A Sophie Germain prime is a prime number such that is also a prime number. That is, , where and are both prime. For example, . The sequence begins Sophie Germain () explored these primes [more…]
Euclid’s Elements, Book IX, Proposition 20. Theorem : Prime numbers are more than any assigned multitude of prime numbers. That is, there are infinitely many primes. Proof : Suppose that there are primes : Let [more…]
In The Basel Problem we saw that Euler answered the question by showing that the sum of the reciprocals of the square numbers is equal to . That is The partial sums slowly converge to [more…]
Wilson’s Theorem is a test for primality. It is inefficient for large numbers since factorials () grow very fast. Nevertheless, it has its uses because of its simplicity. It was conjectured by Wilson and published [more…]
This is Klauber’s Triangle : – He produced it in the 1930s. The underlying numbers are the natural numbers ℕ and are arranged as follows : – 1 2 3 4 5 6 7 8 [more…]
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