Integer Compositions, Gray Code, and the Fibonacci Sequence
... Much as the usual binary code provides a way to represent integers in base 2, Gray Code is a binary encoding method, but with an additional valuable property the Gray Code representations of two consecutive integers differ by only one bit. For instance, the integer representations of zero to three in ...
... Much as the usual binary code provides a way to represent integers in base 2, Gray Code is a binary encoding method, but with an additional valuable property the Gray Code representations of two consecutive integers differ by only one bit. For instance, the integer representations of zero to three in ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.