What’s in a number?
A quick look at the math behind the number 2026
2026 is not just a year; it’s a highly fascinating number! Here are some mathematical features that are interesting about the number 2026.
The first is that it’s composite. A composite number is a positive integer greater than 1 that is divisible by more than two numbers. 2026 in particular is divisible by 1, 2, 1013, and 2026. Composite numbers are especially important in encryption: to create encrypted systems, two prime numbers are multiplied together to create a composite number. Multiplying numbers is an easy process, but finding the factors of a number — especially large ones — is a much more difficult task. Modern encryption systems take advantage of this fact by using 2048-bit numbers to create an encryption key. Because breaking the encryption would require factoring the encryption key — a process that would take modern computers nearly 2,700 years to complete — this system can securely protect sensitive information such as online banking and private messages.
2026 is also evil. A number is considered “evil” if it has an even number of 1s in its binary expansion. The term comes from a playful naming convention in mathematics: numbers with an even number of 1s are called “evil,” while those with an odd number of 1s are called “odious.” The binary expansion of 2026 is 11111101010, which has eight 1s. This fact is used in detecting errors in transmission of data. Sometimes, during the transmission of data, due to electrical noise, bits of information flip from 0 to 1, or vice versa. For example, the number 10110 could turn into 11110. To detect whether information has been modified or not, an extra bit called a parity bit is added to the end. The parity bit is 1 if the number of 1s in the number is odd, and 0 otherwise. For example, the number 10110 would be sent as 101101, since there are three 1s in the number. When the data is received, the system checks the number of 1s again. If the parity does not match the expected value, the system knows the data was likely corrupted and can request that it be resent. Of course, this method is not foolproof; for example, if two bits were flipped, the parity would remain the same and the error wouldn’t be detected. Nonetheless, this method is still a simple and efficient first step for detecting transmission errors.
The number 2026 reveals interesting numerical properties that are used in modern encryption systems and to detect errors in data transmission. Together, these examples demonstrate that numbers are more than symbols or a figure in the corner of our screens; they play a critical role in the technology and systems we rely on daily.
This article was inspired by Dr. Tanya Khovanova and her website, Number Gossip.