Nikitha

Prime numbers are the reason your credit card is safe. When you buy something online, your payment information is encrypted using a system called RSA encryption, and its entire security rests on one simple mathematical fact: Multiplying two large prime numbers together is easy. However, reversing the process and figuring out which two primes were multiplied is effectively impossible. For example, it's trivial for a computer to compute: 12,451 × 18,637 = 232,048,387 But going the other way is much harder. If I hand you 232,048,387 and ask you to find its prime factors without telling you where to start, it becomes a genuinely hard problem. Now scale those primes up to numbers with hundreds of digits, which is what RSA actually uses, and even the fastest computers on Earth would take longer than the age of the universe to crack it by brute force. What makes this philosophically strange is that RSA encryption is built on a problem mathematicians haven't proven is actually hard. We believe factoring large numbers is fundamentally difficult. But nobody has ever proved that no shortcut exists. It is possible, however unlikely, that someone could discover a clever algorithm tomorrow that breaks all encryption instantly, exposing every bank account, every private message, and every government secret simultaneously. This is one of the greatest unsolved problems in mathematics, known as P vs NP. It asks whether problems that are easy to verify are always also easy to solve. If the answer is yes, meaning P equals NP, modern encryption collapses entirely.