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Primes

OldTrout, Going Postal
18th Century

Sophie Germain Primes and Cunningham Chains

28th September 2020 OldTrout 2231 Comments

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…]

Mathematics

The Infinity of the Primes

21st September 2020 OldTrout 2521 Comments

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…]

Hobbies

From a Sum to a Product

20th January 2020 OldTrout 1946 Comments

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…]

Mathematics

Wilson’s Theorem

2nd December 2019 OldTrout 1974 Comments

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…]

Mathematics

A Triangle

4th November 2016 OldTrout 0 Comments

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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