# Science Buzz Cafe # 474 Twin Prime Conjecture – Prime Numbers: The Basic Building Blocks of All Numbers

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Speaker: Roger House, Student of Mathematics

Prime numbers keep your encrypted messages safe, ensuring secure communication. They are the basic building blocks of all numbers. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Euclid’s second theorem demonstrated that there are an infinite number of primes. Around 200 BC Eratosthenes devised an algorithm for calculating primes called the Sieve of Eratosthenes. Every number except 1 has at least two factors. Prime numbers have the unique property of have exactly two factors: 1 and themselves.

It’s not so much the prime numbers themselves that are important, but the algorithms that work with primes. In particular, finding the factors of a number, any number.

Roger House will provide a short history of the Twin Prime Conjecture and the great progress made in recent years towards its resolution. There is a good chance that the conjecture will be proved rather soon, thus transforming the conjecture into a theorem. The Twin Prime Conjecture is a conjecture (i.e., not a theorem) that states that there are infinitely many pairs of twin primes, i.e. pairs of primes that differ by 2.

Roger studied mathematics throughout his university years (1961-1999 with a lot of breaks) and always intended to be a mathematician when he grew up. However, as a young man he was seduced by a computer and has spent most of his working life writing computer programs. But in a parallel universe not too far from this one he is, in fact, a mathematician …